IB Math Studies Internal Assessment Project
A. Description, criteria, grading and due dates
B. Requirements
C. Guidelines
D. Fathom dynamic data and other existing data sources
E. Projects generating your own data
F. Simple Math Processes
G. Sophisticated Math Processes
H. Rough draft assignments and due dates
I. Example Project Titles and Statements of Task
J. IBO Criteria / Grading Rubric
There is no one best method of research for all situations. Rather, there are a wide variety of
techniques for the researcher to choose from. There are three basic methods of research:
1) survey, 2) observation, and
disadvantages.
3) experiment. Each method has its advantages and
The survey is the most common method of gathering information in the social sciences.
Surveys can be face to face; by telephone, or questionnaire, or by mail.
Observation research does not directly interact with people or situation being studied.
Individuals are observed, variables of interest measured, but there is no attempt to influence
responses.
In an experiment, something is deliberately done to individuals in order to observe the
responses. One or more variables are changed during the research. When all other variables
are held constant (except one being manipulated),changes in the dependent variable can be
explained by the change in the independent variable.
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DATA: Both Primary Data and Secondary Data are acceptable for your project.
Data in statistical research all comes from surveys, observational studies, or experiment.
Primary Data: You collect through survey, observation, or experiment.
Secondary Data is obtained directly from educational, scientific, or industrial entities, usually
from websites. Fathom can be used to import data directly. Directions / Examples in Part D.
For your Math Studies project, you should begin deciding which method of data collection you
are most interested in using.
QUESTIONS TO CONSIDER ABOUT DATA
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If your project involves real-world data, think about these questions.
Is the source reliable?
Is your sample representative?
If there is a strong correlati0on, does this necessarily imply causation? What other
factors might contribute to the correlation?
TIPS FOR COLLECTING PRIMARY OR SELF-COLLECTED / GENERATED DATA:
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If your project involves collecting your own data, here are some things to keep in mind:
Think about what attributes you’ll need before you start: If your’re collecting data over time, remember to
record the time ( in days or whatever time unit is appropriate).
Don’t wait until you’re through collecting data to begin your analysis—you’ll probably discover other
attributes you want to look at.
Try to make sure your data isn’t biased. If bias is unavoidable , note that in your analysis.
You may learn more by analyzing data you have collected, than by analyzing data collected by another
person or organization.
Rather than collecting information about an entire "population," random sampling allows one to estimate
population parameters using information obtained from a sample.
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Collect additional data in case you need more. I.E. Collect height and weight in addition to Eye Color
and Gender in case more data will help later to complete your project. All data collected does not have
to be used, but it can be handy to have it if needed later on … (data from the Web, surveys, polls, etc.)
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Analyzing your own data that you have collected will help you appreciate the P-value. Obtaining a very
small P-value might make you think you have achieved results that are real. When a difference you
obtained is large enough to be important but is not statistically significant--- you will learn the advantages
of collecting more data.
You need to have a minimum of 40 pieces of data for your research project.
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A. Description, criteria, grading and due dates
A project is about applying what you know in a task you define. This IB Project is an application of the mathematics studied in the
course. The project involves the collection and/or generation of data, and the analysis and evaluation of that data. This involves
the collection of information or the generation of measurements, and the analysis and evaluation of the information or
measurements. Technology is required mainly the TI-83 or 84 graphing calculator. But other math software programs like Excel,
Math-Type, Geiger, and Sketchpad among others can be used. Students may choose from a wide variety of project types; for
example, modeling, investigations, applications and statistical surveys. Projects may take the form of mathematical modeling,
investigations, applications, statistical surveys, etc. Failure to do a math studies project will result in a forfeiture of the IB
diploma.
Rubric for IB Marking
Criterion A 2 points
Introduction
Criterion B 3 points
Information / Measurement
Criterion C 5 points
Mathematical processes
Criterion D 3 points
Interpretation of results
Criterion E 2 points
Validity
Criterion F 3 points
Structure and communication
Criterion G 2 points
Commitment
Deadlines/ Due Dates: There are 8 project deadlines; each is worth one test grade for LHS grade.
Assignment
Criterion / Description
Due Date
LHS Grade Value
Criterion A & B assignment
Introduction, Info. & Measurement rough draft
December 3
one test grade
Criterion C
assignment
Mathematical processes
January TBA
one test grade
Criterion D
assignment
Interpretation of results / Validity
January TBA
one test grade
Complete rough draft
Submit two copies of rough draft
February TBA
one test grade
Final Project
Submit two copies of Final Project
February 20
one test grade
IB Internal Assessment Grading
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An internal grade of 17-20 is an IB grade of 7 towards the IB diploma. 20 points max 17-20 is a 7
To earn a perfect score of 20, you must earn a “5” in mathematical processes. To do this you must use
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at least two sophisticated statistical or math processes including  (Chi Squared) and linear
regression.
Points will be awarded or deducted from the very beginning on your commitment.
A successful project is required for passing this course, and thus for graduation.
Plagiarism is a major concern; IB uses turnitin.com among other resources to monitor.
Final Project due February TBA; I need one / two weeks to grade; then one week mailing time to IBO
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B. Requirements
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A title (See section below on Example Project Titles and Statements of Task)
Statement of the task (See section below on Example Project Titles and Statements of Task)
Collected / generated measurements, information / data: ( See section with example projects)
An analysis of the measurements, information or data: ( See section with example projects)
An evaluation of the analysis: ( See section with example projects)
A bibliography and footnotes, as appropriate. ( See section with example projects)
First requirement is there must be obtainable data that relates to your research question and project.
You must explain in your opening “Statement of task” why your topic is of interest to you.
Project must be your own individual research project. Collaboration with peers / teachers is allowed.
Must have bibliography; you can use an bibliography application such as “citation machine” or “easy bib”
You need to have a minimum of 40 pieces of data for your research project.
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Must show your work in addition to using technology. Min. of one of each calculation must be done by hand.
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For each math / statistical process an explanation why it was chosen and how it is relevant is required.
When showing work by hand, it is meant showing each step of the calculation along the way, i.e. the
process. Must be done once for each math or statistical process used, both simple or sophisticated.
If your project requires a repeat of a process then you can simply show the calculator output.
no minimum or max length—no word count necessary
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C: Guidelines
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Math Studies Internal Assessment (Project) are Statistics based.
Choose a topic of strong interest; and one you can find, generate or collect data on.
Make sure there exists sufficient good and reliable data to do your research and investigation project.
Data is readily available from numerous reliable government / academic / industry internet sources
Or make sure you can generate your own reliable data for your project.
A great idea / topic is not enough; you still must have at least SOME RELIABLE and OBTAINABLE DATA.
If your project is lacking in good data, but strong in other aspects, you’ll lose some points (see IBO Rubric)
You can choose to use existing data, or create your own data through trials or a survey.
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Most students use secondary data from data sources, survey,or create their own data through trials.
Collect additional data in case you need more. I.E. Collect height and weight in addition to Eye Color and Gender i
You don’t have to use all of the data you collect, but it can be handy to have it and will be easier to collect in 1st step.
The best way to ensure your data integrity is to have YOUR OWN TI 83 / 84. Or enter into FATHOM or EXCEL.
Data can also be imported from the internet into “Fathom”: (SEE SECTION D)
Don’t forget to search for Categorical and Quantitative pairs of data; such as “medication and blood pressure”.
Project ideas can come from any area of mathematics, including below:
NUMBER AND ALGEBRA; SETS AND LOGIC; APPLIED MATH-Sequences/ series; Set Notation; Analyzing linear &Quadratic Graphs;
Data in Groups of two or three categories; Music
GEOMETRY / TRIGONOMETRY AND FUNCTIONS-Calculating angles, distances, areas, volumes (any applied math problem or
research question); Estimation of lengths, heights, angles of building or parts of buildings; Analysis of geometrical shapes and
designs in building and nature; Applied math with Navigation, Maps, Architecture; Data from science subjects, geography;
Trajectories; Waves; Applied math with Natural phenomena such as seasons and tides;
FINANCIAL MATHEMATICS-Financial data from newspapers, banks, etc. on exchange rates, interest rates; information about
businesses; computer, car, home sales; Analysis of stock market; U.S. Debt Crisis, Investments, price of precious metals.
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D: FATHOM DYNAMIC DATA AND FATHOM SURVEYS
One of the objectives of Math Studies (and all Group 5 IB subjects) is to “use technology, accurately,
appropriately and efficiently both to explore new ideas and to solve problems”.
The project offers many opportunities for this objective to be achieved. For the external assessment in May,
the use of technology is limited to the GDC, but for the project there are no technology limitations. It is
expected that in doing projects students will utilize technology such as statistics packages like Fathom, excel,
computer graphing packages, and / or any kind of calculator, the internet, or data logging devices.
Your Fathom license provides access to Fathom Dynamic Data for use with your statistical software package.Fathom
allows you to gather, explore, graph, analyze, and animate your own data sets, and data you pull from the Web.
Fathom allows you to import data from various sources, including web-sites and spreadsheets. Here’s How
TO IMPORT DATA INTO FATHOM:
1. Open a new Fathom file, reshape the file so it lies on the right side of the screen.
2. In a web-browser open: www.census.gov ; then follow the path outline in step 3.
3. Census.gov › People >International Database> International Programs Main › Data › World Population Summary
---- this should bring you to a table of world population.
4. Reshape the desktop so half the screen is the browser, and the other half the Fathom file.
5. Drag the URL for this page into the Fathom worksheet: (it has the CB Census Bureau logo)
http://www.census.gov/population/international/data/worldpop/table_population.php
6. Or simply go to: http://www.census.gov/population/international/data/worldpop/table_population.php
And drag this address with it’s icon into an open Fathom file.
7. The following Fathom data collection is imported, appears as below, and is automatically populated:
Total Midyear Population for the World: 1950-2050
8. Drag a graph into the Fathom worksheet.
9. Double click on the collection to open the inspector. Click on cases. Drag year to x-axis, and population to y axis.
10. You can now do all functions with this data previously studied in Fathom.
11. Experiment with dragging more data files of interest into Fathom.
12. There are numerous reputable academic, research, industry, and government websites in addition to
Census.gov that have “Fathom-Ready” data files for your projects. Read through the Project Handbook for
more, or do your own internet search for data files.
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FATHOM SURVEYS are
an acceptable method to collect project data from peer Fathom users. To begin
Fathom Survey Function, watch the two short help videos below on Fathom Surveys at following links.
A) http://www.keycurriculum.com/resources/fathom-resources/fathom-surveys
B) http://pdonline.keypress.com/key_course_data/Teaching_Statistics_with_Fathom/Week_3/Visual_Media/TeachLea
rnwFathom/Rob.html
C) Use steps below to create an online survey. Get at least 10 people to fill out your survey. Create a report
of results, utilizing graphs, summary tables and other Fathom tools.
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Log on to Fathom at www.keymath.com and take the class survey I’ve posted for you.Username and
Password are: Lecanto High School Student 1
( or YOUR number )
1) Next , to make your own survey, open a Fathom file, drag a collection into the workspace.
2) Click on word collection, and rename the collection as your survey.
3) WITH COLLECTION HIGHLIGHTED, SELECT “CREATE SURVEY” FROM PULLDOWN MENU.
4) Click on the survey collection, Click CASES, enter names of ATTRIBUTES.
5) Click SURVEY and enter the individual research questions that go with each ATTRIBUTE.
6) Click SURVEY, under FORMAT click drop down arrow. For each ATTRIBUTE select DEFINE NEW CATEGORY SET.
7) Type in response choices fo your survey. Enter as many responses as you need, separate each by a comma.
8) To edit, click CATEGORIES, then revise possible answer choices putting a comma between each choice.
9) Type instructions to survey takers in the instructions box.
10) Include your last name and your one/two digit student license number in saved file (e.g., SmithZ_Project4.ftm).
Steps to post, upload, and access all Fathom surveys at: www.keymath.com
On the right side, “ Click here to launch Fathom Surveys”
Next “click here to access Fathom Surveys”.
On next screen select surveys; two surveys will appear, take both and upload for course grade.
Username/Password are same: lhss#
# is 1 or 2 digit number provided: i.e. Lecanto High School Student 1
Non-class members must have Fathom and use mathstudiesibsurvey for both username and password
Outside respondents will access Fathom Surveys same as you, (using www.keymath.com).
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Existing Data Sources and Project Ideas
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General Data Sites:
http://unstats.un.org/unsd/databases.htm United Nations Statistics Division (UNSD)
http://faostat.fao.org/ Food and Agriculture Organization of the United Nations (FAOSTAT)
http://www.who.int/research/en/ World Health Organization of the United Nations (disease and healthcare)
http://www.fedstats.gov/ Federal Government Statistics
http://www.eeps.com/zoo/index.html Data Zoo
http://www.dartmouth.edu/~chance/teaching_aids/data.html
DASL The Dataset and Story Library - a collection of datasets and related documentation (stories)
http://www.keypress.com/x2814.xml - Fathom Data Sites
http://www.keypress.com/x3894.xml - Fathom Data Sites
http://www.census.gov/main/www/a2z/ U.S. Census Bureau A to Z:
http://www.census.gov/compendia/statab/ us stat abstract:
http://www.census.gov/population/international/ world population
http://www.census.gov/population/www/popclockus.html U.S. Population:
Economics Research Questions: Statistics / economics can be used to develop solutions to a wide variety of
problems faced by governments, corporations, non-profit organizations, and other entities.
a)
Calculate the percentage change in the Dow Jones Industrial Average from the close on Thursday the 12th to the close on Friday
the 13th for every Friday the 13th beginning in 1980. Is the average percentage change substantial?
b) Is wealth in the United States becoming more concentrated or more spread out over the past 30 Years?
c) Does legalized gambling raise revenues for a state or county?
d) Do 4 day school weeks save money for school districts?
Economics Data Sources
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http://www.esa.doc.gov/about-economic-indicators U.S. Economics and Statistics Association
http://www.bls.gov/data/ U.S. Department of Labor Bureau of Labor Statistics
http://research.stlouisfed.org/fred2/ Federal Reserve Economic Data (FRED)
http://www.econdata.net/ EconData.net
http://www.fedstats.gov/ Federal Statistics (FEDSTATA)
http://www.brillig.com/debt_clock/ National Debt Clock and Information
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g) http://www.worldbank.org/ World Bank:
h) http://www.imf.org/external/data.htm International Monetary Fund Data and Statistics
Environment /Climate / Agri-science /Engineering / Energy Research Topics
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Which are more accurate for a particular chosen city: the predicted high or predicted low temperatures?
the rainfall one year correlated positively, negatively, or not at all with the rainfall the previous year?
Is wind energy effective and practical?
Are electric vehicles helping to save the U.S. from importing oil?
Global warming – summer of 2011 is described as the second hottest summer ever on record.
Do the numbers of manatee deaths in Kings Bay over the past decade justify the Federal Government mandating
minimum / idle boating speeds year round?
g) Are the world’s oceans being, overfished? Are certain species of fish (wild salmon, or others) becoming extinct?
h) The film Erin Brokovich portrays largest environmental damage settlement in US history (except for BP)
i) Are antibiotics being administered to our food supply causing germ resistance to antibiotics in people?
Environment /Climate / Agriscience / Energy / Engineering Data Sources
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http://www.ncdc.noaa.gov/oa/ncdc.html National Center for Climatic Data (NCDC)
http://www.noaa.gov/index.html National Oceanic Atmospheric Administration (NOAA)
http://www.epa.gov/enviro/html/ef_overview.html U.S. Environmental Protection Agency: (EPA)
http://www.nrel.gov/rredc/ National Renewable Energy Laboratory: (NREL)
http://www.afdc.energy.gov/afdc/ Alternative Fuels and Advanced Vehicles Data Center
http://www.unep.org/ United Nations Environment Program (UNEP)
http://www.ipcc.ch/ Intergovernmental Panel On Climate Change (IPCC)
http://www.nhc.noaa.gov/ National Hurricane Center
http://www.weather.gov/ National Weather Service
http://swera.unep.net/index.php?id=7 Data for Solar and Wind Renewable Energy (SWERA)
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http://www.seattlecentral.edu/qelp/index.html Quantitative Environmental Learning Project (QELP)
Medicine & Public Health
Epidemiology is the study of health patterns. It is cornerstone method of public health research. PH research helps
governments determine policy to help people become / stay healthier, and prevent disease. Method is identifying
risk factors and trying to find associations between factors, or cause. Epidemiologists work on designing studies and
collect data for statistical analysis. Outbreak investigation, disease surveillance, screening, bio monitoring, and
conducting clinical trials are all public health functions.
a) Are deaths worldwide from AIDS, Tuberculosis, or Malaria increasing at a decreasing or increasing rate?
b) The New York Times recently reported that 20% of all U.S. households believe that vaccines are a cause of
the increasing cases of autism. Would data collected show that vaccines are a significant cause of autism?
c) What is dengue (DEN-GAY) fever? Is there cause for alarm in the U.S. and Florida?
d) Is there a correlation between what state a person lives in and their risk for getting cancer?
e) Is there a correlation between the number of TV sets per home and obesity rates?
f) Has there been an increase in bullying from 2000-10 compared to earlier decades?
g) Has there been an increase in smoking from 2000-10 compared to earlier decades?
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h)
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Has there been an increase in teen pregnancy from 2000-10 compared to earlier decades?
Has there been an increase in auto fatalities from 2000-10 compared to earlier decades?
What day of the week are there more deaths recorded?
Do states with lower speed limits have fewer fatalities?
Towns with High schools that have earlier starting times report that students have more accidents than
students attending a school with a later starting time. Can you find data to verify this?
Do more car accidents happen on one particular day of the year such as the first day of Standard time
after going off Daylight Savings time?
Should the minimum age for attaining a driver's license be increased? Should this be a national standard?
Do cameras at intersections stop people from running red lights and lower other traffic violations?
Many states have much harsher penalties than others for drunk driving. Do states with harsher penalties
have fewer fatalities due to alcohol related accidents?
Medicine / Public Health Data Sources
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www.cdc.gov/nchs/ CDC - National Center for Health Statistics Homepage --http://www.cdc.gov/az/ Centers for Disease Control topics A to Z (CDC)
http://www.cdc.gov/DataStatistics/ CDC Data & Statistics
http://www.americashealthrankings.org/ America’s Health Rankings
https://dawninfo.samhsa.gov/default.asp Drug Awareness Warning Network (DAWN):
http://progressreport.cancer.gov/ Cancer Trends Progress Report:
http://www.who.int/phe/health_topics/en World Health Organization (WHO) --http://www.nih.gov/ National Institute of Health (NIH)
http://www.cancer.gov/aboutnci/cis/page1 National Cancer Institute (NCI)
http://www.ncbi.nlm.nih.gov/pubmed PubMed.Gov --http://phpartners.org/health_stats.html Health Data Tools and Statistics:
http://mchb.hrsa.gov/mchirc/chusa/ U.S. Child Health Statistics:
http://www.hivaidssurveillancedb.org/HIVDB/ Aids Surveillance Data Base:
http://www.apa.org/topics/obesity/index.aspx American Psychological Association
Political Science
a) Do Exit polls accurately predict winners of elections?
b) The World Series and the presidency-- During presidential election years, does the league that wins the World
Series determines which party wins the White House?
c) Use secret ballots to survey student preferences for the next president of the United States. On half of the
ballots, list the likely Republican candidate first; on the other half, list the likely Democratic candidate first.
d) There have been 5 election cycles in the last 60 years that had both a poor economy and a divided government:
1948, 1960, 2004 1992, and 2008. In all five elections, one party swept both the presidency and Congress. In
four out of five cases, it was the party that controlled Congress — not the presidency — that did so.
Interestingly the party completing the sweep in all five cases was the Democratic Party. Does this mean that
maybe the Democratic Party has an inherent advantage over Republicans in difficult economic times?
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Political Science / Data Sources
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http://pewresearch.org/
http://www.gallup.com/poll/election.aspx
http://fivethirtyeight.blogs.nytimes.com/
Psychology
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Has capital punishment reduced the amount of violent crime in Tx. or other state?
Do normally patient people become impatient behind the wheel?
Is schizophrenia more common in men or women?
Is there a link between smoking and intelligence?
Do men or women react to stress better? How do people react to invasion of space?
What are the effects on children whose parents push them in sports?
What are effects of video games on growth / development of individuals and society?
Do students who finish an exam first score higher ?
Education
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Do school uniforms make a difference in achievement levels and / or better discipline?
Are children smarter (or more socialized) because of the Internet?
Do teenagers who take a “gap year” between high school and college do better or worse?
In some European schools, fewer than 10% of students get A’s. Is there grade inflation in the U.S.?
Do students learn better in same gender (boys-only and girls-only) schools?
Does home schooling improve students’ scores on standardized tests?
Political Science / Psychology / Education Data Sources
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https://www.cia.gov/library/publications/the-world-factbook/ CIA World Fact Book
http://Fivethirtyeight.com http://fivethirtyeight.blogs.nytimes.com/ FiveThirtyEight is a polling aggregation
http://dawninfo.samhsa.gov/ Drug Awareness Warning Network (DAWN)
http://polisci.lsa.umich.edu/grad/comparative/data.htm
http://www.icpsr.umich.edu/icpsrweb/ICPSR/ InterUniversity Consortium for Political and Social Research:
http://politicaldata.com/Pages/Index.aspx Political Data Inc.
http://einstein.library.emory.edu/international_socsci.html International Statistical and Electoral Resources
Sports / Entertainment Research Questions:
Some possible project ideas could come from studying ambidexterity, various sports and games, especially darts, golf,
basketball, archery and sharpshooting. Below are s general questions which could be investigated as a research project:
a) The World Series and the presidency-during presidential election years, does the league that wins the World
Series determines which party wins the White House?
b) Are reality TV shows increasing at an increasing rate? Are Reality TV shows more popular in the North or
South; East or West, or among what age groups?
c) Has the average professional sports players’ salary increased 10, 100 or more times the average American
worker during the past several decades?
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d) Has the average CEO’s (Chief Executive Officer) salary increased 10, 100 or more times the average
American worker during the past several decades?
e) Can a player's batting average be predicted with reasonable accuracy from his batting average the preceding
season?
f) Which sport or sports are most played or watched in the United States; or most played /watched by region?
Sports / Entertainment Data Sources
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http://www.stats.com/ Sports Data:
http://baseball1.com/ website features baseball statistics -beginning 1871. Includes player salary data
http://www.cbssports.com/mlb/stats CBS Sports Data: - fathom
http://sabr.org/ Saber metrics
NFL Quarterback Passer Rating Data http://www.dartmouth.edu/~chance/teaching_aids/data/NCAA.html
http://www.usatoday.com/life/television/nielsen.htm Neilson Television Ratings:
6 different data types and / or ways to process data statistically
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Dichotomous Trial Data
Numerical- Response Data
Categorical Data
Comparing two sample Data
Linear Regression Data
Chi-Square Data
Dichotomous Trial Data
o Dichotomous (only yes / no; success / fail) Response Trials are research data collected or generated
to try to make inferences about a larger population.
o These inferences can only be valid, if the trial unit results are obtained by random sampling. Random
sampling means that the trials are independent and identically distributed.
o For a dichotomous response, trials are called “Bernoulli Trials”. Keep in mind that more data and
more trials provide more accurate inferences.
Dichotomous trials continued….
o Let goal of study determine the size of the trial; be careful not to make your number of trials too small.
o You can use as trials studying almost any event where the outcomes are limited to just two:
o Success / failure; occurred / not occurred; presence / absence; disease / not diseased; etc.
o Events such as: birth gender, ambidexterity, various sports and games, darts, golf, basketball, archery
and sharpshooting, are also good for dichotomous trial studies and research.
o When analyzing your own data, you’ll begin to learn importance of number of trials and collected data
o Experimental trial units can involve people and the outcome of their behavior or response.
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o Trial units can also be virtually any objective outcome worth investigating.
Below are examples of dichotomous trials observed or obtained by students in math studies projects:
a) A student defined a trial to be her playing a B-flat on her clarinet into a tuner. The tuner classified the note
as sharp, flat, or perfectly in tune. A perfectly in tune note denoted a successful trial, while either of the
other two classifications was labeled a failure.
b) A student defined a trial to be her father’s morning wait for the bus. If the bus arrived within two minutes
of the scheduled time, the trial was a success; otherwise, it was a failure.
c) A trial was defined to be a live birth at a hospital; female babies were successes / males were failures.
d) A trial was defined to be a bicyclist riding through a busy intersection. A rider with a helmet was a success
and a rider without a helmet was a failure.
e) A student defined a trial to be rolling two small balls across the floor in her living room. A trial was a
success if her dog, fetched the red ball and a failure if the dog fetched the blue ball.
Below are examples of trials and experiments used to obtain data for their research. Feel free to model your
research question and project idea similar to one of the scenarios below:
a) A waitress wondered whether suggesting a specific appetizer upon greeting customers would lead to an increase in
sales of appetizers. She was surprised to learn -mentioning a specific appetizer decreased sales of all appetizers.
b) A coffee cart offered two sizes, small and large. The salesperson wants to sell as many large coffees as possible.
Some customers specified the size when they ordered. The worker experimented with the questions: “Would you
like a large?” vs. “Would you like a small or a large?” To see if he could boost sales of large coffees. Which
question would you guess would be statistically significantly superior in eliciting the sale of a large coffee?
c) An ice cream worker sold ice cream which could be served in a plain or a waffle cone. The store made a much larger
profit on the waffle cones. For customers who did not specify the cone type in their order, it was found that the
question, “Would you like a plain cone or a homemade waffle cone?” elicited significantly more sales of waffle cones
than did the same question with the adjective “homemade” deleted.
d) A store purchased used compact discs from customers. The store owner wondered which of the following
statements to the customer would be more effective. I will give you $X, or How does $X sound? (The value of X
was appropriate for the number and quality of the compact discs offered for sale.) It was found that the first
statement performed better (at getting an acceptance of the first offer) than the second, but that the difference
barely missed achieving statistical significance. What do you think is meant by “statistical significance”?
e) At a university, and experimenter showed 25 graduate students part of an essay he said was written by “Jack
McConnell, a student from Iowa.” He then showed 25 other college graduates the same essay, but said it was
written by “Hsiao-Ping Zhang, an international student from China.” When asked, “Do you detect any grammatical
errors in this passage?” 64 percent who had read the Chinese student’s essay said yes, compared to only 20 percent
who had read the Iowa student’s essay! This huge difference is highly statistically significant.
f)
An experimenter visited a minimum-security federal prison camp to obtain her study subjects who were first-time
nonviolent offenders. The first version of her question read: The prison is beginning a program in which inmates
have the opportunity to volunteer for community service with developmentally disabled adults. Inmates who
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volunteer will receive a sentence reduction. Would you participate? The second version was the same, except that
there was no mention of sentence reduction. The experimenter was surprised to learn that her data revealed that
the second version received a much higher proportion of yes responses than the first version, but the difference did
not quite achieve statistical significance. (Of course you cannot visit a prison, but maybe this scenario will provide
you with some other idea…)
g) A member of the university varsity soccer team had two games per week, every Friday evening and Sunday morning.
She wondered whether she played better in the evening or morning.
h) A softball player investigated if the type of bat, aluminum or wood, influenced how far she could hit a pitched ball.
i) Students wanted to investigate whether having a car’s windows open or closed influenced the time required to
accelerate from 40 to 65 miles per hour. (This one is not recommended for obvious reasons…)
j) A study can be performed to investigate the effect of temperature on the growth of a plant, flower, or fungus.
k) A competitive swimmer could perform a study to compare two methods of starting a freestyle swimming race.
l) A punter on the varsity football team could perform a project to estimate how much farther he could punt the ball
with two steps (before kicking) rather than one step. Or,the “hang times” for one step or two steps could be studied
Linear Regression: Go to a local grocery store and collect these data for at least 25 or more breakfast cereals: cereal
name; grams of sugar per serving; and the price per ounce (or gram). If the store you select does not have at least 25
breakfast cereals, then collect data from another store too. Use these data to estimate the simple regression model with
price as the dependent variable and sugar as the explanatory (Independent) variable.
Numerical Response Data Projects
In numerical response trials and projects, pictures and graphs can be drawn and made of the data. Most projects with a
numerical response focus on the center of the distribution; either larger or smaller is better. Next two projects provide
examples in which spread is more important than center. The first project is an example that deals with variation from a
fixed target and the second deals with the more common statistical problem of variation without fixed target.
a) Two dart players had a contest to see who could hit the “20 wedge” the most. Each person attempted 78 throws,
with each toss aimed at the 20 wedge. A response of 0 was noted if the throw hit the target wedge of 20. If the
throw landed one wedge to the right of 20, the response was +1; if it landed two wedges to the right of 20, the
response was +2, and so on. Darts that landed to the left of 20 gave responses of -1, -2, and so on, in the analogous
manner. These data contained more information that only who was the better player. One player was better at
hitting the 20, by a score of 36 to 10, and his mean response was 0.31. The second player’s mean response was
0.65. Since both numbers were positive, this indicates both had a tendency to shoot to the right. Another telling
statistic is that one player’s mean absolute response was 0.62, and the second player’s was 1.71, which shows a
substantial difference in variation.
b) A golfer wanted to compare the distributions of the distance obtained when hitting a golf ball with two seven-irons;
one made of steel and one of graphite. In golf, consistency with a seven-iron is more important than distance; if you
want to hit the ball farther, use a six-iron. By examining dot plots, histograms, and various measures of spread, this
project concluded that there was no substantial difference in the spreads of the two distributions.
Categorical Data Projects
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a) Do comparisons of almost anything by randomly asking 15 male students and 15 female students to find differences
or similarities in likes or dislikes. For example: To find out if as many males are fans of Lady Gage’s music as female
students, or how many males vs. females watch Glee (or some other show)
b) Ask subjects to obtain 5 of the same things that are edible/drinkable such as 5 donuts, 5 water bottles (the water
inside them is what’s needed obviously), or 5 pieces of candy. Do not uses anything that is really small like one
Skittle from a bag - a small, fun size pack works well. Make sure they are all the same thing (5 fun size Skittles as
opposed to 4 fun sizes and one giant bag). Then, eat/drink one at a time until you finish all five and after you eat one
of them, give me your ranking from 1-10 on how satisfying it was. Example: 1st - 9; 2nd - 8; 3rd - 3; 4th - 9; 5th - 10
be sure to eat/drink them all at the same time and take no breaks or other substances with them.
c) Ask 30 people to tell you when 30 seconds has elapsed, perhaps offering a prize if they are within 1 second. Think of
a way to conduct this experiment that avoids this potential problem: if you time the 30 seconds by looking at your
watch, the subject may be able to draw inferences from your facial expressions. Do your data indicate that people
are more likely to underestimate or overestimate the passage of time?
d) People experiencing an earthquake often grossly overestimate how long the quake lasts; for example reporting that
a 6-second quake lasted 30 seconds. Show a random sample of people some memorable event, such a snippet of
loud music or you dancing, and then ask them how long this event lasted. Do your data indicate that people are
more likely to underestimate or overestimate the how long the event lasted?
Chi-square Tests for Categorical Data
(Chi Squared  )
2
a) Administer the following four tests to at least 50 subjects, and then apply a chi-square test to the six possible
pairs of tests: a with b, a with c, and so on:
I.
Ask the subject to stand with his or her back to you. Then ask the subject to jump around in a single motion to face
you. Record whether the person jumps clockwise (pushing off with a dominant left foot) or counterclockwise
(pushing off with a dominant right foot).
II.
Ask the subject to look at an object 10 feet away through a tube made with the hands held a foot in front of his or
her face. Close or cover first one eye and then the other and record whether the subject can still see the object
through the tube when the left eye is open (left-eye dominance) or when the right eye is open (right-eye
dominance).
III.
Ask the subject to put his or her hands together behind the head, with the fingers interlaced. Record whether the
thumb on the bottom (the dominant thumb) is from the left or right hand.
Ask the subject whether he or she is left-handed or right-handed.
IV.
b) The nine positions on a baseball team can be divided into four categories: pitcher, catcher, the four infielders, and
the three outfielders. Collect all the data you can on major league baseball managers and test the null hypothesis
that, among those managers who played baseball, the probabilities of having played in these four categories are
1/9, 1/9, 4/9, and 3/9, respectively.
c) Ask 100 randomly selected students if, aside from the obvious gender differences, they most resemble their
biological mother or father. (Evolutionary psychologists suggest that people are more likely to say that a child
resembles the father—apparently so that the father will be more likely to protect and care for the child.) For each
gender, test the null hypothesis that p = 0.5. (Alternatively, this can be done as a female/male chi-square test.)
14
d) Use computer software to simulate 1,000 spins of a roulette wheel that has 18 red slots, 18 black slots, and 1 green
slot. Record the fraction of the spins that are red after 10, 100, and 1,000 spins. Repeat this experiment 100 times
and then use three box plots to summarize your results.
Comparing Two Samples
a) Compare the prices of men's and women's T-shirts.
b) Compare the prices of men's and women's shaving cream
c) Would you bet $10 on the flip of a coin if you stood to win $20? (You have a 50% chance of losing $10 and a
50% chance of winning $20.) Select a grocery store chain and compare the prices at stores in two different
areas of town.
d) Post a sign on the main entrance to a campus building requesting the use of a less convenient entrance; for
example, "Please use the door on the north side of building." From an inconspicuous location, observe how
many people ignore the sign and use the main entrance and how many people do not use the main entrance.
Compare the behavior of students and professors or males and females. Try to pick a building and time when
traffic is light, so that large numbers do not try to enter simultaneously.
F. Simple Mathematics Process
Simple Mathematical Processes
percentages
areas of plane shapes
linear and quadratic functions
bar charts, pie charts
mean and standard deviation
simple probability
frequency distribution
grouped frequency distribution
relative frequency distribution
cumulative frequency distribution
measures of central tendency
frequency table
joint, marginal, & conditional probability table
standard error of the sample mean
15

The primary math to be used for your project is Statistics, which is why this course will cover Stat first.
Only Algebra II is required to begin Statistics. Basic Statistics, such as entering data into x and y lists in the
calculator and generating scatterplots, histograms, and cumulative frequency tables and charts are
considered simple math processes. Use of: Standard Deviation, Pearson Product Moment Calculation,
 2 (Chi Squared) and some other techniques to be studied are sophisticated math processes. To earn a
perfect mark for Criteria C, or a perfect score for your project, you will need to use two of these processes,
including linear regression and  (Chi Squared).
If a scatter diagram is used, and it is clear from the diagram that there is no correlation then it is ok to
calculate the correlation coefficient to verify that fact but it is not relevant to calculate the regression line.
Project Math can also be: Trigonometry, Probability, Linear, Quadratic, Power, and other regressions.
I must check your math processes—so bring data already in lists in your calculator.
Surveys must be approved by me prior to your using them.
Data obtained from academic, scientific, or industry internet sources is acceptable
You must write minimum of one good quality paragraph for each project related math process—explaining
the relevance of the process towards answering your research question.
2






G. Sophisticated Math Processes
Sophisticated Mathematical Processes
compound probability
volumes of pyramids and cones
analysis of trigonometric functions
analysis of exponential functions
Optimization
statistical tests including: (below)
linear regression
Chi-square
"r" value or Pearson Product Moment Correlation
Population mean
Sample mean
Variance
Population variance
Sample variance
hypothesis test

Use of: Standard Deviation, Pearson Product Moment Calculation,  (Chi Squared) and some other
techniques to be studied are sophisticated math processes. To earn a perfect mark for Criteria C, or a
2
16
perfect score for your project, you will need to use two of these processes, including linear regression and
 2 (Chi Squared).





If you draw the scatter diagram and it seems that there is some correlation then you can continue to find
r and, if the correlation is strong enough, then you may calculate the regression line and use it to count as
one of your sophisticated processes.
If you do not draw a scatter graph, then the relevancy of a regression line will depend on the value of r. if
you simply just write down the value of r from your GDC then this will be graded as a simple process only.
Always try to add idea of showing understanding by explaining what r value indicates. Strive to keep
context and not forget about the actual subject of your project.
Both the linear regression calculations and the Pearson’s product moment correlation coefficient of “r” or
PMCC calculation are considered sophisticated processes.
The calculation of the regression line is ONLY relevant if the R-value calculated shows a strong correlation
and you are intending to use the equation for modeling, extrapolating, and conveying information,
association, and causation (cause and effect).
H. CRITERIA A & B ROUGH DRAFT ASSSIGNMENT
DUE November / December TBA
Criteria A: Produces a title, a clear statement of the task and a clear description of the plan.
The plan need not be highly detailed, but must describe how the task will be performed.
1. PROVIDE A TITLE (SEE EXAMPLES SECTION K)
2. Produce a clear statement of task (SEE SAMPLES IN SECTION K)
3. Prepare a clear description of the plan; i.e. what math processes will you use to try and
demonstrate what result or prediction or hypothesis?
Criteria B: (along with criteria A) is due November / December TBA
“In this context, generated measurements include those that have been generated by computer, by
observation, by investigation, by prediction from a mathematical model or by experiment or conducting trials.
Mathematical information includes data that is collected empirically or assembled from outside sources. ..
IBO.org Math Studies Syllabus




Collect relevant information and data; or generate relevant data and measurements.
Data, information, and measurements can include those that have been generated by computer, by
observation, by investigation, by prediction from a mathematical model, or by experiment.
Mathematical information includes data that is collected empirically or assembled from outside sources
such as educational, scientific, or industry internet sources.
Collected data and information should be organized in a form appropriate for analysis and is sufficient in
both quality and quantity.
17
Answer or do the following. Write at least one paragraph for each.
1. Will you generate your own data or collect and analyze data from pre-existing academic, scientific or
industry sites? Explain you’re rational and plan for obtaining your data whether you are generating your
own or collecting it from already established sources.
2. If you are conducting trials, or generating your data through experiment or observation, describe your
rationale and process. Explain how you generated or collected your data. What do you hope to show,
prove, disprove, or simply investigate?
If you are collecting pre-existing data answer or do the following:
1.
2.
3.
4.
Give a complete description of the source and bibliography of your data.
Give a complete description of the specific data you will use; what is it measures
Identify the independent and dependent variable (if it’s two variable data)
Assemble your data in lists (entered into TI-84); or entered into an Excel spreadsheet; assembled in
tables or charts; or stored in a digital file format that can be read by Mr. Carella. Remember, collected
data and information should be organized in a form appropriate for analysis and is sufficient in both
quality and quantity.
CRITERIA C ROUGH DRAFT MATH PROCESSES ASSIGNMENT
DUE January TBA
Criteria C assignment is due January TBA. Any elements of the below listed assignment
completed satisfactorily and done carefully can also be turned in as part of your final
project due February TBA. All of the assignments together are worth 1 test grade.
1) Choose and complete a minimum of 5 simple and 2 sophisticated processes as relevant tests to answer
your research question and project statement of task.
2) One example of each process must be done by hand; the rest may do with technology.
3) Graphing calculator should be utilized, along with any other appropriate technology or software such
as Excel, Microsoft equation editor, Geiger, Sketchpad, etc.
4) I must check your math—so you must come to me with the data already in lists in your calculator.
Calculators will be assigned to individual students, so your data can be permanently stored in the
calculator.
5) If you use a survey to collect your data, it must be approved by me first.
6) You must write at least one good quality paragraph for each math process used, describing the
process; what makes the process relevant and why you chose that process. See example of projects in
last section.
Simple Mathematical Processes
percentages
areas of plane shapes
linear and quadratic functions
bar charts, pie charts
mean and standard deviation
18
simple probability
frequency distribution
grouped frequency distribution
relative frequency distribution
cumulative frequency distribution
measures of central tendency
frequency table
joint, marginal, & conditional probability table
standard error of the sample mean
Line of Best Fit by Eye
THE TYPICAL PROJECT WILL INCLUDE E THE FOLLOWING WITH YOUR DATA:
a)
b)
c)
d)
e)
f)
g)
SCATTERPLOT
BOX AND WHISKER
LINE OF BEST FIT “BY EYE”
ENTER DATA LISTS INTO CLASSROOM GRAPHING CALCULATORS
LINE OF BEST FIT CALCULATOR OR COMPUTER GENERATED
MAKE LINEAR REGRESSION LINES ON TI-84, GEOGEBRA OR SKETCHPAD
CALCULATE “R” VALUE AND PEARSON PRODUCT MOMENT CORRELATION FOR ONE SET OF DATA, OR THE MOST
LIKELY ONE YOU WILL SUBMIT WITH YOUR PROJECT.
Criteria C math processes continued…






Simple project math can also be: Trigonometry, Probability, Linear, Quadratic, Power, and other
regressions.
Basic Statistics, such as entering data into x and y lists in the calculator and generating scatterplots,
histograms, and cumulative frequency tables and charts are considered simple math processes.
Use of: Standard Deviation, Pearson Product Moment Calculation,  (Chi Squared) and some other
techniques to be studied (from chapter 20) are sophisticated math processes. To earn a perfect mark for
Criteria C, you will need to use two of these processes, including linear regression and (Chi Squared).
If a scatter plot diagram is used, and it’s clear from the diagram that there is no correlation, it is ok if you
calculate the correlation coefficient to verify that fact but it is not relevant to calculate the regression line.
I must check your math—so you must come to me with the data already in lists in your calculator.
Calculators are assigned to individual students, so if anyone messes with your data—please report it to
me. it is perfectly fine to use data obtained from internet sources--- this is by far and away how most
Math Studies projects are done.
Must write good quality paragraphs on their project related math—see examples!
2
Sophisticated Processes: must use two or more to earn grade of an on project.

Use of: Standard Deviation, Pearson Product Moment Calculation,  (Chi Squared) and some other
techniques to be studied are sophisticated math processes. To earn a perfect mark of 5 for Criteria C, or a
perfect score for your project, you will need to use two of these processes, including linear regression and
2
 2 (Chi Squared).
19






If you draw the scatter diagram and it seems that there is some correlation then you can continue to find
r and, if the correlation is strong enough, then you may calculate the regression line and use it to count as
one of your sophisticated processes.
If you do not draw a scatter graph, then the relevancy of a regression line will depend on the value of r.
Other words, if you simply just write down the value of r from your GDC then this will be graded as a
simple process only.
Always try to add the idea of showing understanding by explaining what that r value indicates. Strive to
keep things in context and don’t get carried away with equations and formulas while forgetting about the
actual subject of your project.
Both the linear regression calculations and the Pearson’s product moment correlation coefficient of “r” or
PMCC calculation are considered sophisticated processes.
Linear Regression and Pearson Product Moment Correlation (PMCC) are 2 separate sophisticated
processes so they can allow for a mark of 5 in Criterion C.
However the key word at this level is also "relevant". The calculation of the regression line is ONLY
relevant if the R-value calculated shows a strong correlation and you are intending to use the equation
for modeling, extrapolating, and conveying information, association, and causation (cause and effect).
CRITERIAS D & E
DUE January TBA
Criteria D & E assignment are due Any elements of the below listed assignment completed
satisfactorily and done carefully can also be turned in as part of your final project due
February TBA. All of the assignments together are worth 1 test grade.
FOR CRITERIA D & E YOU MUST WRITE Y OUR OWN INTERPRETATIONS AND CONCLUSIONS, AND GIVE
SPECIFIC REASONS. WHAT DOES YOUR DATA TELL YOU? WHAT DO THE RESULTS OF THE STATISTICAL MATH
PROCESSES SHOW? “IS THERE AN ASSOCIATION OR CAUSATION?” IS A VERY RELEVANT AND IMPORTANT
QUESTION TO ADDRESS?
QUESTIONS TO ANSWER FOR CRITERIA D & E
a)
b)
c)
d)
e)
f)
g)
RESEARCH AND USE THE TERMS “VALIDITY AND GENERALIZABILITY” OF RESEARCH RESULTS
WHAT ARE SOME POSSIBLE CAUSES OF INVALID DATA BEING OBTAINED IN YOUR PROJECT?
WHAT ARE SOME EXAMPLES OF HOW BIAS COULD HAVE AFFECTED YOUR CONCLUSIONS?
DO YOUR PROJECT RESULTS APPEAR TO PROVE, DISPROVE, OR BE INCONCLUSIVE?
WHAT ARE THE INDEPENDENT AND DEPENDENT VARIABLES, AND:
“IS THERE AN ASSOCIATION BETWEEN THE INDEPENDENT AND DEPENDENT VARIABLES?
IN YOUR OWN WORDS, WHAT DOES IT MEAN ABOUT THE DATA IF THERE IS AN ASSOCIATION? WHAT
DOES IT MEAN ABOUT THE DATA IF THERE IS NO ASSOCIATION?
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h) IN YOUR OWN WORDS, WHAT DOES VALIDITY MEAN IN RELATION TO THE RESULTS OF A STATISTICAL
STUDY OR INVESTIGATION? IN GENERAL, VALIDITY MEANS -“GOOD MATH + GOOD DATA = VALID
PROJECT”
i) DO NOT HESITATE TO “REHASH” ALL CONCLUSIONS AT EACH STEP OF THE PROCESS—THIS IS ONE
AREA WHERE IT IS OK TO BE REDUNDANT. RE-EXAMINE YOUR 5 DATA SETS, DOES YOUR DATA
SUGGEST AN ASSOCIATION OR CAUSATION WHICH APPEARS TRUE, BUT IS REALLY NOT? EXPLAIN.
I
IB Mathematical Studies
Example Project Titles and Project Statement of Tasks
Below is a compilation of Titles and Statement of Tasks used by IB students.The inclusion of a title on this list in
no way guarantees a project written on such a topic was graded outstanding. The list is just to provide ideas.
1. What is the relationship between a person’s weight classification in Rowing and their times on an
ergometer (rowing machine)?
2. Does Racial Bias exist in North Carolina’s traffic enforcement?
3. Is There a Correlation Between Autism Rates and Family Income Level?
4. Title- How Does Age Play a Role in the Tony Awards Winner for Best Actress in a Musical?
5. An Investigation of People’s Knowledge of Art in Relation to Their Age
6. Caffeine Consumption And Sports Achievement
7. Why People Lie.
8. Do Vaccines cause Autism?
9. Investigation Into Letter and Point Distribution in Scrabble
10. Does playing a musical instrument raise SAT scores?
11. Energy Drinks and Your GPA, is there a cause and effect?
12. Population Growth
13. Lung Capacity
14. Pascal’s Triangle
15. Fractals
21
16. A Comparison Between Two Different Collections of ‘Magic the Gathering’ Cards
17. A Comparison of the Agricultural Economy of a Developed and a Developing Country
18. Is It Possible to Determine an Author Mathematically Analyzing His or Her Texts?
19. Patterns of the Graph of y = ax^4 + bx^3 + cx^2 + dx + e
20. Increasing Traffic Flow
21. Limits on Infinity: Examining Answers to Theory
22. A Model Investment
23. Accommodating Comfort for the Majority of Viewers in a Movie Theater
24. How Seating Effects Grades in the Classroom
25. The Use of Tessellations and Other Mathematical Concepts in the Works of M. C. Escher
26. Tidal Predictions
27. A Wave of Music
28. The Perception of Weight
29. The Resilience of the Baseball and Its Effects on Home Run Production
30. Is There a Relationship Between the Length of a Turbine Blade and Voltage?
31. Fibonacci Ratios in Sea Shells and in Aesthetics
32. Determining the Correlation Between Economic Class and the Social Behavior of Adolescents
33. Football Statistics
34. A Study of What is Mathematically Beautiful in Musical Melodies
35. Pressure Points on Dancers’ Feet
36. The Golden Rectangle in Art
37. Probability of Similar Birthdays
38. Polynomial Functions and Their Graphs
39. Fact or Myth: Comparison of Shoe Size to Forearm Length and Height to Arm Span
40. The Effect of Weight, Friction, and Aerodynamics on the Velocity of a Toy Car
41. Relationship Between Maternal Age and Incidences of Down Syndrome
1. In the last three years, I rowed for the Rowing Organization of Citrus County Students (ROCCS), and I really
came to love the sport. For the fall of my first year in 2008 I rowed with the men’s four, because there
weren’t enough boys for the boat and not enough girls for another boat. Come spring of that year I began
rowing a women’s double, which I rowed until summer of 2011. I found that I loved sculling (rowing with
two oars) much more than sweeping (rowing with one oar), because it made me feel more balanced.
During my time on the team I won over 30 medals, and my boat in 2010 was the first in ROCCS history to
medal at the Southeastern Regionals event, we took third and won a bid for Nationals, though we did not
attend that event. Rowing has four different classifications for the rowers: Sweep, Sculler, Heavyweight,
and Lightweight. These weight classifications are a little broad, a lightweight for women is under 135lbs,
while a lightweight for men is under 155lbs. anyone that doesn’t meet lightweight is a heavyweight,
though there is an unofficial classification called “midwieght” which are rowers who are able to row both
by dropping a couple pounds right before an event, but there is no official recognitions of this weight class.
Weight classes exist to make the events more fair, so that you don’t have a 150lbs lightweight male rowing
against a 230lbs wall of muscle, often heavyweights are seen as being stronger that lightweights. In my
experience with ROCCS both my Women’s double and our Men’s double had a heavyweight and a
lightweight rowing in the same boat in a heavyweight class, (for a boat to be considered lightweight both
rowers must meet the weight requirement) and dominating, in 2009-2010 both boats were ranked second
in the state. What I really noticed about our lightweights (I am a heavyweight) is that when we were
training together on the Ergs (short for Ergometer), their times were never very far from ours. Especially
with the boys double, I noticed that the lightweight could match the heavyweight rower on the Erg almost
22
every time. This observation prompted me to ask whether the weight classifications really mattered. So in
this investigation I decided to test my theory. I went on to the Southern Sprints Ergathon’s archives and
pulled up last year’s results, I chose the men’s Heavyweight and Lightweight 500 meter dash because I felt
it would have the least variables to contend with. Knowing that the heavyweights would have outliers at
the upper end with very low times I decided to control for 10% of the lowest heavyweight scores so I
would eliminate the odd 250lb wall of meat. After looking at my data I realized that there are outliers at
the lower end of the spectrum for both classifications, so in another separate calculation I decided to
control for the bottom 10% (those with the highest times) to eliminate any novices or extremely bad/out
of shape rowers. To process this data I am going to use the Chi-squared test for independence.
My
hypothesis is that weight classification and Erg times will be independent of each other, or in other words,
the null hypothesis will be proved.
2. An investigation on traffic stops in the state of North Carolina will be conducted to indicate whether a nonWhite person (Black, Asian, and Native American) is more likely to be stopped than a White person. Online
data published by the North Carolina Department of Justice and the Census Bureau will be used. Forty
enforcement agencies and their published data will be randomly selected and analyzed. Consequently,
various statistical and mathematical processes will be used to determine whether race plays a key factor in
being stopped. Indeed correlation does not necessarily mean causation and that several factors may apply;
thus the analysis can only be viewed as a logical inference through the use of statistical and mathematical
processes. However, since traffic stops are ubiquitous, it is more likely that not many extraneous factors
apply. Therefore, statistical results should lead to viable analyses and inferences. Although not
representative of the entire United States, North Carolina is the 10th most populous state in the country
and therefore hosts a variety of people of different races. Therefore an analysis on North Carolina’s traffic
enforcement can be a good starting point for further investigation.
3. Statement of Task: I plan to investigate the relationship between autism rates and income levels in the
United States to see whether a lower or higher median family income level in each state affects the
amount of diagnoses of autism. This project personally relates to me as my older brother has autism and I
am curious as to whether the amount of money your family makes affects a condition such as autism. Also,
my mother is a strong advocate for people with developmental disabilities; I’ve gone to conferences and
meetings with her and I believe have seen some type of relationship between the people who have
developmental disabilities and their income level. I want to specifically investigate autism because I would
like to know whether a low income level really does affect people regarding their susceptibility to having it.
Detailed Plan: I plan on comparing the median family income for each state in the United States with the
autism rate for that state by using data from Centers for Disease Control and Prevention and the United
States Census Bureau. I plan on using the following math processes: comparative bar graphs, probability,
standard deviation, Chi-square test, Pearson’s Product Moment Calculation, and linear regression
calculations and the measures of central tendency. The comparative bar graphs and linear regression
calculations will show the relation between autism rates and income level. I will calculate the probability of
a person being diagnosed with autism in each state. I will find the standard deviation to show how much
variation exists from the mean. I will conduct a Chi-square test null and alternative hypotheses. I will
calculate Pearson’s Product Moment Calculation, or r, to see how accurate my data is. Finally, I will use the
measures of central tendency to show the average, median, and mode of my data.
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4. Statement of Task- Ever since I was thirteen years old, I have always been fascinated by Broadway
musicals. The songs, the dances, the costumes, everything seemed to have me falling more and more in
love with this art. Now every year in June, I watch the Tony Awards to see which shows come out on top
and which fall flat. The award that has always fascinated me the most is who won for Best Actress in a
Musical. Recently, I noticed that not one specific age group wins out over the other. This is why for my
project I want to see how age correlates to the winner of the Best Actress in a Musical award for the
Tonys. I plan on taking information from the Tiny Awards official website and looking up past winners of
this award from 1947 to present day. I will write down each actress’ name, age, and what show she was in.
I will then create a certain age groups and apply my findings to a scatter plot diagram. The results of this
survey will help me determine if younger actresses or older actresses are more likely to win the award.
Detailed Plan- The math processes that I plan on using so far to try and find my results are making a
frequency table and a scatter plot diagram. If there is any correlation within the scatter plot I will proceed
to find r.
5. I’ve decided to focus on the cell phone industry, and compare the cost of a basic service across Canada. I
also decided to focus on four provinces representing the regions of Canada: New Brunswick (Atlantic),
Ontario (Central), Manitoba (Prairies) and British Columbia (West Coast). Two leading mobile
communication providers will be chosen for each province. One basic plan will be chosen from each
company. The plan will not involve a long-term contract, but will be based on monthly charges per airtime
usage. For each plan, the prices per minute of airtime will be found and then used to calculate the cost of
200 minutes of airtime per month for all the companies. To try to understand the wide range of prices
across the country, an economic indicator such as the Annual Personal Disposable Income will be
introduced. The price per year of each plan will be expressed as a percentage of the Annual Personal
Disposable Income for each province. The results will be displayed on separate table, charts and graphs.
6. For my project I have chosen to investigate the effect, if any, that the number of extracurricular activities
has upon a high school students grades. I will interview as many students as possible with the minimum
being 20 students in order to achieve a substantial base of information. These students will all be in the full
International Baccalaureate program to ensure that the level of difficulty in coursework is the same. The
effect of involvement in activities can be anything from sports teams to chess clubs as long as there is a
level of dedication and time required to participate in them. The object is to see whether over involvement
or under involvement has any drastic effect on a student's grade due to the time taken away from their
studies. The data collected will be the number of activities currently involved in throughout the first term
coupled with the total number of hours during an average week they would spend participating in them
combined. An example of this would be that a student may be a member of the chess club, soccer team,
yearbook, and swimming giving them a total of 4 activities and an estimate 10 hours a week away from
studies. The student's grade average will then be taken up to this point in the semester. Since the data is
being collected at the end of the term just prior to the mid-year exams the grade will give a good
indication as to what the student’s actual mark is and would be by the end of the term. This data will then
be graphed to show the effects and correlations that may become apparent between the grades and
activities. The students will be asked to accurately fill out a table in which they will state the number of
activities they have participated in since the beginning of the year, the number of hours per week spend
on these activities in total, and their current grade mean. A sample table of the format the subjects will be
asked to follow is found below.
7. I will investigate the probability of winning with certain hands of poker, namely the "Texas Hold 'me"
variation. The test will simulate "heads up" poker, or, when there are only 2 people playing. First, the
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players will be dealt 2 cards, with only one of the players visible. Then, the probability of winning will be
determined after the third community card, or the flop has been laid. After the probability has been
calculated the last 2 community cards, the turn and the river will be placed and the opponent's cards
revealed. After the observations are taken, the first player's cards and the flop will remain unchanged
while the rest of the deck is shuffled and new cards are given to the opponent and the last 2 cards again
dealt. The odds will remain the same as the visible cards and the first 3 used for the calculations will
remain unchanged. This will be repeated ten times before totally new cards will be dealt. After the tests
are complete, the calculations will be repeated with the same cards but with the opponent's hand visible
and thus the probability recalculated for each hand. After all the calculations are complete, graphs will be
drawn to display the differences in percentage that the first player will win. Conclusions will then be drawn
as to why certain hands have better chances of beatings others.
8. The purpose of this project is to analyze in which months the most people are born, what the average
number of births in a month out of the grade 11 and 12's in Saint John High School is and to discover the
probability of the number of birthday matches among students in grade 11 and 12 at Saint John High
School. The number of births in the seasons of spring, summer, fall and winter will also be studied. The
assumptions need to be made that there are 365 possible birth dates, not including the odd leap year. Also
there is an equal chance of being born on any given date in the 3 65 days. A list of student's birthdays will
be used from the office, with a total of 547 students. The students used will be in both grade 11 and 12.
Twins and triplets are included in the study as having the same birthday. The number of birthdays in each
month will be tallied and produced in data tables and then as graphs. The same will be done with people
sharing the same birthday. The probability for the number of birthdays being shared will be used by a
formula. The mean for each month will be calculated as well as the mean number of birthdays in a month.
9. For my math project it has been decided to do an analysis of the purchases made at New York Fries in the
theater where I work. New York Fries (or NYF) makes a relatively large number of sales in a day and yet it is
unknown to whom we sell the most fries, what we sell most often or even what times of day would be the
busiest and therefore needing the largest amount of fries made. To accomplish this I will record the time
of day each purchase is made, the relative age of the buyer (Child, youth, adult or senior) (this will
determine to which group they most likely belong), what they purchased, how much it cost and the
number in the group and if they are family. This data will be analyzed using mathematical methods such as
finding a mean, drawing graphs, analyzing mass data and the concept of outliers will be used in analysis.
Conclusions will be drawn as to who buys must often from NYF, how much they spend and at what time do
they normally make their purchases. As well as this the weather conditions will be recorded and see if this
has a limiting effect on the number of patrons in a day, their age or how much they spend.
10. Investigating the effect of extracurricular activities and part time jobs on high school students marks.
Background: While attending a secondary school, one must learn to balance all sort of responsibilities.
These responsibilities may include extracurricular activities including athletics, musicals and perhaps a part
time job to earn some extra money. However, while taking part in these other activities; one must keep
their marks in school up as much as possible. By doing a survey, I will compare the relationship between
the amount of time given to extracurricular activities and/or part time job to that individual's average
while attending school these results will be classified into two groups, male and female. From here, the
data collected will be graphed using three different graphs for each gender: 1. Average in School vs.
Number of Hours Spent at Work and/or Extracurricular Activities per Week: 2. Average in School vs.
Number of Hours Spent on Homework per Week; 3. The Combined Data i.e. "graphs 1 and 2 placed on
same axes to make it easier to visualize). The expected result for this survey will be that the majority of the
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data will be situated around the middle with a moderate number of extracurricular hours and a moderate
number of homework hours.
11. Sleep is as important as food and air. Quantity and quality are very important. Most people need between
7.5 to 8.5 hours of uninterrupted sleep. If you need to press the snooze alarm in the morning you are not
getting the sleep you need. This could be due to not enough time in bed, external disturbances, or a sleep
disorder. About 120 million Americans suffer from sleep disorders including narcolepsy, sleep apnea,
restless less syndrome, the insomnias and simple sleep deprivation. Most of these people are unaware.
Evidence is mounting that taking a power nap during the day appears to enhance information processing
and learning. New experiments by a group at Harvard University show that a midday sleep reverses
information overload and shows a 20 percent improvement in learning a motor skill While the so-called
"super-achievers" are out on their coffee breaks, researchers say real achievers have discovered a much
more effective method—the power nap. Comely psychologist Dr. James Maas writes that a 20-minute nap
in the afternoon actually provides more rest than sleeping an extra 20 minutes in the morning. He also
writes that napping should be considered a part of one's "daily exercise routine." Due to all of the sleeping
problems that people have, and the frequent razzing that I receive about taking naps, I have decided to
focus on sleeping habits of people. Since younger children tend to have different sleeping habits than
adults, I decided to split up the categories into different age categories. The age categories that I'm going
to split these into are from 10-14, 15-19, 20-30, and 31+. I will questions five females and five males from
each age category. I have gathered my data primarily through fellow students, and their younger and older
siblings, as well as parents for the older age category. I am going to ask them various questions that discuss
their sleeping habits. This includes whether they nap anytime throughout the day, what their sleeping
environment is like, as well as many others. Through my research, I hope to find out which age category
tends to have the best sleeping habits. The best sleeping habits will be judged on the age category that has
the most answers that correspond with what experts in the field of sleeping say.
12. The National Hockey League will be holding its annual Super Skills Competition on February 7 in Saint Paul
Minnesota; I will be examining many parts of this competition and attempt to draw relevant conclusions.
There are two teams in this competition, the Eastern Conference, and the Western Conference. The first
thing I am going to analyze the hardest shot competition. There has been a lot power. I will examine the
sticks used by the players and see if there is any relation between (be sticks used by the players and the
force of their shots- The next event I will be analyzing is the shooting accuracy. Again this will be examining
the sticks used by the players. I am trying to see if there is any relation to the type of stick and the accuracy
of your shot. In addition I am going to find out what the probability of scoring a goal in the breakaway
competition. A lot of the time in breakaways the advantage is said to be given to the shooter, but I believe
that the advantage lies with the goalie so I am going to test that. In the fastest skater events I am going to
see if a certain brand of skates produces more winners than another brand. Each company claims that
their skates will improve performance. I would like to see if there is a type of skate that makes players
skate faster. In the shooting events I am going to compare shooting right handed to shooting left handed.
For all the events I am going to see if players from a particular country do better at certain events then
players from other country. Also, I am going to try and determine if players of a particular size excel in one
event.
13. I am going to look at Asthma with eight different age groups ranging from twelve years old to over
seventy-five years old. Asthma is "a condition often of allergic origin that is marked by continuous or
paroxysmal labored breathing accompanied by wheezing, by a sense of constriction in the chest, and often
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by attacks of coughing or gasping."] The purpose of this project is to examine the effect of age and gender
on asthma. The graphs are going to be done by age group and by gender. I will also be looking at if there is
an increase or decrease in asthma rates over in the seven year time frame that is being looked at To
analyze the data I will be using graphs, pie charts, means, standard deviation and percentages.
L.
Criteria / Grading Rubric
Criterion A: Introduction
Achievement level
Descriptor
0
The student does not produce a clear statement of task.
1
The student produces a clear statement of the task.
2
The student produces a title, a clear statement of the task and a clear description of
the plan.
Criterion B: Information/measurement
Achievement level
Descriptor
0
The student does not collect relevant information or generate relevant
measurements.
1
The student collects relevant information or generates relevant measurements.
2
The relevant information collected, or set of measurements generated by the
student, is organized in a form appropriate for analysis or is sufficient in both
quality and quantity.
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3
The relevant information collected, or set of measurements generated by the
student, is organized in a form appropriate for analysis and is sufficient in both
quality and quantity.
Criterion C: Mathematical Processes
Achievement level
Descriptor
0
The student does not attempt to carry out any mathematical processes.
1
The student carries out simple mathematical processes.
2
The simple mathematical processes are mostly or completely correct, or the student makes
an attempt to use at least one sophisticated process.
3
The student carries out at least one sophisticated process, and all the processes used are
mostly or completely accurate.
4
The student carries out at least one sophisticated process; the process used is mostly or
completely accurate and all the processes used are relevant.
5
The student accurately carries out a number of relevant sophisticated processes.
Criterion D: Interpretation of results
Achievement level
Descriptor
0
The student does not produce any interpretations or conclusions.
1
The student produces at least one interpretation or conclusion.
2
The student produces at least one interpretation and/or conclusion that are consistent
with the mathematical processes used.
3
The student produces a comprehensive discussion of interpretations and conclusions that
are consistent with the mathematical processes used.
Criterion E: Validity
Achievement level
Descriptor
28
0
The student does not comment on the mathematical processes used or the
interpretations/conclusions made.
1
The student has made an attempt to comment on either the mathematical processes used
or the interpretations/conclusions made.
2
The student has made a serious attempt to comment on both the mathematical processes
used and the interpretations/conclusions made.
Criterion F: Structure and Communication
Achievement level
Descriptor
0
The student has made no attempt to structure the project.
1
The student has made some attempt to structure the project or has used appropriate
notation and terminology.
2
The student has made some attempt to structure the project and has used appropriate
notation and terminology.
3
The student has produced a project that is well structured and communicated in a
coherent manner.
Criterion G: Commitment
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Achievement level
Descriptor
0
The student showed little or no commitment.
1
The student showed satisfactory commitment.
2
The student showed full commitment.
30