M A T H E M A T I C S
Grade 7
Mathematics
Frameworks
Unit 1
Dealing with Data
Student Edition
Georgia Performance Standards Framework
Grade 7 Mathematics
Unit 1
2nd Edition
Unit 1
DEALING WITH DATA
TABLE OF CONTENTS
Overview ................................................................................................................................3
Enduring Understandings.......................................................................................................3
Essential Questions ................................................................................................................4
Key Standards and Related Standards ...................................................................................4
Selected Terms and Symbols .................................................................................................6
Tasks ......................................................................................................................................7
 Notes on What’s in a Name?..................................................................................8
 Notes on “The Simple Joy of Burgers” ................................................................ 9
 Notes on Where’s the Middle? Finding the “Best” Measure of Center ............... 11
 Notes on The “eyes” have it ................................................................................. 14
 Notes on Touchdown! .......................................................................................... 16
 Notes on Literacy Rates ....................................................................................... 18
 Notes on Who Was the Greatest Yankee Home Run Hitter?............................... 20
 Notes on Congress, Pizza, and Predictions .......................................................... 22
 Notes on Relationships......................................................................................... 25
 Notes on Emergency 911! Bay City .................................................................... 26
 Notes on Culminating Task: “Boys Versus Girls”............................................... 29
Georgia Department of Education
Brad Bryant, State Superintendent of Schools
MATHEMATICS  GRADE 7  UNIT 1: DEALING WITH DATA
July 22, 2010  Page 2 of 30
Copyright 2010 © All Rights Reserved
Georgia Performance Standards Framework
Grade 7 Mathematics
Unit 1
2nd Edition
Grade 7 Mathematics
Dealing with Data
OVERVIEW
In this unit, students will continue to develop statistical problem solving through a four-step
process: formulating questions, collecting data, analyzing data, and interpreting results. In Grade
5 Mathematics, students collected, organized, and displayed data and analyzed data using the
measures of central tendency and the range of a set of data. In Grade 6 Mathematics, students
extended this understanding by comparing groups and examining variability of data. In Grade 7
Mathematics, students will extend their understanding of the measures of central tendency and
measures of variation to included the five-number summary and population and sample statistics.
Students will also use these measures to recognize and discuss similarities and differences
between different data sets.
Students will formulate questions that can be answered with data and collect appropriate data by
taking surveys and conducting experiments. Data will be collected from a census and a sample.
Organization of data should include stem-and-leaf plots and representation of data should include
previously learned graphs, line plots, histograms, box-and-whisker plots, and scatter plots.
Students will learn how to analyze data using the five-number summary; minimum, lower
quartile, median, upper quartile, maximum. Students will also display the five-number summary
using box-and-whisker plots. The measures of central tendency and measures of variation will
also be used to analyze data. Both range, quartiles, and interquartile range are used as measures
of variation and students should recognize that the interquartile range is a better measure for
comparing data sets because it is less sensitive to outliers and because it takes more of the data
into account. Students will also investigate the effect of outliers on measures of central tendency.
For distributions involving one variable data, students will display the data using graphs such as
line plots or box-and-whisker plots. Students will describe the data using measures of center and
measures of variation. For distributions involving two variable data, students will display the
data using scatter plots to explore the relationship between the two variables.
In Grade 6 Mathematics, students compared groups using the measures of central tendency and
the range of a data set. In Grade 7 Mathematics students will extend this concept to included
sample statistics and population statistics. Students will explore the relationship between sample
statistics and the corresponding population parameters by using the measures of central tendency
and variation. Students will also observe that sample statistics are more likely to approximate
population parameters as sample size increases.
ENDURING UNDERSTANDINGS
Data can be represented graphically in a variety of ways. The type of graph is selected to best
represent a particular data set.
Georgia Department of Education
Brad Bryant, State Superintendent of Schools
MATHEMATICS  GRADE 7  UNIT 1: DEALING WITH DATA
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Georgia Performance Standards Framework
Grade 7 Mathematics
Unit 1
2nd Edition
Measures of center (mean, median, mode) and measures of variation (range, quartiles,
interquartile range) can be used to analyze data.
Larger samples are more likely to be representative of a population.
Conclusions can be drawn about data sets based on graphs, measures of center, and measures
of variation.
We can use graphs to investigate the relationship between data sets.
ESSENTIAL QUESTIONS
What is meant by the center of a data set, how is it found and how is it useful when analyzing
data?
How can I describe variation within a data set?
In what ways are sample statistics related to the corresponding population parameters?
How do I choose and create appropriate graphs to represent data?
What conclusions can be drawn from data?
STANDARDS ADDRESSED IN THIS UNIT
Mathematical standards are interwoven and should be addressed throughout the year in as
many different units and activities as possible in order to emphasize the natural
connections that exist among mathematical topics.
KEY STANDARDS
M7D1. Students will pose questions, collect data, represent and analyze the data, and
interpret results.
a. Formulate questions and collect data from a census of at least 30 objects and from
samples of varying sizes.
b. Construct frequency distributions.
c. Analyze data using measures of central tendency (mean, median, and mode),
including recognition of outliers.
d. Analyze data with respect to measures of variation (range, quartiles, interquartile
range).
e. Compare measures of central tendency and variation from samples to those from a
census. Observe that sample statistics are more likely to approximate the population
parameters as sample size increases.
f. Analyze data using appropriate graphs, including pictographs, histograms, bar graphs,
line graphs, circle graphs, and line plots introduced earlier, and using box-andwhisker plots and scatter plots.
g. Analyze and draw conclusions about data, including a description of the relationship
between two variables.
M7A3. Students will understand relationships between two variables.
a. Plot points on a coordinate plane.
c. Describe how change in one variable affects the other variable.
Georgia Department of Education
Brad Bryant, State Superintendent of Schools
MATHEMATICS  GRADE 7  UNIT 1: DEALING WITH DATA
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Grade 7 Mathematics
Unit 1
2nd Edition
RELATED STANDARDS
M7P1. Students will solve problems (using appropriate technology).
a. Build new mathematical knowledge through problem solving.
b. Solve problems that arise in mathematics and in other contexts.
c. Apply and adapt a variety of appropriate strategies to solve problems.
d. Monitor and reflect on the process of mathematical problem solving.
M7P2. Students will reason and evaluate mathematical arguments.
a. Recognize reasoning and proof as fundamental aspects of mathematics.
b. Make and investigate mathematical conjectures.
c. Develop and evaluate mathematical arguments and proofs.
d. Select and use various types of reasoning and methods of proof.
M7P3. Students will communicate mathematically.
a. Organize and consolidate their mathematical thinking through communication.
b. Communicate their mathematical thinking coherently and clearly to peers, teachers,
and others.
c. Analyze and evaluate the mathematical thinking and strategies of others.
d. Use the language of mathematics to express mathematical ideas precisely.
M7P4. Students will make connections among mathematical ideas and to other disciplines.
1. Recognize and use connections among mathematical ideas.
2. Understand how mathematical ideas interconnect and build on one another to produce
a coherent whole.
3. Recognize and apply mathematics in contexts outside of mathematics.
M7P5. Students will represent mathematics in multiple ways.
a. Create and use representations to organize, record, and communicate mathematical
ideas.
b. Select, apply, and translate among mathematical representations to solve problems.
c. Use representations to model and interpret physical, social, and mathematical
phenomena.
Georgia Department of Education
Brad Bryant, State Superintendent of Schools
MATHEMATICS  GRADE 7  UNIT 1: DEALING WITH DATA
July 22, 2010  Page 5 of 30
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Georgia Performance Standards Framework
Grade 7 Mathematics
Unit 1
2nd Edition
SELECTED TERMS AND SYMBOLS
The following terms and symbols are often misunderstood. These concepts are not an
inclusive list and should not be taught in isolation. However, due to evidence of frequent
difficulty and misunderstanding associated with these concepts, instructors should pay
particular attention to them and how their students are able to explain and apply them.
 Census: Collection of data from every member of a population.
 Sample: A selected part of a population.
 Outlier: A value that is very far away from most of the values in a data set.
 Quartile: When data in a set are arranged in order, quartiles are the numbers that split the
data into quarters (or fourths).
 Interquartile Range: The difference between the first and third quartiles. (Note that the first
and third quartiles are sometimes called upper and lower quartiles.)
 Parameter: A measured characteristic of a population.
 Statistic: A measured characteristic of a sample.
 Stem-and-Leaf Plot: A graphical method used to represent ordered numerical data. Once the
data are ordered, the stem and the leaves are determined. Typically, the stem is all but the last
digit of each data point and the leaf is that last digit.
 Box-and-whisker Plot: A diagram that summarizes data using the median, the upper and
lower quartiles, and the extreme values (outliers). Box-an-whisker plots (box plots) are
constructed from the five-number summary of the data (minimum value, maximum value,
median, lower quartile, and upper quartile).
You may visit http://intermath.coe.uga.edu or http://mathworld.wolfram.com to see definitions
and specific examples of many terms and symbols used in the seventh-grade GPS.
Georgia Department of Education
Brad Bryant, State Superintendent of Schools
MATHEMATICS  GRADE 7  UNIT 1: DEALING WITH DATA
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Georgia Performance Standards Framework
Grade 7 Mathematics
Unit 1
2nd Edition
TASKS
The collection of the following tasks represents the level of depth, rigor and complexity
expected of all seventh grade students. These tasks or tasks of similar depth and rigor
should be used to demonstrate evidence of learning.
Georgia Department of Education
Brad Bryant, State Superintendent of Schools
MATHEMATICS  GRADE 7  UNIT 1: DEALING WITH DATA
July 22, 2010  Page 7 of 30
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Georgia Performance Standards Framework
Grade 7 Mathematics
Unit 1
2nd Edition
What’s in a Name?
Adapted from: A Collection of Performance Tasks and Rubrics: Middle School Mathematics, by
Charlotte Danielson
The Spiritwear company embroiders names on its sweatshirts; they charge customers for the
service. It costs the company $0.50 to embroider each letter, and they want to make 100% profit
on the service. But they also want to charge a flat fee per name, rather than charging different
amounts for different names. Most people just want their first name on their sweatshirt.
The company has asked you to advise them on the length of first names of young people so they
can set a fair price for embroidering the names on sweatshirts. How long is the average name?
What could the company charge for an embroidered name so that they would make money
overall?
In order to complete this task, you should:
Devise a method to determine the average length of a first name;
Collect and analyze sufficient data to make you confident of your results;
Determine a fair price for the sweatshirt company to charge for embroidering the names.
Write a letter to the president of Spiritwear with your recommendation for the price to charge for
embroidering a name. Justify your recommendation by explaining in detail how you determined
the price to charge.
Georgia Department of Education
Brad Bryant, State Superintendent of Schools
MATHEMATICS  GRADE 7  UNIT 1: DEALING WITH DATA
July 22, 2010  Page 8 of 30
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Georgia Performance Standards Framework
Grade 7 Mathematics
Unit 1
2nd Edition
“The Simple Joy of Burgers”
Have you ever wondered how many fat grams are in the food you
eat? Are there sandwiches that have less grams of fat than others?
Let’s see how many fat grams are in your favorite sandwich.
Sandwiches
Total Fat (g)
Hamburger
9
Cheeseburger
12
Double Cheeseburger
23
McDouble
19
Quarter Pounder®
19
Quarter Pounder® with Cheese
26
Double Quarter Pounder® with Cheese
42
Big Mac®
29
Big N' Tasty®
24
Big N' Tasty® with Cheese
28
Angus Bacon & Cheese
39
Angus Deluxe
39
Angus Mushroom & Swiss
40
Filet-O-Fish®
18
McChicken ®
16
McRib ®†
26
Premium Grilled Chicken Classic Sandwich
10
Premium Crispy Chicken Classic Sandwich
20
Premium Grilled Chicken Club Sandwich
17
Premium Crispy Chicken Club Sandwich
Source: McDonald’s USA
28
Georgia Department of Education
Brad Bryant, State Superintendent of Schools
MATHEMATICS  GRADE 7  UNIT 1: DEALING WITH DATA
July 22, 2010  Page 9 of 30
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Georgia Performance Standards Framework
Grade 7 Mathematics
Unit 1
2nd Edition
Part I.
1. Make a stem-and-leaf plot of the fat grams.
2. Which sandwich has the smallest amount of fat grams?
3. Which sandwich has the largest amount of fat grams?
4. Find the median amount of fat grams. Explain what the median tells us.
5. Find the lower quartile. Explain how you found the lower quartile and explain what it tells
us.
6. Find the upper quartile. Explain how you found the upper quartile and explain what it tells
us.
Part II.
1. Find the range of fat grams. Explain what the range tells us.
2. Find the interquartile range. Explain how you found the interquartile range and explain what
it tells us.
Part III.
1. Find the mean of fat grams.
2. Find the mode of fat grams.
3. Explain which measure of variation (range, interquartile range) is most useful in analyzing
the fat grams of the sandwiches.
Georgia Department of Education
Brad Bryant, State Superintendent of Schools
MATHEMATICS  GRADE 7  UNIT 1: DEALING WITH DATA
July 22, 2010  Page 10 of 30
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Georgia Performance Standards Framework
Grade 7 Mathematics
Unit 1
2nd Edition
Where’s the Middle?
Finding the “Best” Measure of Center
The data below represent grades of students on a mathematics test:
84 71 100 88 23 100 81 93 92 100 87 75
1. Find the mean:
_____________________
2. Find the median: _____________________
3. Find the mode:
_____________________
4. Which of these numbers do you think best describes the middle of the data? ____________
Explain your reasoning.
Remove the outlier from the data, and then do the following:
5. Find the mean:
_____________________
6. Find the median: _____________________
7. Find the mode:
_____________________
Compare these results to the original measures. Keep your observations in mind for some
questions later.
Georgia Department of Education
Brad Bryant, State Superintendent of Schools
MATHEMATICS  GRADE 7  UNIT 1: DEALING WITH DATA
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Georgia Performance Standards Framework
Grade 7 Mathematics
Unit 1
2nd Edition
Now go back to the original data set (with the outlier included). One of the scores listed is 92.
Suppose that had been recorded incorrectly and that it should have been 99 rather than 92. How
would that have affected these measures of center?
Replace the score of 92 with a score of 99, and then do the following:
8. Find the mean:
_____________________
9. Find the median: _____________________
10. Find the mode:
_____________________
11. Which measure(s) of center take the value of every item of data into account? Explain your
thinking.
12. Which measure(s) of center are affected by outliers? Explain.
13. Which of these numbers in questions 1-3 do you think best describes the middle of the data?
Explain your reasoning.
Georgia Department of Education
Brad Bryant, State Superintendent of Schools
MATHEMATICS  GRADE 7  UNIT 1: DEALING WITH DATA
July 22, 2010  Page 12 of 30
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Grade 7 Mathematics
Unit 1
2nd Edition
Differentiation
Suppose your math grade for this grading period is to be determined using 10 test, homework,
and project scores. All of the scores are equally important. You get to decide which measure of
central tendency, the mode, median, or mean, will be used for your grade.
1. Would you ever prefer to use the median rather than the mean? If so, what would have to
be true about the scores? If not, explain why you think using the median wouldn’t ever
help your grade.
2. Would you ever prefer to use the mean rather than the median? If so, what would have to
be true about the scores? If not, explain why you think using the mean wouldn’t ever help
your grade.
3. Is it possible that you could prefer the mode rather than the median or mean? If so, what
would have to be true about the scores? If not, explain why you think using the mode
wouldn’t ever help your grade.
Georgia Department of Education
Brad Bryant, State Superintendent of Schools
MATHEMATICS  GRADE 7  UNIT 1: DEALING WITH DATA
July 22, 2010  Page 13 of 30
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Georgia Performance Standards Framework
Grade 7 Mathematics
Unit 1
2nd Edition
The “eyes” have it
1. Estimate how long you think that you can go without blinking your eyes. Write down your
estimate and share it with your partner.
2. With your partner and using a stop watch, collect data from five experiments to determine
how long you can actually go without blinking your eyes.
3. Find the mean of the experimental data.
4. Collect the estimates and the means of the experiments from exactly 9 other classmates. Use
a method of organizing your data. (This gives 10 pieces of data for estimates and 10 pieces of
data for means of the experiments.)
5. Find the median of the estimates and the median of the means of the experiment.
a. About what percent of the values in a data set are below the median? Why?
b. About what percent of the values in a data set are above the median? Why?
6. Find the Upper and Lower Quartiles for the data set. Explain why they are called the upper
and lower quartiles and how you found them.
a. About what percent of the values in a data distribution are in each quartile?
b. About what percent of the values fall above the lower quartile?
c. About what percent of the values fall below the upper quartile?
d. Were there any outliers? Justify your answer.
e. Why is it useful to know the outliers of a set of data?
f. If there were any outliers, how did they affect the means, medians, modes, and ranges
of the data sets?
7. Using the collected data, make a double Box-and- Whisker plot that shows the comparison of
the estimates and the means of the experiments:
a. Explain the procedures for making a box-and-whisker plot.
b. How do the numbers on a box-and-whisker plot summarize the data and separate the
data into standard percent groupings?
c. What are some of the disadvantages of using a box-and-whisker plot?
d. Describe the comparisons of the two Box-and-Whisker plots. Tell what this means.
Georgia Department of Education
Brad Bryant, State Superintendent of Schools
MATHEMATICS  GRADE 7  UNIT 1: DEALING WITH DATA
July 22, 2010  Page 14 of 30
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Georgia Performance Standards Framework
Grade 7 Mathematics
Unit 1
2nd Edition
8. Collect all of the class data. Using this data and a graphing calculator, make triple Box-andWhisker plot that compares the estimates, the actual experiment data, and the means of your
individual classmates.
a. How did using the entire data from the class vary from using the data of only ten
classmates? Explain why you think this happened.
b. Name at least three situations in which a box-and-whisker plot would be useful.
Explain why you named these situations.
Differentiation
First create a human box plot.
Once everyone has determined how long they can go without blinking their eyes, write the
number large on a sheet of paper (one per student).
Direct the students to stand in line from the smallest number to the largest number – and hold
the pages in front of them.
Find the median of these numbers by counting off. Put a sticky note on his/her page.
Then just look at the left side. Find the median of those numbers. Put a sticky note on the
median page.
Then just look at the right side. Find the median of those numbers. Put a sticky note on the
median page.
Use a Chinese jump rope (the stretchy kind that is just one piece) to create the “box” around
these 3 sticky notes. Then put string from the ends of the box out to the minimum and the
maximum.
You have now created a human version of a box-and-whisker plot.
 Repeat this process on paper for the students to see.
 Repeat this process on a graphing calculator for the students to see.
 NOW have them explain the procedure for making the box-and-whisker plots.
Georgia Department of Education
Brad Bryant, State Superintendent of Schools
MATHEMATICS  GRADE 7  UNIT 1: DEALING WITH DATA
July 22, 2010  Page 15 of 30
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Georgia Performance Standards Framework
Grade 7 Mathematics
Unit 1
2nd Edition
Touchdown!
The tables below show the total number of touchdowns for the 2009-2010
season. The Southeastern Conference (SEC) and the Atlantic Coast
Conference (ACC) include two nationally ranked teams from Georgia.
Southeastern Conference
Atlantic Coast Conference
Team
Total
Touchdowns
Team
Total
Touchdowns
Alabama
52
Boston
College
40
Arkansas
60
Clemson
54
Auburn
55
Duke
35
Florida
63
Florida State
48
Georgia
45
Georgia Tech
62
Kentucky
44
Maryland
29
LSU
39
Miami (FL)
50
Mississippi
49
North Carolina
35
37
North Carolina
St.
48
31
Virginia
26
Tennessee
49
Virginia Tech
51
Vanderbilt
21
Wake Forest
40
Mississippi
St.
South
Carolina
Georgia Department of Education
Brad Bryant, State Superintendent of Schools
MATHEMATICS  GRADE 7  UNIT 1: DEALING WITH DATA
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Grade 7 Mathematics
Unit 1
2nd Edition
1. Make a line plot for each conference.
2. Make a back-to-back stem-and-leaf plot to compare the SEC with the ACC.
3. Answer the following questions for the Southeastern Conference (SEC) and the Atlantic
Coast Conference (ACC).
a. Find the minimum number of total touchdowns.
b. Find the maximum number of total touchdowns.
c. Find the median.
d. Find the lower quartile.
e. Find the upper quartile.
f. Make a box plot of the total number of touchdowns.
g. Find the interquartile range.
h. Discuss the differences in touchdowns between the Southeastern Conference and the
Atlantic Coast Conference for the 2009-2010 season.
Georgia Department of Education
Brad Bryant, State Superintendent of Schools
MATHEMATICS  GRADE 7  UNIT 1: DEALING WITH DATA
July 22, 2010  Page 17 of 30
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Georgia Performance Standards Framework
Grade 7 Mathematics
Unit 1
2nd Edition
Literacy Rates
The table below shows the literacy rates for various countries
in Africa, Southwest Asia (Middle East), and Southern and
Eastern Asia. The literacy rate for these countries is defined as
the percentage of people age 15 and over that can read and
write. In Grade Seven Social Studies, you will “evaluate how
the literacy rate affects the standard of living.”
Africa
Country
Literacy Rate (%)
Democratic Republic of the Congo
67
Egypt
71
Kenya
85
Nigeria
68
South Africa
86
Sudan
61
Source: Central Intelligence Agency-The World Factbook
Southwest Asia (Middle East)
Country
Literacy Rate (%)
Afghanistan
28
Iran
77
Iraq
74
Israel
97
Saudi Arabia
79
Turkey
87
Source: Central Intelligence Agency-The World Factbook
Georgia Department of Education
Brad Bryant, State Superintendent of Schools
MATHEMATICS  GRADE 7  UNIT 1: DEALING WITH DATA
July 22, 2010  Page 18 of 30
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Georgia Performance Standards Framework
Grade 7 Mathematics
Unit 1
2nd Edition
Southern and Eastern Asia
Country
Literacy Rate (%)
China
91
India
61
Indonesia
90
Japan
99
North Korea
99
South Korea
98
Vietnam
90
Source: Central Intelligence Agency-The World Factbook
Make a box-and-whisker plot of the percentages for Africa, Southwest Asia (Middle East), and
Southern and Eastern Asia. Compare the percentages for the various countries of the world.
Explain what you have learned about the literacy rates in Africa, Southwest Asia (Middle East),
and Southern and Eastern Asia.
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Brad Bryant, State Superintendent of Schools
MATHEMATICS  GRADE 7  UNIT 1: DEALING WITH DATA
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Georgia Performance Standards Framework
Grade 7 Mathematics
Unit 1
2nd Edition
Who Was the Greatest Yankee Home Run
Hitter?
The following table lists four of the greatest New York Yankees’ home run hitters with the
number of home runs each hit while a Yankee.
Adapted from: James M. Landwehr and Ann E. Watkins, Dale Seymour Publications,
Mathematics, 1986, p. 160
Babe Ruth
Year
Home
runs
1920
54
Lou Gehrig
Year
Home
runs
1923
1
Mickey Mantle
Year
Home
runs
1951
13
Roger Maris
Year
Home
runs
1960
39
1921
59
1924
0
1952
23
1961
61
1922
35
1925
20
1953
21
1962
33
1923
41
1926
16
1954
27
1963
23
1924
46
1927
47
1955
37
1964
26
1925
25
1928
27
1956
52
1965
8
1926
47
1929
35
1957
34
1966
13
1927
60
1930
41
1958
42
1928
54
1931
46
1959
31
1929
46
1932
34
1960
40
1930
49
1933
32
1961
54
1931
46
1934
49
1962
30
1932
41
1935
30
1963
15
1933
34
1936
49
1964
35
1934
22
1937
37
1965
19
1938
29
1966
23
1939
0
1967
22
1968
18
Source: Macmillan Baseball Encyclopedia, 4th edition
Georgia Department of Education
Brad Bryant, State Superintendent of Schools
MATHEMATICS  GRADE 7  UNIT 1: DEALING WITH DATA
July 22, 2010  Page 20 of 30
Copyright 2010 © All Rights Reserved
Georgia Performance Standards Framework
Grade 7 Mathematics
Unit 1
2nd Edition
1.
Study these records. Which player appears to be the greatest home run hitter? Why did
you choose this player? Share your predictions with the class.
2.
Make a stem and leaf plot for each player.
a. Using your stem and leaf plot, create a grouped frequency table for each player.
b. Using your frequency table, create a histogram for each player.
c. Use your graphical displays to discuss the home run hitting of each player.
c. Using your frequency table, create a histogram for each player.
d. Use your graphical displays to discuss the home run hitting of each player.
3.
Find the mean, median and mode for each player. Compare the three values you
computed for each player. Which value do you think best describes the performance of
each player? Why?
4. Find the range and interquartile range for each player. Which player has the greatest
range for home runs per year? Which player has the greatest interquartile range? In
trying to determine which players perform consistently from year to year, would you
compare ranges or interquartile ranges? Explain why you chose the measure you did.
5.
Construct a box and whisker plot for each player and graph them together so that you are
able to make comparisons. Write a paragraph describing what you can tell by comparing
the four box and whisker plots.
6.
Based on your graphs and computations in problems 2 - 5, is your prediction still the
same as it was in problem 1? Why or why not?
Georgia Department of Education
Brad Bryant, State Superintendent of Schools
MATHEMATICS  GRADE 7  UNIT 1: DEALING WITH DATA
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Copyright 2010 © All Rights Reserved
Georgia Performance Standards Framework
Grade 7 Mathematics
Unit 1
2nd Edition
Congress, Pizza, and Predictions
Used with permission from Navigating Through Data Analysis in Grades 6-8, NCTM, 2003.
Congress and Pizza
What do pizzas have to do with the United States House of Representatives? In particular, how
does the number of pizza restaurants in a state relate to the number of U.S representatives for that
state?
Below is a table showing the number of pizza restaurants and U.S. representatives for forty
states.
State
Alabama
Alaska
Arizona
Arkansas
Colorado
Connecticut
Delaware
Georgia
Hawaii
Idaho
Indiana
Iowa
Kansas
Kentucky
Louisiana
Maine
Maryland
Missouri
Montana
Nebraska
Number of U.S.
Representatives
7
1
8
4
7
5
1
13
2
2
9
5
4
6
7
2
8
9
1
3
Number of
pizza
Restaurants
1071
149
919
776
929
732
133
1515
217
298
1394
838
708
879
952
212
721
1195
236
471
State
Nevada
New Hampshire
New Jersey
New Mexico
North Carolina
North Dakota
Oklahoma
Oregon
Pennsylvania
Rhode Island
South Carolina
South Dakota
Tennessee
Utah
Vermont
Virginia
Washington
West Virginia
Wisconsin
Wyoming
Number of U.S.
Representatives
3
2
13
3
13
1
5
5
19
2
6
1
9
3
1
11
9
3
8
1
Sources of data: U.S. Department of Commerce, U.S. Census Bureau (n.d.a; n.d.b)
1. Make a scatterplot to display the data to determine if a relationship exists between the
number of pizza restaurants and the number of U.S. representatives.
2. Describe any relationship you see.
Georgia Department of Education
Brad Bryant, State Superintendent of Schools
MATHEMATICS  GRADE 7  UNIT 1: DEALING WITH DATA
July 22, 2010  Page 22 of 30
Copyright 2010 © All Rights Reserved
Number of
pizza
Restaurants
406
119
1182
454
1673
165
1034
816
1682
136
1011
158
1652
469
128
1701
1357
314
1286
108
Georgia Performance Standards Framework
Grade 7 Mathematics
Unit 1
2nd Edition
People, Congress, and Pizza
Below is a table showing the population, the number of U.S. representatives, and the number of
pizza restaurants for forty states.
State
Alabama
Alaska
Population
(2000)
4,461,130
628,933
Number of
Representatives
7
1
Number of
Pizza
Restaurants
1071
149
Arizona
Arkansas
Colorado
5,140,683
2,679,733
4,311,882
8
4
7
919
776
929
Connecticut
3,409,535
5
732
Delaware
Georgia
Hawaii
Idaho
Indiana
785,068
8,206,975
1,216,642
1,297,274
6,090,782
1
13
2
2
9
133
1515
217
298
1394
Iowa
2,931,923
5
838
Kansas
Kentucky
Louisiana
Maine
Maryland
Missouri
2,693,824
4,049,431
4,480,271
1,277,731
5,307,886
5,606,260
4
6
7
2
8
9
708
879
952
212
721
1195
Montana
Nebraska
905,316
1,715,369
1
3
236
471
State
Nevada
New
Hampshire
New Jersey
New Mexico
North
Carolina
North
Dakota
Oklahoma
Oregon
Pennsylvania
Rhode Island
South
Carolina
South
Dakota
Tennessee
Utah
Vermont
Virginia
Washington
West
Virginia
Wisconsin
Wyoming
Population
(2000)
2,002,032
1,238,415
Number of
Representatives
3
2
Number of
Pizza
Restaurants
406
119
8,424,354
1,823,821
8,067,673
13
3
13
1182
454
1673
643,756
1
165
3,458,819
3,428,543
12,300,670
1,049,662
4,025,061
5
5
19
2
6
1034
816
1682
136
1011
756,874
1
158
5,700,037
2,236,714
609,890
7,100,702
5,908,684
1,813,077
9
3
1
11
9
3
1652
469
128
1701
1357
314
5,371,210
495,304
8
1
1286
108
Sources of data: U.S. Department of Commerce, U.S. Census Bureau (n.d.a; n.d.b)
Make a scatter plot to display the relationship between state population and the number of U.S.
representatives. Then make a scatter plot to display the relationship between state population
and the number of pizza restaurants.
1. Compare the two scatter plots with the scatter plot you made earlier that shows the
relationship between the number of U.S. representatives and the number of pizza restaurants
in each state. Which pair of variables seems to have the strongest relationship? Explain your
answer.
Georgia Department of Education
Brad Bryant, State Superintendent of Schools
MATHEMATICS  GRADE 7  UNIT 1: DEALING WITH DATA
July 22, 2010  Page 23 of 30
Copyright 2010 © All Rights Reserved
Georgia Performance Standards Framework
Grade 7 Mathematics
Unit 1
2nd Edition
2. How is state population related to the number of U.S. representatives and to the number of
pizza restaurants?
Georgia Department of Education
Brad Bryant, State Superintendent of Schools
MATHEMATICS  GRADE 7  UNIT 1: DEALING WITH DATA
July 22, 2010  Page 24 of 30
Copyright 2010 © All Rights Reserved
Georgia Performance Standards Framework
Grade 7 Mathematics
Unit 1
2nd Edition
Relationships
Arm Span (in)
Height (in)
Georgia Department of Education
Brad Bryant, State Superintendent of Schools
MATHEMATICS  GRADE 7  UNIT 1: DEALING WITH DATA
July 22, 2010  Page 25 of 30
Copyright 2010 © All Rights Reserved
Georgia Performance Standards Framework
Grade 7 Mathematics
Unit 1
2nd Edition
Emergency 911! Bay City
Used with permission from Balanced Assessment: Middle Grades Package 1, Dale Seymour Publications.
This problem gives you the chance to
 Select appropriate methods to analyze a data
set, including appropriate graphs and
calculations
 Read and interpret a graph
 Use data analysis to make recommendations
With a partner
Last week there was an accident at the Waterfront Amusement Park in Bay City. A seat on one
of the rides broke loose, resulting in the deaths of two teenagers. The owners of the amusement
park have charged that if ambulances had responded more quickly, the two teens would have
survived. They have threatened to sue the Bay City 911 emergency service for failing to
dispatch ambulances efficiently.
The Bay City Council has hired your firm to conduct an independent investigation of the city’s
911 response. Upon completion of your investigation, you are to make a report to the City
Council on your findings, along with any recommendations for improving the Bay City 911
emergency service.
Your investigation has uncovered the following information.



The 911 operators dispatch ambulances from two companies: Arrow Ambulance
Service and Metro Ambulances.
The 911 operators aren’t always sure which company to send when an emergency call is
received.
Data on the response times of the two companies for an area of a one-mile radius of the
Amusement Park show that responses can take as little as 6 minutes or as long as 19
Georgia Department of Education
Brad Bryant, State Superintendent of Schools
MATHEMATICS  GRADE 7  UNIT 1: DEALING WITH DATA
July 22, 2010  Page 26 of 30
Copyright 2010 © All Rights Reserved
Georgia Performance Standards Framework
Grade 7 Mathematics
Unit 1
2nd Edition
minutes. (The response time is the length of time from when a 911 operator receives an
emergency call to when an ambulance arrives at the scene of the accident.)
You need to continue your investigation by analyzing the response time data from the 911 log
sheets for May. (The log sheets are shown on the next page.)
Based on the information above and on your analysis of the response time data, you conclude
that he Bay City Council needs to establish a policy about which service to call.
Write a report to the Bay City Council advising them of your recommendations about how
the 911 operators should make dispatches in the area around the amusement park.
You will need to prepare charts, graphs, calculations, or other materials to support your
recommendations. Be sure to give clear reasons for the policy you are recommending.
Georgia Department of Education
Brad Bryant, State Superintendent of Schools
MATHEMATICS  GRADE 7  UNIT 1: DEALING WITH DATA
July 22, 2010  Page 27 of 30
Copyright 2010 © All Rights Reserved
Georgia Performance Standards Framework
Grade 7 Mathematics
Date of call
Time of call
Wed., May 1
Wed., May 1
Wed., May 1
Thurs., May 2
Thurs., May 2
Fri., May 3
Fri., May 3
Sat., May 4
Sat., May 4
Sat., May 4
Sun., May 5
Mon., May 6
Mon., May 6
Mon., May 6
Tues., May 7
Tues., May 7
Thurs., May 9
Thurs., May 9
Fri., May 10
Sat., May 11
Mon., May 13
Mon., May 13
Tues., May 14
Thurs., May 16
Thurs., May 16
Fri., May 17
Fri., May 17
Fri., May 17
Mon., May 20
Mon., May 20
Thurs., May 23
Thurs., May 23
Fri., May 24
Sat., May 25
Sun., May 26
Mon., May 27
2:20 AM
12:41 PM
8:14 AM
6:23 AM
4:15 AM
8:41 AM
6:23 PM
4:15 AM
8:41 AM
7:12 AM
7:43 PM
10:02 PM
12:22 PM
6:47 AM
7:15 AM
6:10 PM
5:37 PM
9:37 PM
6:25 AM
1:03 AM
6:40 AM
3:25 PM
4:59 PM
10:11 AM
11:45 AM
11:09 AM
9:15 PM
11:15 PM
7:25 AM
4:20 PM
2:39 PM
3:44 PM
8:56 PM
8:30 PM
6:33 AM
4:21 PM
Unit 1
2nd Edition
Company
name
Arrow
Arrow
Metro
Metro
Metro
Metro
Arrow
Metro
Metro
Arrow
Metro
Metro
Arrow
Arrow
Metro
Metro
Arrow
Arrow
Arrow
Metro
Arrow
Metro
Metro
Metro
Metro
Arrow
Arrow
Metro
Arrow
Metro
Arrow
Metro
Metro
Arrow
Metro
Arrow
Response time in
minutes
11
8
11
8
16
7
19
11
11
7
12
9
16
8
16
11
17
6
16
12
17
15
14
8
10
7
8
8
17
19
10
14
10
8
6
9
Georgia Department of Education
Brad Bryant, State Superintendent of Schools
MATHEMATICS  GRADE 7  UNIT 1: DEALING WITH DATA
July 22, 2010  Page 28 of 30
Copyright 2010 © All Rights Reserved
Georgia Performance Standards Framework
Grade 7 Mathematics
Unit 1
2nd Edition
“BOYS VERSUS GIRLS”
Do girls in your class remember better than boys? Are boys in your class quicker to react than
girls? Who spends the most time on homework? Who spends the most time watching TV? Who
spends the most time shopping?
1. Your group should come up with a question that can be answered by collecting numerical
data. The data can be gathered either by experiment (for things like remembering or reaction
time) or by a survey (for things like time spent on various tasks).
If you decide on an experiment, be sure you carefully consider what “better” or “quicker”
means and think about what you’ll do to find out. If you decide on a survey, think about the
question or questions you plan to ask to be sure that everybody you ask will interpret them
the same way.
Turn in a preliminary proposal including the following:
Question or questions you hope to answer by collecting and analyzing data.
Detailed description of your experimental procedure or a copy of the questions you
intend to ask in your survey.
2. After your proposal is approved, collect data from 5 boys and 5 girls selected at random from
your class. Make appropriate graphs for both boys and girls. Calculate appropriate measures
of center and variation for each group.
3. Collect data from 10 boys and 10 girls selected at random from your class. Make appropriate
graphs and calculate appropriate measures of center and variation for both boys and girls.
4. Decide as a group which sample above (5 of each or 10 of each) you think best represents the
entire class. Write an article for the school newspaper explaining your choice.
5. Collect data from everybody in your class. Make appropriate graphs and calculate
appropriate measures of center and variation for both boys and girls. Were you correct about
which sample best represents the class?
6. Present your findings using a project board. Include the following sections:
Question or questions you collected the data to answer.
Procedure. This is an explanation of how you gathered data to answer the question.
Include a detailed description of the experiment or a copy of the questionnaire.
Data. This section should show all the data you gathered for the entire class.
Analysis. In this section, include the graphs you made and measures of center and
variation you calculated for the entire class, along with brief statements about what you
Georgia Department of Education
Brad Bryant, State Superintendent of Schools
MATHEMATICS  GRADE 7  UNIT 1: DEALING WITH DATA
July 22, 2010  Page 29 of 30
Copyright 2010 © All Rights Reserved
Georgia Performance Standards Framework
Grade 7 Mathematics
Unit 1
2nd Edition
determined from comparing graphs, comparing means, comparing ranges, etc., for boys
and girls
Conclusions. In this section, state the answer to the question which began the
investigation. Include a discussion of how analysis of the data supports your conclusion.
Georgia Department of Education
Brad Bryant, State Superintendent of Schools
MATHEMATICS  GRADE 7  UNIT 1: DEALING WITH DATA
July 22, 2010  Page 30 of 30
Copyright 2010 © All Rights Reserved