Collecting Data,
Graphing,
And,
Analyzing
Summer 07
By
Dawn Seopa
And
Sarah Stearns
Table of Contents
Pre Test
Lesson 1
Lesson 2
Lesson 3
Lesson 4
Lesson 5
Lesson 6
Lesson 7
Lesson 8
Post Test
Watching TV Part 1
Watching TV Part 2
Traveling Through Line Plots
Traveling Through Line Plots
Traveling Through Line Plots
Box and Whiskers
Alphabet Soup
State Names
Pre Test
Name: _________________________________
Date:___________________________________
Line Plots/Range, Median, Mode, and Mean, Box and Whiskers Plot
Directions: Use the set of data to answer numbers 1-4. Circle the appropriate answer
choice.
Alyssa's basketball team scored the following number of points during the playoff games:
102, 98, 60, 110, and 50
1. What is the team's mean score?
A. 84
B. 60
C. 98
D. 110
2. What is the range of the team’s scores?
A. 10
B. 60
C. 50
D. 40
3. What is the median of the team’s scores?
B. 98
C. 110
D. 50
E. 102
4. What is the mode of the team’s scores?
A. 98
B. 84
C. no mode
D. 60
Directions: Use the Line Plot to answer numbers 5-7. Circle the appropriate answer
choice.
5. How many students were surveyed?
A. 11
B. 29
C. 32
D. 28
6. What is the mode of the data?
A. 9
B. 7
C. 11
D. 4 and 5
7. How many students have an even number of family members?
A. 17
B. 29
C. 2
D. 5
Mrs. Plater’s Class’ Family Tree
X
X
X
X
X
X
X
X
X
X
X
X
X
X
2
3
4
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
5
6
7
X
X
8
9
10
11
Number of People in our Families
Brief Constructed Response
Mr. Dale’s class took a spelling test on Friday. Their scores
were 65, 82, 95, 100, 77, 82, and 90. Find the range,
median, mode, and mean of the score.
Part A
Question?
Range: ________________ Mode: ________________
Median: _______________ Mean: _______________
Part B
Use what you know about range, median, mode, and mean to
explain why your answer is correct. Use number and/or words
in your explanation.
Part C
In Mr. Smith’s class last Friday they had several contests in
there room to celebrate the 100th day of school. The last contest
of the day was to see how many marshmallows each student could
fit into their mouth. The students mouth had to be completely
closed (meaning their lips had to touch). Here are the results:
5,7,6,8,9,11,15,12,14,20,6,7,8,9,3,4,5,6,7,10,12
Create a box and whisker plot.
Median_________ Q1_________ Q3__________ Outliers________
Pre Test Key
Name: _________________________________
Date:___________________________________
Line Plots/Range, Median, Mode, and Mean Quiz
Directions: Use the set of data to answer numbers 1-4. Circle the appropriate
answer choice.
Alyssa's basketball team scored the following number of points during the
playoff games:
102, 98, 60, 110, and 50
1. What is the team's mean score?
A. 84
B. 60
C. 98
D. 110
2. What is the range of the team’s scores?
A. 10
B. 60
C. 50
D. 40
3. What is the median of the team’s scores?
A. 98
B. 110
C. 50
D. 102
4. What is the mode of the team’s scores?
A. 98
B. 84
C. no mode
D. 60
5. How many students were surveyed?
A. 11
B. 29
C. 32
D. 28
6. What is the mode of the data?
A. 9
B. 7
C. 11
D. 4 and 5
7. How many students have an even number of family members?
A. 17
B. 29
C. 2
D. 5
Brief Constructed Response
Mr. Dale’s class took a spelling test on Friday. Their scores
were 65, 82, 95, 100, 77, 82, and 90. Find the range,
median, mode, and mean of the scores.
Part A
Question?
Range: 35
Median: 82
Mode: 82
Mean: 84
Part B
Use what you know about range, median, mode, and mean to
explain why your answer is correct. Use number and/or words
in your explanation.
Answers will vary.
Part C
In Mr. Smith’s class last Friday they had several contests in
there room to celebrate the 100th day of school. The last contest
of the day was to see how many marshmallows each student could
fit into their mouth. The students mouth had to be completely
closed (meaning their lips had to touch). Here are the results:
5,7,6,8,9,11,15,12,14,20,6,7,8,9,3,4,5,6,7,10,12
Create a box and whisker plot.
Check students plot
Median 8
Q1
6
Q3 11.5
Outliers 20
MSA Brief Constructed Response “Kid Speak”
Mathematics Rubric
Grades 1 through 8
2
Score
My answer shows I completely understood the problem and how to solve it:
• I used a very good, complete strategy to correctly solve the problem.
• I used my best math vocabulary to clearly explain what I did to solve
the problem.
My explanation was complete, well organized and logical.
• I applied what I know about math to correctly solve the problem.
• I used numbers, words, symbols or pictures (or a combination of
them)
1
to show how I solved the problem.
My answer shows I understood most of the problem and how to solve it:
• I used a strategy to find a solution that was partly correct.
• I used some math vocabulary and most of my reasons were correct to
explain
how I solved the problem. My explanation needed to be more complete,
Well organized or logical.
• I partly applied what I know about math to solve the problem.
• I tried to use numbers, words, symbols or pictures (or a combination
of them)
0
to show how I got my answer, but these may not have been completely
correct.
My answer shows I didn’t understand the problem and how to solve it:
• I wasn’t able to use a good strategy to solve the problem.
• My strategy wasn’t related to what was asked.
• I didn’t apply what I know about math to solve the problem.
• I left the answer blank.
This was took directly from the website:
http://www.nsa.gov/teachers/es/data87.pdf
Lesson 1
Standard: Determine mean, median and range for quantitative data and from data
represented in a display. Use these quantities to draw conclusions about the data,
compare different data sets, and make predictions. Data Analysis & Probability 7.4.1.1
Lesson Plans: TV Watching
Overview: This is a lesson that starts with gathering data from the students on how much
TV they watch and what they watch. They need to record this daily for a week. Then
bring it in to the classroom. They will then interpret the data and graph it in different
ways to help with the interpreting.
Goals: Make an appropriate graph for discrete data
Describe the characteristics of the graph
Use the shape of the graph to draw conclusions about the data.
Materials: Paper
Pencils
Graph Paper
Motivation: At the start of the lesson each of the students would make a prediction on
which T.V. show they think that there classmates watch the most. Pose the question we
want to find out what day this class watches the most TV and how much TV do you
watch. They would need to then answer what T.V. show do they watch the most? How
often do they watch TV on Monday, Tuesday, Wednesday, Thursday, Friday, Saturday,
Sunday? By having them answering questions that are about themselves they are more
likely to become involved.
Procedure: After the students have written down the data on their own, it is time to
collect the data as a class. Starting with Monday write down everyone’s number for the
amount of time that they watch TV on that particular day. Then continue collecting for
the other 6 days. The data will look similar to this.
Monday: 2,3,4,4,3,2,6,8,2,3,1,3,4,5,6,4,2,4,3,2,4,5,7,3,1,2,3,2,1,3,4,4
Tuesday: 0,0,0,1,3,4,6,7,6,4,5,4,3,3,2,0,3,0,1,2,4,0,2,3,0,3,2,1,0,1,2,0
Wednesday: 1,3,3,4,5,6,7,9,8,0,3,4,5,3,6,3,2,1,2,3,4,4,5,5,7,8,7,8,0,0,0
Thursday:1,2,3,2,1,2,3,4,5,0,0,0,0,0,0,0,0,4,5,4,3,2,1,2,3,4,1,0,1,2,3,4,5,
Friday: 1,2,3,4,0,8,5,3,4,5,6,7,8,9,1,2,3,0,1,2,3,4,0,1,2,0,3,2,3,6,1,2,2,0
Saturday: 0,8,3,2,4,5,1,2,3,4,5,0,8,7,9,6,4,3,2,2,1,2,3,4,6,8,9,5,3,0,1,2,0
Sunday: 2,4,3,6,0,9,8,1,1,2,3,1,2,3,4,5,3,2,2,1,1,3,3,4,3,2,2,4,5,4,5,3,3
Ask the students to find the number that occurs the most often in the data from Monday.
Give them 3-5 seconds.
Ask them to find the middle number of the data on Monday. Give them 10 seconds.
Ask them to find the range of the data on Monday, give them 10 seconds.
Create a discussion on if it is easy or hard to find the mode, median, and range of the
numbers with how the data is set up.
Show how you set up a stem and leaf plot as a class for the data on Monday. Practice then
with the data from Tuesday. When those two are complete go over median, mode, range
again.
Then work on the mean.
Have them put the rest of the data in stem and leaf plots then find the mean, median,
mode, and range.
Sharing: This is a discussion time that is created by the teacher with questions about the
data. Such as: What day does this class on the average watch the most TV?
What day is there the biggest range in the amount of hours that TV is
being watched?
Why do some of the data sets have 0’s in them and others have higher
numbers? What causes that change in these numbers?
Resource: Navigating through Data Analysis in Grades 6-8
National Council of Teachers of Mathematics
Lesson 2
Continued Lesson from Day 1:
Standard: Determine mean, median and range for quantitative data and from data represented in
a display. Use these quantities to draw conclusions about the data, compare different data sets,
and make predictions. Data Analysis & Probability 7.4.1.1
Lesson Plans: TV Watching
Overview: This is a lesson that starts with gathering data from the students on how much TV
they watch and what they watch. They will then interpret the data and graph it in different ways
to help with the interpreting.
Goals: Make an appropriate graph for discrete data
Describe the characteristics of the graph
Use the shape of the graph to draw conclusions about the data.
Materials: Paper
Pencils
Graph Paper
Data from TV watching
Procedure: Ask the students for the mode on Wednesday’s data. Why is that the mode?
What is the mode for Friday’s data?
Is there a reason that the mode is not the same on Wednesday and Friday’s?
Is there any modes that are the same?
Next show the students how to make a Line Plot for Tuesday’s data. As a class work on
Wednesday’s data then let them make a Line Plot for the rest of the 5 days.
Have the students find the median, range, mode for the Thursday’s data. Is it the same as when
we used the stem and leaf plot? Why is it or is it not the same?
Have the students separate the data into boys and girls.
Share:
Have a vote which graph is easier to use? Make it a debate.
Is one better then the other?
Which one is easier to find the mean? Explain why?
Extension: Separate the data into boys and girls. Have the girls make a new stem and leaf plot or
line plot, they can choose then use the data that is just from the girls. Split them into groups have
each group do one day. The same happens with the boys. Compare this data. Make predictions.
You could also separate the date into the month that they were born, is there anything interesting
there?
Resource: Navigating through Data Analysis in Grades 6-8
National Council of Teachers of Mathematics
Lesson 3
Standard: Create and analyze double-bar graphs and line graphs by applying
understanding of whole numbers, fractions and decimals. Know how to create
spreadsheet tables and graphs to display data. 5.4.1.2
Lesson Plans: Traveling Through Line Plots
Overview: The students will use their knowledge of graphs and central tendencies to
explore and extend their understanding of line plots, range, median, mode, and mean. In
order to help their local shoe factory, they will generate a graph of shoe sizes and decide
what the most popular size is using the appropriate central tendency of 15 to 18 year olds.
This is an overview of all three lessons.
Duration/Length: Three 60-minute lessons
Goals: • Students will interpret and analyze data in a line plot
• Students will compose and create a line plot using data collected in class
• Students will apply knowledge of range, median, mode, and mean in order to
analyze the data present in the line plot
Materials and Resources:
Chart Paper
Math Journals
Highlighters
Markers
Ruler/Meter Stick
Student Resource Sheets
Teacher Resource Sheets
Scissors
Glue
Procedures:
Preassessment – Given a bar graph (SR1) students will label the important features of the
graph and their purpose.
Motivation: Reintroduce examples of simple graphs such as bar and pictograph. Display
both types of graphs on the overhead and discuss their elements (titles, labels,
key, scale, axis) and purposes (display and organize specific data). See Teacher
Resource 1. Show the class a line plot and allow the students to compare its
elements to the other two types of graphs.
Teacher Facilitation – Distribute definition list to students (SR2) and an example of a line
plot (SR3). Review with students and label vocabulary on the graph. Ask
questions to focus the students on the parts of the graph (What is the title? What
does the graph tell us? What does the number line represent? What does each “x”
represent? How many people responded to this data collection? etc.) As students
answer the questions they will highlight the appropriate element of the graph and
label it with the vocabulary term. Students will then glue the sheets into their
math journals. Survey the class to find out the class makeup. Use tally chart to
record data.
Student Application – Students will receive an outline of a line plot (SR4). They will be
responsible for imputing the classroom survey data correctly using their outline
and definition sheet.
Experimental Design – After students complete the line plot they will interpret the data in
their math journal. Example of criteria would be: explanation and purpose of title,
label, and scale choices. Students will also explain why this was the appropriate
graph choice for the given data set.
Reteaching/Extension –
• Reteach- Student will be given a blank line plot (SR4) and a sheet with
elements of a line plot. Student will be asked to match the appropriate
elements to its place on the line plot based on the given data set (SR 5) that
the student will cut apart and paste on SR 4. Students will then cut and paste
the definitions onto the line plot (SR2) beside the appropriate element. SR 3
works as the answer key
Extend- Students will be given a data set (SR6) in paragraph form and will be
asked to display the data on a line plot using SR4. Answers may be found on
TR2.
1. paragraph form and will be asked to display the data on a line plot
using SR4. Answers may be found on TR2.
.
Resource: This was taken directly from the website:
http://www.nsa.gov/teachers/es/data87.pdf
Overview for lesson 1: Lesson- The purpose is to tell anyone looking at the graph what
the graph is about. This label tells what is found on the y-axis and that the units on this
graph measure the number of student responses. Mention scale if students do not. This
bar shows the student response for the type of pet that they like. These labels show the
different responses children can have to the questions. This label tells us about the type of
information found on the x-axis.
Ms. Hansen’s Class’ Family Tree
X
XXX
XXX
X XXXX
XXXXXX
XXXXXXX
X
XXXXXXX
X
---------------------------------------------------------------------2 3 4 5 6 7 8 9 10 11
Number of People in our Families
Resource: This was taken directly from the website:
http://www.nsa.gov/teachers/es/data87.pdf
Lesson 4
Standard: Determine mean, median and range for quantitative data and from data
represented in a display. Use these quantities to draw conclusions about the data,
compare different data sets, and make predictions. Data Analysis & Probability 7.4.1.1
Lesson : Mean, Median, Mode, Range
Overview: Students are looking at Sports teams scores to find the mean, median, mode,
and range.
Goals: Students will feel comfortable with mean, median, mode, and range.
Materials: Calculator
Paper
Pencil
Journals
Preassessment- Students will arrange a set of data (31, 22, 15, 20, 15) in order from least
to greatest. Posted the data on the board. Students will discuss the terms range,
median, mode, and mean and see if they can relate them to every day life. At this
point students will not have the definitions.
Launch- The class will talk about a major sports event that has taken place recently or
will. Then use this to talk about the stats.
Teacher Facilitation – Using the data from (SR6), explain range, median, mode, and
mean, define the terms, and show how to solve for each. Give visual clues for
students to use.
Student Application- In pairs, students will analyze the data and solve for range, median,
mode, and mean using SR7.
Experimental Design- Students will solve for the mean, median, mode and range from
one set of data on SR 7 and explain their results in their math journals. Examples
of criteria should include: paragraph form explaining how data was analyzed and
interpreted (example: Scores for the DC United Soccer team were 12, 17, 17, and
15). Students will then explain how they found the range, median, mode, and
mean of that data and what that means for the stats of the team. Answers may be
found on TR3.
Reteaching: Students will review addition, subtraction, and division skills on the
chalkboard. Given a set of data and answers, students will identify range, median, mode,
and mean by matching the term to its correct answer (SR8).
Extension: Students will use the information from the line plot in lesson one to find the
range, median, mode, and mean.
DC United Soccer Scores
................................................................................
New England 15
Chicago 17
Chicago 12
Metro Stars 19
Dallas 17
Argentina’s Soccer............................................................................................
Racing Club 28 United States 9
Boca Juniors 36 France 6
San Lorenzo 26 Korea DPR 3
River Plate 40 Nigeria 0
Banfield 32 Brazil 7
Quilmes 39 Sweden 6
Los Angeles Soccer Scores..............................................................................
Kansas 16
San Jose 22
Kansas 24
Colorado 15
Columbus 17
Range, Median, Mode, and Mean Vocabulary
Range – difference between high and low numbers (-)
Median – the number that is the middle of data
when the data is arranged from smallest to largest.
Mode – the number that appears most MOST
Mean – found by adding all the values and dividing by + / ÷
the total number of value
DC United Soccer Scores
................................................................................
New England 15
Chicago 17
Chicago 12
Metro Stars 19
Dallas 17
Range
Median
Mode
Mean
7
17
17
16
Argentina’s Soccer............................................................................................
Racing Club 28
Boca Juniors 36
San Lorenzo 26
River Plate 40
Banfield
32
Range 14
Mode No Mode
Median 32
Mean 32
United States 9
France
6
Korea DPR 3
Nigeria
0
Brazil
7
Range 9
Median 6
Mode No Mode
Mean 5
Los Angeles Soccer Scores..............................................................................
Kansas 24
San Jose 22
Kansas 24
Colorado 15
Columbus 17
Range 9
Mode 24
Median 22
Mean 20
Grades for Mrs. Zoo’s Classroom
Zebras 15
Lions 18
Monkeys 13
Cougars 19
Seals 15
MODE 16
MEAN 15
MEDIAN 6
RANGE 15
Range, Median, Mode, and Mean Vocabulary
Range – difference between high and low numbers (-)
Median – the number that is the middle of data
when the data is arranged from smallest to largest.
Mode – the number that appears most MOST
Mean – found by adding all the values and dividing by + / ÷
the total number of values
Lesson 5
Standard: Determine mean, median and range for quantitative data and from data
represented in a display. Use these quantities to draw conclusions about the data,
compare different data sets, and make predictions. Data Analysis & Probability 7.4.1.1
Lesson: Mean, Median, Mode, Range
Overview: Students will have a review of measurement with pictures. They will then
use that to measure their own foot so that the class has new
data to put into a line plot in order to find the mean,
median, mode, and range.
Goals: Students will accurately measure to the nearest inch.
Students will use data to make a line plot
Students will calculate the mean, median, mode, and range.
Materials: Ruler
Paper
Pencil
Graph Paper
Preassessment- Students will review measurement by measuring different items using the
inches ruler (SR9). Answers may be found on TR5.
Launch- HaPla’s Shoes is trying to open a factory in Accokeek, MD. They are interested
in the 8-10 year old market. They would like our help in determining the correct
shoe size for this area. Discuss with the class what HaPla Shoes will need in order
to appropriately service our community. Discussion should include: create a line
plot of the specific grade levels’ shoe sizes, find the mean, median, range, and
mode of the sizes, write a letter to HaPla Shoes explaining our data
Teacher Facilitation- Go over the directions and answer any questions that the children
have as a review of the concepts taught in the previous lessons.
Student Application- Students will measure their left foot and complete the chart with the
class data in their journals that the teacher has written on the board (TR10).
Students will use the measurement data to make a line plot and give the range,
median, mode, and mean of the data set (SR11). Answers may be found on TR6.
Experimental Design - Students will write a letter to HaPla Shoes in their journals
explaining their data and what shoe sizes they think the company should make
based on the information they found.
Reteach- Work with students needing extra assistance in a small group to complete the
“Student Application and Embedded Assessment” to monitor progress and offer support
where needed.
Extension- Students will design a shoe and create a “sales pitch” and include both in their
letters to HaPla Shoes.
Directions- Use inch ruler to measure each picture. Write your answer on the line.
REMEMBER to label your answer.
Measure the entire width of the picture.
____________________________
_____________________________
Measure the entire width of the picture.
Measure the height of the dog.
____________________________
Student Left Foot
Measurement
James
Jeff
Mary
Rose
Fran
12 inches
13 inches
8 inches
5 inches
9 inches
EXAMPLE OF LEFT FOOT DATA
Help HaPla Shoes by creating a line plot and finding the mode, median, range, and mean
shoe sizes in your classroom.
Range: ___________________
Median: __________________
Mode: ___________________
Mean: ___________________
*Use for the example above
Key Points should be present. Information on chart will vary
depending on students in your class.
Range: ___________________
Median: __________________
Mode: ___________________
Mean: ___________________
*Use for your classroom data
Summative Assessment:
Students will answer seven selected response questions and one brief constructed
response question as an evaluation of line plots, range, median, mode and mean (Student
Resource 12). See Teacher Summative Assessment for answers (TR7).
Authors:
Alisha Monique Plater Christine R. Hansen
Henry G. Ferguson Elementary School Manassas Park Elementary School
Prince George’s County Manassas Park City Schools
Lesson 6
Standard: Describe a data set using data displays, such as box-and-whisker plots; describe and
compare data sets using summary statistics, including measures of center, location and spread.
Measures of center and location include mean, median, quartile and percentile. Measures of
spread include standard deviation, range and inter-quartile range. Know how to use calculators,
spreadsheets or other technology to display data and calculate summary statistics. 9.4.1.1
Lesson: Box and Whiskers Plot
Outcomes:
•
•
Students will construct and interpret box and whisker plots.
Students will interpret and analyze box and whisker plots.
Time required for lesson
90 Minutes
Materials/resources
•
•
•
•
•
•
•
heights of students in class in centimeters
index cards (write each student's height on a card)
construction paper
2 rolls of cash register tape
strip of bulletin board paper about one foot wide and 20 feet long
flags (2 of one color and 1 of another)
large open area (large classroom, gym, etc.)
Pre-activities
Students must understand how to find the median of a data set.
Teacher needs to construct flags (for example 2 red and 1 blue). I use rulers or drinking
straws and construction paper.
Activities
1. Explain that we are going to learn how to make an interesting graph with an
interesting name - a box and whisker plot. We are going to do this based on our
heights.
2. Distribute index cards with student's height to each student.
3. Instruct students to order themselves from shortest to tallest (shoulder to shoulder)
across the front of the room with students of the same height standing beside each
other.
4. Explain that we (the class) need to find the median student (the student in the
middle). Give this student the flag that is a different color from the other two. If
by chance you have an even number of students in your class, then review how to
find the median in this situation. These two students must hold the flag between
them.
5. At this point, explain to the students that we have divided the class into two
groups or halves - the short half and the tall half.
6. Explain that we are now going to find the quartiles of our data set. Discuss the
word quartile (For example: What does it sound like? A quarter? What is a
quarter? 25 cents? One fourth? What is the relationship between one fourth and
one half?) The quartiles of a data set are middle (half) of each half. Who is in the
middle of the short half? This person is the lower quartile. Give them a flag. Who
is in the middle of the tall half? This person is the upper quartile. Give them a flag
as well.
7. At this point, students of the same height need to stack themselves (stand behind
one another). All students but one may return to their seats.
8. Place pieces of construction paper on the floor for heights that are not represented
by individual students (for example: if you have a student who is 138 cm tall and
the next is student in 140 cm, then you need to place a piece of construction paper
on the floor to represent the height of 139 cm).
9. Explain that there are two other important data points/people in the making of our
graph - the endpoints - in this case the shortest person and the tallest person in our
class. These people are the lower and upper endpoints (respectively).
10. Explain that in a box and whisker plot the box runs from quartile to quartile.
Again, go over and ask - who are our quartiles? Unroll your strip of bulletin board
paper, beginning at the lower quartile and ending at the upper quartile. Students
should assist in holding the paper.
11. Have students locate the median student in relationship to the box. Discuss that
the median student should be in the box but not necessarily in the middle of the
box.
12. Now for the whiskers. Explain that the whiskers run from quartile to endpoint.
Unroll each roll of register tape so that it goes from lower quartile to lower
endpoint and upper quartile to upper endpoint. Students should assist in holding
paper.
13. Have all students except the endpoints, quartiles, and median return to their seats
so that they can see the box and whisker plot.
14. Review the process with students, answering any questions they have. Record the
steps on the board/overhead for reference.
15. Collect all materials and have all students return to their seats.
16. Explain how to make box and whisker plots on paper. Make a number line that
begins a bit before and extends a bit after your endpoints. For example, if your
endpoints are 131 and 182, I would have my number line range from 130 to 185
and use increments of five. The next step is to plot the five points (median,
quartiles, and endpoints) on the number line, approximating when needed. Then,
draw the box (quartile to quartile) and draw a line through the median. Last, draw
in the whiskers (quartile to endpoint).
Assessment (see below)
In an effort to teach students how to analyze and interpret box and whisker plots, display
one on the overhead. Explain to students that 25% of data is held between the lower
endpoint and the lower quartile and 25% between the upper endpoint and upper quartile.
This leaves 50% of the data to be held within the box. Ask students if they can determine
what percent of the data would be held from the lower quartile to the upper endpoint?
(75%) The other type of question students should be able to answer from a graph of this
type requires them to know how many items there are in the data set. For example, you
give students a box and whisker plot and tell them that it represents the prices of twenty
pair of running shoes. If the median price was $70, then you ask the students what
percent of the running shoes cost $70 or more? (one half of twenty is 10) If the lower
quartile is $55, what percent of the shoes cost $55 or more? (three fourths of twenty is
15)
Assessment
In order to assess student's comprehension of the activity, give them a similar data set (I
use my other class's heights) and have them go through the process on paper. They
should identify the median, upper and lower quartiles, and upper and lower endpoints,
then draw the graph on a number line.
Supplemental information
None.
Related websites
The Box Plot - an interactive online illustration of creating a box plot
http://www.learner.org/channel/courses/learningmath/data/session4/part_d/drawing.html
Comments
I have a large classroom, so this activity works fine for me. If you have a large class but a
not so large classroom you might think about doing this activity in a larger space, such as
the gym or outside.
I have found that students have some difficulty actually making the box and whisker plot
on the number line.
North Carolina Curriculum Alignment
Hypothesis:
Null: Students can’t understand how to interpret a box and whiskers plot.
Alternative: Students can interpret a box and whiskers plot.
Resource:
http://www.learnnc.org/lessons/NikkiHoneycutt5232002643
Lesson 7
Standard: Describe a data set using data displays, such as box-and-whisker plots;
describe and compare data sets using summary statistics, including measures of center,
location and spread. Measures of center and location include mean, median, quartile and
percentile. Measures of spread include standard deviation, range and inter-quartile range.
Know how to use calculators, spreadsheets or other technology to display data and
calculate summary statistics. 9.4.1.1
Lessons: Alphabet Soup
In this lesson, students construct box-and-whisker plots. Students use the box-andwhisker plots to identify the mean, mode, median, and range of the data set.
Representation is the major focus of this lesson.
Learning Objectives
Students will:
ƒ construct and read box-and-whisker plots
ƒ identify the mean, median, mode, and range for a given set of data
Materials
Crayons
Looseleaf or Copy Paper
Index cards
Yarn
Dried pasta in the shape of alphabet
letters
Calculators
Glue
Class Notes Recording Sheet
Instructional Plan
Give each student a small handful of pasta letters of the type used in alphabet soup. Ask
the students to sort the letters, write their first and last names using the letters, and then
glue the alphabet letters found in their name onto an index card. [Optional opening: Ask
the students to write their first and last names on an index card, then count the number of
letters altogether.] Have the students write the total on the other side of the card. [In this
lesson, the students will learn about a different way to graph data, the box-and-whisker
plot (or box plot). This graph clearly displays the endpoints, range, and median of
quantitative data. Its construction begins with ordering the data.]
Now help the students form a line in which they order themselves from greatest to least
according to the number on their index card. [If more than one student has the same
number, the students should stand side by side.] Ask them to face front. Now give the
student with the smallest number a card on which you have written "Minimum." Now
give the student with the highest number a card on which you have written "Maximum."
Ask the students to find the range of the data. [To find the range, subtract the minimum
from the maximum.] Record the range on the board.
Next, have the students determine whether any value occurs more times than all others.
Identify that value as the mode, and record it on the board.
Next, ask the students at the two ends of the line to say "one" at the same time, then the
students next to them to say "two." Continue counting off in this fashion until the middle
of the line is reached. [If there is an odd number of students, one student will be at the
middle; if there is an even number, two students will be there. If there is one student, the
number he or she holds is the median. If there are two students, the arithmetic average of
their numbers is the median. If this happens, you may need to work out the problem on
the board.] Ask the students what this "middle" number is called. Write the median on the
board under the mean, and label it. Provide the student(s) who represent the median with
a card on which you have written "Median." Tell the students that the halfway mark is
called the 50th percentile, just as a half-dollar represents 50 cents.
Now have the students on either side of the median find the median of just their side.
Provide a card that says "75th Percentile" to the center student on the higher end and a
card that says "25th Percentile" to the center student on the lower end. [As this
terminology may be new to students, you may wish to explain that the 25th percentile is
that point greater than 25 percent of the score. In the money analogy, it is like a quarter.
Similarly, the 75th percentile is the point greater than 75 percent of the scores, and, in the
money analogy, is like 75 cents.]
Give the student at the 75th percentile place one end of a long piece of yarn to hold in his
or her right hand. Then, holding the yarn, walk to the student who holds the 25th
percentile card and place yarn in his or her right hand. Walk in front of that student and
place the yarn in his or her left hand as well. Then, carrying the yarn, walk back to the
student holding the 75th percentile card and put the other end of the yarn in his or her left
hand to complete the loop. Now have those students hold out their arms, so that a yarn
"box" is formed. Explain that they have made a human box-and-whisker plot.
Allow students, a few at a time, to leave the line and stand where they can see the box.
Call on a volunteer to draw the figure on the board. Then collect the yarn and the cards
and ask the students to take their seats and copy the plot, naming the high and low scores
and the median. Encourage them to use color to show the various parts of the plot.
Now tell the students to use their calculators to find the mean. When they have found it,
enter the mean under the median on the board. Now ask them how they could find the
mode. When they have suggested a way and found the mode, have them add it to the list
of measures of center. Identify these statistics as measures of center or central tendency.
[The mode, which cannot be determined from a box plot, is the data point that occurs
most often. The mean is the arithmetic average. The median is the halfway point in the
ordered data, one-half the observations are above it and one-half are below it. These three
statistics are called measures of central tendency or averages.] Ask the students what they
notice about the averages and which one best describes the "average" length of names in
the class. [The averages are probably not the same. The median is the best average in this
case.]
Go to the National Library of Virtual Manipulitives Box Plot. Call on one or more
students to collect the index cards and enter the data on the Web site. When it is entered,
generate the box plot. You may wish to line the index cards up on the board tray so the
data is visible to all the students. If you do so, you could indicate the low and high values,
the median, the mean, and the mode with the labeled index cards used in the human boxand-whisker plot.
If time allows, ask the students how the box-and-whisker plot would change if the length
of the teacher's name were included in the data set. Finally, ask the students to add the
measures of central tendency to their copy of the box plot so they can have a record for
their files.
Questions for Students
What type of graph did we make today?
[Box-and-whisker plot, or box plot]
What length of name was most common in our class? What name is given to this
measure of central tendency?
[The name will depend upon the data collected. This measure of central tendency is
known as the mode.]
What was the shortest name in the class? The longest? How did we show these values
on the box plot? What was the difference between these numbers? What do we call that
difference?
[These will depend upon the data collected. The range is what we call that difference.]
What were the mean and median of the data set? What does each term mean? How did
we find the mean? The median?
[The mean and median will depend upon the data collected. To find the mean, add up all
of the data, and divide by the number of people (in this case.) To find the median, order
all of the data from least to greatest, and find the middle number. (If there are two
"middle" numbers, find the average of those two numbers to find the median.)]
Suppose a new student named Michael Burton came into the class. How would that
change the plot that we made? (Repeat with other scenarios.)
[The answer will depend upon the data collected.]
Suppose (student name) moved away. How would that change the graph we made?
(Repeat with other scenarios.)
[The answer will depend upon the data collected.]
How many students in the class had names longer than the name at the 75th percentile?
How many students had names shorter than the length of the name at the 25th
percentile?
[The answers will depend upon the data collected.]
Suppose the median is like a half-dollar. What amount is the 25th percentile like? What
does 25th percentile mean?
[25 cents or a quarter; 25 percent of the class is accounted for when we get to this piece
of data.]
How were these two points shown on the plot?
[They form the ends of the box.]
Assessment Options
1. At this stage of the unit, it is important to know whether students can do the
following:
ƒ Construct and read a box-and-whisker plot
ƒ Identify the mean, median, mode, and range in a set of data
2. Ask students, "Is your food diary chart up-to-date?"
Extensions
1. Students may also wish to use the NCTM Box Plotter to create their box-andwhisker plots. Compare these box-and-whisker plots to those created using the
other tool.
Box Plotter
Teacher Reflection
ƒ
ƒ
ƒ
ƒ
Which students were able to copy the box-and-whisker plot with minimum
supervision?
Which students easily found the range and mode? The median? The mean?
Which students could compare the measures of central tendency with
understanding?
How can I extend this instructional experience? What will I do differently the
next time that I teach this lesson?
Lesson 8
Lesson: State Names
Overview: Using multiple representations, student analyze the frequency of letters that
occur in the names of all 50 states.
Objectives: Students will determine the number of times that each letter of the alphabet is
used when writing the names of all 50 states.
Students will understand how various representations, including steam-and-leaf plots,
box-and-whisker plots, and histograms, can be used to organize the data
Materials
Map of the United States (optional)
State Names Activity Sheet
Procedure: Say to students, "Spell the names of all 50 states." Before they get too far in
writing all the state names, ask the following questions as an introduction to this lesson:
ƒ Which letter will you use most? Which letter will you use least?
ƒ Will you use every letter of the alphabet? Are there any letters that you will not
use at all?
ƒ Which state name has the most letters?
Allow students to speculate answers to each of these questions, and have them justify
their guesses.
Display the names of all 50 states. (You can display the names as an alphabetical list, or
you can simply display a map of the United States that shows the state names.) Ask,
"Could you answer those questions just by looking at all of the names like this?" The
point in asking this question is to make students realize that the data needs to be
organized in a better way.
Then, have students use the State Names activity sheet to identify the frequency of each
letter.
Questions for Students
Is it possible to determine which letter is used most in the names of all 50 states just by
looking at a list of names? What is a better way to determine what letter is used most?
[Count the number of times each letter is used, and organize the data in a table or
graph.]
What are some of the advantages of using bar graphs, stem-and-leaf plots, and boxand-whisker graphs?
[Bar graphs show the relative amounts of items in the data. Just by looking at the
heights of the bars, you can easily determine which items are more common. A stemand-leaf plot allows you to easily determine where most of the data occurs—at the
upper end, the lower end, or in the middle. A box-and-whisker plot allows you to easily
see how the data is divided.]
Assessment Options
Have students write a paragraph in their math journals about the advantage of
organizing data in bar graphs, stem-and-leaf plots, and box-and-whisker plots, as
opposed to interpreting raw data. In addition, have them compare bar graphs, stem-andleaf plots, and box-and-whisker plots, and indicate which representation is most useful.
Allow students to use the number of letters in the state names, state postal codes, or
other sets of data to create various representations. (Using the data for the number of
letters in each state name will allow students to answer the question, "What state
requires the most letters to spell?", which was asked during the lesson but could not be
answered using the letter frequency data.)
Extensions
1. Allow students to do a frequency analysis by including the Canadian provinces
or the Mexican states when collecting data, or repeat the activity for these other
countries in North America.
2. Students can use the State Data Map to investigate other data about states. In
addition to considering the number of letters in state names, students can also
explore population, number of senators, gasoline usage, and other data sets.
State Data Map
Teacher Reflection
ƒ
ƒ
ƒ
ƒ
How did technology help or hinder student learning?
Did students attain the objectives for this lesson? That is, did students
understand that various representations can be used to organize data?
Were students enthusiastic about this lesson? If so, what contributed to their
enthusiasm? If not, what can be done to get them more enthused the next time
this lesson is taught?
Was it necessary to adjust the lesson plan while teaching? Why were
adjustments necessary?
Resource:
http://illuminations.nctm.org/LessonDetail.aspx?ID=L579
Post Test
Name: _________________________________
Date:___________________________________
Line Plots/Range, Median, Mode, and Mean, Box and Whiskers Plot
Directions: Use the set of data to answer numbers 1-4. Circle the appropriate answer
choice.
Alyssa's basketball team scored the following number of points during the playoff games:
102, 98, 60, 110, and 50
1. What is the team's mean score?
A. 84
B. 60
C. 98
D. 110
2. What is the range of the team’s scores?
A. 10
B. 60
C. 50
D. 40
3. What is the median of the team’s scores?
B. 98
C. 110
D. 50
E. 102
4. What is the mode of the team’s scores?
A. 98
B. 84
C. no mode
D. 60
Directions: Use the Line Plot to answer numbers 5-7. Circle the appropriate answer
choice.
5. How many students were surveyed?
A. 11
B. 29
C. 32
D. 28
6. What is the mode of the data?
A. 9
B. 7
C. 11
D. 4 and 5
7. How many students have an even number of family members?
A. 17
B. 29
C. 2
D. 5
Mrs. Plater’s Class’ Family Tree
X
X
X
X
X
X
X
X
X
X
X
X
X
X
2
3
4
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
5
6
7
X
X
8
9
10
11
Number of People in our Families
Brief Constructed Response
Mr. Dale’s class took a spelling test on Friday. Their scores
were 65, 82, 95, 100, 77, 82, and 90. Find the range,
median, mode, and mean of the scores.
Part A
Question?
Range: ________________ Mode: ________________
Median: _______________ Mean: ________________
Part B
Use what you know about range, median, mode, and mean to
explain why your answer is correct. Use number and/or words
in your explanation.
Part C
In Mr. Smith’s class last Friday they had several contests in
there room to celebrate the 100th day of school. The last contest
of the day was to see how many marshmallows each student could
fit into their mouth. The students mouth had to be completely
closed (meaning their lips had to touch). Here are the results:
5,7,6,8,9,11,15,12,14,20,6,7,8,9,3,4,5,6,7,10,12
Create a box and whisker plot.
Median_________ Q1_________ Q3__________ Outliers________
TEACHER Summative Assessment
Name: _________________________________
Date:___________________________________
Line Plots/Range, Median, Mode, and Mean Quiz
Directions: Use the set of data to answer numbers 1-4. Circle the appropriate
answer choice.
Alyssa's basketball team scored the following number of points during the
playoff games:
102, 98, 60, 110, and 50
1. What is the team's mean score?
A. 84
B. 60
C. 98
D. 110
2. What is the range of the team’s scores?
A. 10
B. 60
C. 50
D. 40
3. What is the median of the team’s scores?
A. 98
B. 110
C. 50
D. 102
4. What is the mode of the team’s scores?
A. 98
B. 84
C. no mode
D. 60
5. How many students were surveyed?
A. 11
B. 29
C. 32
D. 28
6. What is the mode of the data?
A. 9
B. 7
C. 11
D. 4 and 5
7. How many students have an even number of family members?
A. 17
B. 29
C. 2
D. 5
Brief Constructed Response
Mr. Dale’s class took a spelling test on Friday. Their scores
were 65, 82, 95, 100, 77, 82, and 90. Find the range,
median, mode, and mean of the scores.
Part A
Question?
Range: 35
Median: 82
Mode: 82
Mean: 84
Part B
Use what you know about range, median, mode, and mean to
explain why your answer is correct. Use number and/or words
in your explanation.
Answers will vary.
Part C
In Mr. Smith’s class last Friday they had several contests in
there room to celebrate the 100th day of school. The last contest
of the day was to see how many marshmallows each student could
fit into their mouth. The students mouth had to be completely
closed (meaning their lips had to touch). Here are the results:
5,7,6,8,9,11,15,12,14,20,6,7,8,9,3,4,5,6,7,10,12
Create a box and whisker plot.
Check students plot
Median 8
Q1
6
Q3 11.5
Outliers 20
Instructional Changes
Lesson Plans
We both work in Native American Schools and have found that the students get
easily discouraged with the “normal lesson from the text book”. With these lessons there
are lots of activities that can be done in group work. Most of the activities relate either to
families, names, sports, or interests in their lives. This is critical in the Native American
population, it creates a sense of ownership and togetherness. Their culture and families
are the most important aspects in their lives and when we can tie them into education it is
very beneficial and meaningful.
The attempts of change are that the students will become more involved and
complete the lesson. The improvement would be that they will understand and feel
comfortable finding the mean, median, mode, range, making and interpreting line plots
and box and whisker plots.
At the end of this unit, we would like for the students to be able to use this
information on other sets of data. The prior knowledge that they will have gained, will
help them to be able to interpret different sets of data.
The hypotheses for this lesson is:
Null: Students test scores will not change.
Alternative: Students test scores will change.
Experimental Design: Is going to be collected in many different ways. In one of the
lessons we will use observations from the discussions at the beginning of our lesson
compared to discussions that we are having at the end of the lesson. Others they are
journaling about what they have learned and the process of finding the mean, median,
mode, and range.
Data Analysis:
We will use a box and whisker plot with our test scores. We will compare the
students scores with their pre and post tests. We will also compare classrooms and look
at the gains that the students have made. If there is not a significant amount of gain, then
we will discuss ways of improvement.
Statisical Results
Interpretation in the appropriate context.
Action and dissemination.