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DATA ANALYSIS
6th – 8th Grade Unit
Maureen Wilke
Heritage Middle School
[email protected]
Angela Schultz
Crosslake Community School
[email protected]
Elaine Erickson
Red Lake Middle School
[email protected]
Overview:
Data analysis is the process of organizing and examining collected data using charts,
graphs, or tables.
Data analysis is a unit that will take approximately three weeks to teach. We will start out
with a pretest to determine the prior knowledge that the students possess. We will instruct
and inform students how to create and analyze stem-and-leaf plots, histograms, box-andwhisker plots, scatter plots, and circle graphs. We believe by teaching data analysis as a
unit it will help students better understand the connection between data and presenting
data in a way that allows you to analyze and interpret the given data.
The majority of the lessons will span two to three days to help students deepen their
understanding on how to interpret graphs. It is our hope that with the amount of time we
will be spending on our entire unit students will be able to analyze and interpret all kinds
of graphs.
Contents:
Pretest For Data Analysis Unit……………………………………….Pages 3-6
Histograms: Hours of TV Watching in One Week (Lessons 1-4)……Pages 7-9
Box and Whisker Plots (Lessons 1-4)………………………………...Pages 10-15
Scatter Plots (Lessons 1-4)……………………………………………Pages 16-26
Circle Graphs………………………………………………………….Pages 27-28
Posttest For Data Analysis Unit……………………………………….Pages 29-32
Assess Instructional Changes………………………………………….Page 33
2
Pretest For Data Analysis Unit
Name_____________________
Hour____Date_____________
Create a stem-and-leaf plot from the chart below:
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21
21
20
25
Ages of the top 20 solo pop artist in 1997
33
28
22
19
14
27
21
26
32
31
25
26
26
13
Find the following information:
Minimum:
Maximum:
Range:
Median:
Mean:
Mode:
What average best represents the data of the stem-and-leaf plot? Explain.
3
A group of students has been investigating information about their pets. Several students
have cats. They decided to collect some information about each of the cats. One set of
data they collected was the lengths of the cats measured from the tip of the nose to the tip
of the tail. Here is a bar graph showing the information they found:
Length of cats
5
Frequency of lengths
4
3
2
1
0
16
25
27
28
29
30
31
32
33
35
36
37
length in inches
How many cats measured 30 inches long from nose to tail? How do you know?
How many cats were measured in all? How do you know?
If you added the lengths of the three shortest cats, what would the total of those lengths
be?
What is the typical length of a cat from nose to tail? Explain.
If we measured another cat, how long do you think it would be? Explain.
4
The table below shows history test scores for two classes. The same data are used in the
box-and-whisker plots below. Use the table to construct a box-and-whisker plot.
History Test Scores
66
54
68
86
100
59
59
68
85
Class A
100
90
72
64
59
100
100
84
100
78
76
87
45
78
76
76
90
45
Class B
64
77
93
47
80
76
76
100
83
_________________________________________________________
45 50 55 60 65 70 75 80 85 90 95 100
Lower extreme
Upper extreme
Lower quartile
Median
Upper quartile
In your opinion which class did better on the test? Explain.
Explain the similarities of the plots.
Explain the differences of the plots?
5
Make a scatter plot of the data below. Put high temperature on the horizontal axis.
High
Temperature
Cups of
cocoa sold
77
72
75
70
71
68
69
65
64
60
55
58
54
51
6
6
4
7
5
9
11
14
15
18
25
21
28
31
If it makes sense, draw a fitted line.
When the temperature decreases, what happens to the cups of cocoa sold? Explain.
When the temperature increases, what happens to the cups of cocoa sold? Explain.
Suppose one pot makes 10 cups of cocoa. How many pots should the owner make when
the high temperature is 50°? 40°?
Below is a circle graph of students who participate in school activities
Number of students
Other
15%
Discussion
Group
40%
School Clubs
25%
School
calendar
20%
What is the percent of students who participated in group discussion?
What is the percent of students who participated in school clubs and school calendar?
What do you notice about the percents from discussion groups to other?
6
Histograms: Hours of TV Watching in One Week-Day One
Cited from: Navigating through Data Analysis in Grades 6-8; pages 23-25, 85.
NCTM standard: DATA ANALYSIS and PROBABILITY
In grades 6-8 all students shouldFormulate questions that can be addressed with data and collect, organize, and
display relevant data to answer them
•
•
Formulate questions, design studies, and collect data about a characteristic shared
by two populations or different characteristics within one population;
Select, create, and use appropriate graphical representations of data, including
histograms, box plots, and scatter plots.
Activity: "Hours of TV Watching in One Week"
Objective: Students will be able to construct a Histogram from given data to display
relevant data to answer questions on handout, "TV WATCHING".
Materials:
• A copy of the black line master "TV Watching" for each student or group of
students (page 85).
• Half-centimeter grid paper for each student or group of students (copy on CDRom)
Launch: Introduce the activity by asking, "Do you think middle-school students watch
too much TV? Some students may claim that they don't watch too much but that other
students do. Some students may ask what is meant by too much. Predict how much TV
you watch in a week. Let's see how many hours this group of 49 seventh graders
watched.
Explore: Introduce and distribute "TV Watching", and grid paper. Have the students
complete lesson in groups.
Share: Have groups display their graphs on board. Ask how close they were to their
predictions.
Summarize: Discuss choices for graphs, and what their conclusions are. Construct the
bar graph on page 24 on the board and discuss.
7
Histograms: Hours of TV Watching in One Week-Day Two
Cited from: Navigating through Data Analysis in Grades 6-8; pages23-25, 85.
NCTM standard: DATA ANALYSIS and PROBABILITY
In grades 6-8 all students shouldFormulate questions that can be addressed with data and collect, organize, and display
relevant data to answer them
•
•
Formulate questions, design studies, and collect data about a characteristic
shared by two populations or different characteristics within one population;
Select, create, and use appropriate graphical representations of data, including
histograms, box plots, and scatter plots.
Activity: "Hours of TV Watching in One Week"
Objective: Compute and graph how much time our class watches TV in one week.
Materials:
• A pad of 3-M Sticky notes, enough for each student
• Half-centimeter grid paper for each student
Launch: Have students predict how many hours that our class watches TV in one week.
Record on board. First we are going to find out how much TV we actually do watch in
one week. Suggest they compute the time watched each day of the week and add them
up for their total.
Explore: Have them come up to the board, hand them a sticky note and have students
place their sticky notes on the appropriate place on a histogram you have on the board.
Then, give each student grid paper and have him or her make a histogram using the class
data from the board.
Share: Have groups share histograms and at least two conclusions they noticed. Ask
how close they were to their predictions.
Summarize: Discussion notes (pg. 25). Discuss what they noticed (about the number of
the hours they watch, the number of hours their parents would approve of, how too much
TV can interfere with other kinds of activities, (e.g., studying, exercise, sleep).
8
Histograms: Hours of TV Watching in One Week-Day Three and Four
Cited from: Navigating through Data Analysis in Grades 6-8; pages23-25, 85.
NCTM standard: DATA ANALYSIS and PROBABILITY
In grades 6-8 all students shouldFormulate questions that can be addressed with data and collect, organize, and display
relevant data to answer them
•
•
Formulate questions, design studies, and collect data about a characteristic
shared by two populations or different characteristics within one population;
Select, create, and use appropriate graphical representations of data, including
histograms, box plots, and scatter plots.
Activity: "Hours of TV Watching in One Week"
Objective: Design study (survey) and collect data from another population and graph
who watches more TV, between our Seventh grade class and a Sixth grade class.
PRE-PREP: Check with sixth grade teacher beforehand.
Materials:
• Paper for Student Designed Survey for sixth graders. (How much time they
watch TV/week.)
• Half-centimeter grid paper for each student or group of students (copy on CDRom
Launch: "Last chance for predictions! This time…who do you think watches more TV,
between the seventh grade and the sixth grade? How can we figure it out?"
Explore: Have them get in groups to design a survey, collect necessary data, construct
histogram on new data.
Share: Have each group share histograms and conclusions.
Summarize: Ask how their predictions went. Discuss conclusions and interpretations.
9
Box and Whisker Plots
Lesson 1: Collect Data
Standard
8
IV. DATA
ANALYSIS,
STATISTICS AND
PROBABILITY
A. Data and
Statistics
Represent data and use various
measures associated with data
to draw conclusions and
identify trends.
1. Construct and analyze histograms, circle graphs,
stem-and-leaf plots and box-and-whisker plots.
2. Compute the quartiles of a data set.
Objective
• Collect a variety of data to compare.
Materials
• Paper
• Pencil
• Notebook
• 5 Meter sticks/tape
• Access to other classrooms
Launch
• What type of numerical data can we collect from grades K-8? Example: height,
foot length, circumference of head ect.
• Is it important how accurate and consistent our measurements are?
• How do plan on recording the data in an organized manner?
Explore
• Create a record keeping sheet.
• Agree on a way to find the best measurement.
• Take measurements of all students in the classroom.
• Go to other classrooms and record their measurements.
Share
• Share what went right and what could be improved.
Summarize
• Making precise measurements is crucial when collecting data.
Assessment
• Describe your method of measurement.
10
Lesson 2: Organize Data
Standard
8
IV. DATA
ANALYSIS,
STATISTICS AND
PROBABILITY
A. Data and
Statistics
Represent data and use various
measures associated with data
to draw conclusions and
identify trends.
1. Construct and analyze histograms, circle graphs,
stem-and-leaf plots and box-and-whisker plots.
2. Compute the quartiles of a data set.
Objective
• Organize data using a stem and leaf plot
• Introduce statistical vocabulary (mode, median, min/max, range, upper and lower
quartile
Materials
• Paper
• Pencil
• Notebook
• Graph paper
• Post-it notes
• Data from lesson 1
Launch
• Activity: Write the last digit of the student’s height on a post-it note. Have them
come up to the board and place their post-it on the correct line. Rearrange in
numerical order.
Heights of Students
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14
15
16
17
:8 8 8 9
:1 2 7 7 7
:0 0 1 1 1 2 2 2 2 3 3 6 6 7 8
:1
Key: 14 : 7 means 147 cm
1. How many students are in the class?
2. How many students are 150cm tall? How can you tell?
3. What height occurs the most often (mode)? Explain your answer.
4. What is the shortest height (min/lower extreme)?
5. What is the tallest height (max/upper extreme)?
6. What height falls in the middle of al the data (median)?
7. What is the difference between the tallest and the shortest (range)?
8. What is the center height of the upper 50% (quartile 3/upper quartile)?
9. What is the center height of the lower 50% (quartile 1/lower quartile)?
10. What can you conclude from the data given?
Explore
• Students create a stem and leaf plot of the data they collected.
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Share
• Make conclusions based on your stem and leaf plot.
• Turn plot sideways to show it’s resemblance to a line plot
Summarize
• The purpose of a stem and leaf plot is to organize data.
• Mode: # that occurs the most often
• Median: # in the middle
• Range: difference of the max and min
• Upper Quartile: median of the upper 50%
• Lower Quartile: median of the lower 50%
Assessment
• Complete a stem and leaf plot based on collected data
• Find the mode, min/max, median, range, upper and lower quartile
12
Lesson 3: Create Box and Whisker Plots
Standard
8
IV. DATA
ANALYSIS,
STATISTICS AND
PROBABILITY
A. Data and
Statistics
Represent data and use various
measures associated with data
to draw conclusions and
identify trends.
1. Construct and analyze histograms, circle graphs,
stem-and-leaf plots and box-and-whisker plots.
2. Compute the quartiles of a data set.
Objective
• Construct an analyze a box plot
Materials
• 3 meter sticks
• 4 pieces of yarn
• Cards with data
• Graph paper
• Pencil
• Colored pencils
• Data lessons from lesson 1
Launch
• Have students hold their numbers and stand in numerical order side by side
across the front of the classroom to form a number line.
• Students with the same number line up behind each other.
• What is the range? Find the lower extreme and the upper extreme.
• Locate the center student(s) (median) and hand a meter stick to them. Repeat to
find the upper and lower quartiles.
• Use a piece of yarn to box in the middle 50%. Have students leave their numbers
in the box and step out to observe. They have now created the box portion of a
box and whisker plot.
• Use two more pieces of yarn to finish the construction. Extend one piece of yarn
from the upper extreme to the side of the box. This represents the upper 25% of
the data, a WHISKER.
• Repeat with the lower extreme. Students may now step around to observe the box
and whisker plot they have created.
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127
123
126 127 128
130
123 124
126 127 128
130
122 123 124 125 126 127 128 129 130
132 133 134 135
Explore
• Students construct a box and whisker plot on graph paper using their data.
Share
• The median of this group is ______.
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• Fifty percent of the students are less than _______.
• Fifty percent of the students are more than _______.
• The smallest data is ______.
• The largest data is ______.
Summarize
• Making a box and whisker plot creates a five-number summary of the data. This
helps to simplify the data for reasons of comparisons.
Assessment
• Complete a box and whisker plot
• Label the lower extreme/upper extreme, median, lower/upper quartile
Technology Extension
• Use graphing calculators and/or Tinker Plots to create box and whisker plots.
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Lesson 4: Compare Stacked Box and Whisker Plots
Standard
8
IV. DATA
ANALYSIS,
STATISTICS AND
PROBABILITY
A. Data and
Statistics
Represent data and use various
measures associated with data
to draw conclusions and
identify trends.
1. Construct and analyze histograms, circle graphs,
stem-and-leaf plots and box-and-whisker plots.
2. Compute the quartiles of a data set.
Objective
• “Stack” and compare two box and whisker plots on the same horizontal scale.
• Analyze differences or similarities in data.
Materials
• Data from Lesson 1
• Graph paper
• Colored pencils
Launch
• What will your horizontal scale need to be?
Explore
• Construct multiple box and whisker plots on the same horizontal scale.
• Where there any similarities in your data?
• Where there any differences in you data?
Share
• Present box and whisker plots to the class.
Summarize
• Box plots are useful for comparing data sets when the numbers of data are
different, especially if the numbers are very different.
Assessment
• Observe presentations and check for understanding.
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Scatter Plots Lesson 1
Minnesota Standards:
Interpret data
using scatter plots
Collect, display and interpret data using scatter plots. Use
and approximate
the shape of the scatter plot to informally estimate a line of best
Data Analysis lines of best fit.
8.4.1.1 fit and determine an equation for the line. Use appropriate titles,
& Probability Use lines of best
labels and units. Know how to use graphing technology to
fit to draw
display scatter plots and corresponding lines of best fit.
conclusions about
data.
Objective: Students will be able to collect data and display and interpret it using scatter
plot. (One to three days)
Materials:
• Meter sticks
• Rulers
• Graph paper
• Instructions for constructing a graph
• Transparencies of black lines
Launch:
Ask students if they have ever thought about if their foot size and height are related?
Today we are going to collect data and see if there is a relationship.
Explore:
1) Put students into groups of 4
2) Directions:
• Have students get materials
• Your group will measure each person’s foot and height.
• Keep track of your data on a piece of paper
• When you are finished with your data, go to the board and enter your data
in the two columns.
• While waiting for the class to finish, start constructing your graph
• When all groups finish recording their data on the board, instruct groups to
start plotting the data on their scatter plots.
Share:
1) Looking at the scatter plot, what can you tell about the heights? What is the tallest
height in this class? What is the shortest height? What is the range?
2) What information does the graph show about the foot size of the students?
3) Do the student’s heights seem to affect the size of a person’s foot size? Is this
what you expected? Were their exceptions? Explain.
4) Do the data plots seem to make a pattern? If so, explain.
5) Take your black line and see if you can put it through your pattern.
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6) Can you make future predictions on height and foot size using your black line?
7) What would be the foot size of a person whose height is 74 inches?
Summarize:
1) Scatter plots are used to find a relationship between two variables (foot size,
height). Can you name others?
2) The black line is a fitted line that helps you make predictions about future data in
your plot.
Assignment:
Review the terms
Scatter plot
Scale
Fitted line
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Constructing a Scatter Plot
1) Use the class data to help construct your scatter plot.
2) On graph paper, draw and label the horizontal and
vertical axes for your graph. Include the scale for each
axis.
3) Title your graph and each axis.
4) Plot the class’s foot size to height on your coordinate
grid. You should have one point for each member of
the class.
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Scatter Plots Lesson 2
Minnesota Standards:
Interpret data
using scatter plots
Collect, display and interpret data using scatter plots. Use
and approximate
the shape of the scatter plot to informally estimate a line of best
Data Analysis lines of best fit.
8.4.1.1 fit and determine an equation for the line. Use appropriate titles,
& Probability Use lines of best
labels and units. Know how to use graphing technology to
fit to draw
display scatter plots and corresponding lines of best fit.
conclusions about
data.
Objective: Students will be able to collect data and display and interpret it using scatter
plot. (One to two days)
Materials:
• Masking tape
• Tape measure
• Ruler
• Meter stick
• Graph paper
• Questions for assessment
Launch:
Yesterday we looked at the relationship between foot size and height. Did we find a
relationship? Today we are going to look at height to jump height. You should have your
height recordings from yesterday and you can use them today.
Explore:
1) Put students into groups of 4
2) Directions:
• Have students get materials
• Your group will measure each person’s jump height.
• Keep track of your data on a piece of paper
• When you are finished with your data, go to the board and enter your data
in the two columns.
• While waiting for the class to finish, start constructing your graph
• When all groups finish recording their data on the board, instruct groups to
start plotting the data on their scatter plots.
Share:
1) Looking at the scatter plot, what can you tell about the jump heights? What is the
tallest height in this class? What is the greatest height reached? What is the least
height reached? What is the range?
2) What information does the graph show about the heights of the students?
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3) Does the students’ heights seem to have an effect on high they could jump? Is this
what you expected? Were their exceptions? Explain.
4) Do the data plots seem to make a pattern? If so, explain.
5) Take your black line and see if you can put it through your pattern.
6) Can you make future predictions on height and jump height using your black line?
7) What would be the jump height of a person whose height is 74 inches?
Summarize:
1) Scatter plots are used to find a relationship between two variables (jump height,
height). Can you name others?
2) The black line is a fitted line that helps you make predictions about future data in
your plot.
3) A positive linear relationship is when the pattern of points increase to the right.
Assessment:
Have students turn in their graph and answers to the graph.
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Name_________________________
Hour_________________________
Questions for “Jump Height to Height”
Looking at the scatter plot, what can you tell about the jump heights? What is the tallest
height in this class? What is the greatest height reached? What is the least height
reached? What is the range?
What information does the graph show about the heights of the students?
Does the students’ heights seem to have an effect on high they could jump? Is this what
you expected? Were their exceptions? Explain.
Do the data plots seem to make a pattern? If so, explain.
Take your black line and see if you can put it through your pattern.
Can you make future predictions on height and jump height using your black line?
What would be the jump height of a person whose height is 74 inches?
21
Scatter Plots Lesson 3
Minnesota Standards:
Interpret data
using scatter plots
Collect, display and interpret data using scatter plots. Use the
and approximate
shape of the scatter plot to informally estimate a line of best fit
Data Analysis lines of best fit.
8.4.1.1 and determine an equation for the line. Use appropriate titles,
& Probability Use lines of best
labels and units. Know how to use graphing technology to
fit to draw
display scatter plots and corresponding lines of best fit.
conclusions about
data.
Objective: Represent bivariate data and determine the relationship between two
variables. (One day)
You can access the materials from Navigating Through Data Analysis Grades 6-8
Pages 73-75 & 100-102
Materials:
• Black line masters “Congress and Pizza” for each student
• Computer cart
• Transparency of black lines
Launch: Which two states do you expect to have the greatest number of pizza
restaurants? Why? Which two states do you would you expect to have the fewest pizza
restaurants? Why? Which two states would you expect to have the most U.S.
representatives? Why? Which two states would you expect to have the fewest U.S.
representatives? Why?
Explore:
1) Pass out black line masters
2) Have students go to excel and enter data from black line masters. Show them
how.
• Go to chart wizard and click on scatter plots.
• Highlight data and hit next
• Chart title: Congress and Pizza
• Value x: Pizza Restaurants
• Value y: US Representatives
• Next then Finish
Share:
1) Looking at the scatter plot, do you see a relationship between US representatives
and Pizza restaurants?
2) What is happening to the pattern of data plots?
3) What would we call this trend?
22
4) Using our black line, could we make a future prediction if there were 21 pizza
restaurants, how many US representatives would there be? (Click on scale to
change range)
Summarize:
Scatter plots are used to find a relationship between two variables (jump height, height).
Can you name others?
The black line is a fitted line that helps you make predictions about future data in your
plot.
A positive linear relationship is when the pattern of points increase to the right.
Assignment:
Reading a Scatter Plot (black line master pages 100-101)
23
Scatter Plots Lesson 4
Minnesota Standards:
Interpret data
using scatter plots
Collect, display and interpret data using scatter plots. Use the
and approximate
shape of the scatter plot to informally estimate a line of best fit
Data Analysis lines of best fit.
8.4.1.1 and determine an equation for the line. Use appropriate titles,
& Probability Use lines of best
labels and units. Know how to use graphing technology to
fit to draw
display scatter plots and corresponding lines of best fit.
conclusions about
data.
Objective: Explore negative linear relationship in data and make predictions. (One day)
You can access the materials from Navigating Through Data Analysis Grades 6-8
Pages 79-80 & 107
Materials:
• Black line masters “Olympic Gold Times” for each student
• Transparencies of black lines
• Computer cart
Launch: How many of you have watched the Olympics? Who likes the Summer
Olympics and who likes the Winter Olympics? What is your favorite sport in the
Olympics? Today you are going to make a scatter plot on your computer using the
Olympic winning times for the men’s 200-meter dash.
Explore:
3) Pass out black line masters and computers
4) Have them work with a partner to help each other with problems with the
program.
5) If students are having problems:
• Go to chart wizard and click on scatter plots.
• Highlight data and hit next
• Chart title: Congress and Pizza
• Value x: Pizza Restaurants
• Value y: US Representatives
• Next then Finish
Share:
5) Looking at the scatter plot, do you see a relationship between the year and
winning times?
6) What is happening to the pattern of data plots?
7) What would we call this trend?
8) Using our black line, could we make a future prediction of the winning time for
1998? (Click on scale to change range)
24
Summarize:
Scatter plots are used to find a relationship between two variables (jump height, height).
Can you name others?
The black line is a fitted line that helps you make predictions about future data in your
plot.
A negative linear relationship is when the pattern of points decrease to the right.
Assessment:
Have students print out their chart and pass in their chart and answers to the sharing.
25
Name_________________________
Hour_________________________
Questions for “Olympic Gold Times”
Looking at the scatter plot, do you see a relationship between the year and winning
times? Explain your answer.
What is happening to the pattern of data plots?
What would we call this trend?
Using our black line, could we make a future prediction of the winning time for 1998?
(Click on scale to change range)
26
Circle Graphs
Minnesota Standard:
8
IV. DATA
ANALYSIS,
STATISTICS
AND
PROBABILITY
A. Data
and
Statistics
Represent data and use
various measures
associated with data to
draw conclusions and
identify trends.
1. Construct and analyze histograms,
circle graphs, stem-and-leaf plots and boxand-whisker plots.
2. Compute the quartiles of a data set.
Objective: Students will be able to create and interpret a circle graph.
Materials:
• Fun size packs of M&Ms
• Paper
• Compass
• Protractors
• Markers (optional)
Launch: How many of you like M&Ms. Have you eaten them? Have you ever thought if
there was the same amount of the different colors? Today we are going to collect data to
see if there are the same amounts of color or different amounts of color.
Explore:
1) put students into groups of 4
2) Pass out M&Ms. One to each group.
3) Have students count the different colors and record data.
4) After the students complete their recording, they are to go to the board and put
their data on the line plot for collecting our class data.
5) Students will then fill out the chart (of class data) of changing numbers from
fraction to decimal to percent to degree.
6) Students will take their compass and draw a circle.
7) Then students will take their protractors and section off the circle by degrees.
8) Label each category with percents and name.
Share:
1) Which color appears the most?
2) Which color appears the least?
3) Can you put two colors together to equal one color?
4) Why do you think some colors appear more than others? If not can we find out
why?
Summarize:
To create a circle graph you must take your data and change from a fraction to a degree.
A circle graph shows percents of a whole. (Parts of a whole)
27
Color
Total Fraction Decimal Percent Degree
M&M
28
Post Test For Data Analysis Unit
Name_____________________
Hour____Date_____________
Create a stem-and-leaf plot from the chart below:
26
29
21
21
20
25
Ages of the top 20 solo pop artist in 1997
33
28
22
19
14
27
21
26
32
31
25
26
26
13
Find the following information:
Minimum:
Maximum:
Range:
Median:
Mean:
Mode:
What average best represents the data of the stem-and-leaf plot? Explain.
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A group of students has been investigating information about their pets. Several students
have cats. They decided to collect some information about each of the cats. One set of
data they collected was the lengths of the cats measured from the tip of the nose to the tip
of the tail. Here is a bar graph showing the information they found:
Length of cats
5
Frequency of lengths
4
3
2
1
0
16
25
27
28
29
30
31
32
33
35
36
37
length in inches
How many cats measured 30 inches long from nose to tail? How do you know?
How many cats were measured in all? How do you know?
If you added the lengths of the three shortest cats, what would the total of those lengths
be?
What is the typical length of a cat from nose to tail? Explain.
If we measured another cat, how long do you think it would be? Explain.
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The table below shows history test scores for two classes. The same data are used in the
box-and-whisker plots below. Use the table to construct a box-and-whisker plot.
History Test Scores
66
54
68
86
100
59
59
68
85
Class A
100
90
72
64
59
100
100
84
100
78
76
87
45
78
76
76
90
45
Class B
64
77
93
47
80
76
76
100
83
_________________________________________________________
45 50 55 60 65 70 75 80 85 90 95 100
Lower extreme
Upper extreme
Lower quartile
Median
Upper quartile
In your opinion which class did better on the test? Explain.
Explain the similarities of the plots.
Explain the differences of the plots?
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Make a scatter plot of the data below. Put high temperature on the horizontal axis.
Use excel to create the scatter plot.
High
77 72 75 70 71 68 69 65 64 60 55 58 54
Temperature
Cups of
6
6
4
7
5
9 11 14 15 18 25 21 28
cocoa sold
51
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If it makes sense, draw a fitted line.
When the temperature decreases, what happens to the cups of cocoa sold? Explain.
When the temperature increases, what happens to the cups of cocoa sold? Explain.
Suppose one pot makes 10 cups of cocoa. How many pots should the owner make when
the high temperature is 50°? 40°?
Below is a circle graph of students who participate in school activities
Number of students
Other
15%
Discussion
Group
40%
School Clubs
25%
School
calendar
20%
What is the percent of students who participated in group discussion?
What is the percent of students who participated in school clubs and school calendar?
What do you notice about the percents from discussion groups to other?
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Assess Instructional Changes
1. Lesson Plans – what are you attempting to change or improve?
We are trying to get students to gain knowledge in how to create and
analyze stem and leaf plots, histograms, box plots, circle graphs and
scatter plots.
2. What actual changes are you making?
We are moving away from the text book and creating my activity-based
lessons. We are also teaching the unit as a whole instead of spreading the
lessons out over time.
3. What effect should these changes have?
The student’s should be able to analyze graphs at a deeper level than prior
to the unit.
4. Formulate hypotheses – null and alternative
Ho: There wasn’t any increase of knowledge in interpreting and analyzing
graphs
Ha: Instruction resulted in an increase of understanding how to interpret
and analyze graphs
Ho: There is a difference between the results of our class data
Ha: There is no difference between the results of our class data
5. Experimental design for collecting data
Students will take a cumulative pre and post test. We will conduct paired
t-test to compare within our class and an unpaired t-test to compare class
to class.
6. Data is collected, reviewed for problems and documented
To be determined
7. Data analysis – statistical tools you will use to analyze your data:
a. Graphical tools: We will construct box plots to compare pre and post data.
b. Statistical tools: We will conduct a paired t-test to look at data within our
class and an unpaired t-test to look at any differences between classes.
8. Statistical results and statements of conclusions
To be determined
9. Interpretation in the appropriate context
To be determined
10. Action and dissemination
a. Local – students, administrators, parents, community
b. State – conferences
c. National – conferences and journal
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