Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
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Do Now 13
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Date:
Do Now 13 – Data All Around Data is just another word for information. Data are pieces of information. Some data is categorical. 1. Think of some ways that you could put food into categories. 2. Think of some of the ways that you could put clothing into categories. 3. Think of some of the ways you could put activities into categories. 4. Think of some of the ways you could put books into categories. Math 2 Week 5 Packet Page 1
Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Name:
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Categorical Data
Definition:
The post office uses a lot of data about each package it delivers. Some is categorical data and
some is not.
1. Which of the following data about a package are categorical data?
a. the town or city in the address
b. the state in the address
c. its weight
d. the ZIP code
e. the postage on it
2. List at least three more items of data about a package. For each one, say whether it is
categorical data or not.
Today, we are going to be collecting data about our class. Let’s brainstorm some types of
categorical data that we could use.
Math 2 Week 5 Packet Page 2
Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Name:
Date:
Name
Math 2 Week 5 Packet Page 3
Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
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Homework 9 – Describing Categorical Data
NOTE: There are 8 exercises in this homework assignment.
1. Looking at the data you collected in class, answer the following questions about the first two
category columns.
a. How many students surveyed answered YES in BOTH categories?
b. How many students surveyed answered NO in BOTH categories?
c. How many students surveyed answered YES in the first category and NO in the second
category?
d. How many students surveyed answered NO in the first category and YES in the second
category?
e. Write one sentence that describes the students in part d.
2. Come up with a way to organize and display the information in question 1 a - d. Make sure
someone who has not seen the data in the table from class can easily understand your
display.
Math 2 Week 5 Packet Page 4
Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Name:
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3. Looking at the data you collected in class, answer the following questions.
a. How many students answered YES in the first category column?
b. How many students answered NO in the first category column?
c. How many students answered YES in the second category column?
d. How many students answered NO in the second category column?
e. Write one sentence that describes the students in part d.
4. Think about how you might include the information in question 3 a - d in the display you
created in question 2. Add it to your display now.
5. In the following list, circle the data types that are categorical data.
Hair Color
Salary
Area code in phone #
Temperature
Speed of car
Blood type
Height
Age
GPA
Political party
Number of states
visited
Martial Status
6. Above, explain why you did or did not circle BLOOD TYPE.
7. Above, explain why you did or did not circle GPA.
8. Above, explain why you did or did not circle NUMBER OF STATES VISITED.
Math 2 Week 5 Packet Page 5
Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Do Now 14
Name:
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Do Now 14 – Organization Strategies Question 2 on last night’s homework asked you to organize your data in some way. Compare your organization system with those of the other students sitting in your group. 1. What, if anything, do your organization systems have in common? 2. What is different about your organization systems? 3. As a group, discuss which system that someone in your group created you would most like to use (you don’t have to come to an agreement). What about the systems that you like makes them useful? Math 2 Week 5 Packet Page 6
Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Name:
Date:
Two-Way Tables
Two-way tables are one way to organize categorical data when you have two variables. Here is
an example of a two-way table.
Right
Handedness Left
Total
Yes
9
8
17
Musician
No
Total
10
19
4
12
14
31
We will begin using Microsoft Excel to help us analyze data. Open the file of data provided on
my web site http://lps.lexingtonma.org/Page/2441.
Today, we will learn how to do the following in Excel:
• Sort data
• Merge cells
• Count data
• Sum data
• Create a new sheet
Your group will be responsible for creating a two-way table for two of the variables. Below, copy
your two-way table from Excel.
Math 2 Week 5 Packet Page 7
Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Name:
Date:
Homework 10 – Two Way Tables
1. A survey was done on 30 high school students. The results are listed below.
Plays a sport
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Yes
No
No
No
No
No
No
No
No
No
Yes
No
No
Yes
No
No
No
Yes
Yes
No
No
No
Yes
Yes
No
No
No
Yes
No
No
Is a member of a
club
Yes
Yes
No
Yes
Yes
No
Yes
No
Yes
No
Yes
Yes
No
Yes
No
No
No
Yes
No
Yes
No
No
Yes
Yes
Yes
No
No
Yes
No
Yes
Complete the following two-way table to summarize the results.
Yes
Plays a sport
No
Total
Yes
Is a
member
of a club
No
Total
30
Math 2 Week 5 Packet Page 8
Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
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2. Answer the following questions about the two-way table below.
Brown
Gender
Eye color
Blue Green
Male
22
18
10
Female
18
20
12
Total
Total
a. Fill in the missing values in the table.
b. What percent of the people surveyed have blue eyes?
c. What percent of the males surveyed have blue eyes?
d. What percent of brown-eyed people surveyed are female?
e. Explain what the number 12 from the table tells us about the people surveyed.
Math 2 Week 5 Packet Page 9
Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Name:
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3. Katrina surveyed her classmates and noticed something unusual about the data. Katrina: It
looks like being left-handed and being from Connecticut are somehow related! That’s very
strange.
Name
Elham
Michael
Danielle
Frederick
Jessica
Location
Connecticut
Connecticut
L.A.
Connecticut
L.A.
Eyedness
right
right
right
right
left
Handedness
right
right
right
left
right
Athlete
yes
yes
yes
yes
no
Gender
female
male
female
male
female
Kaily
Anmol
Aaron
Sahar
Sam
Alex S
Mitchell
Alex L
Christian
Mariana
Anna
Nicolai
Connecticut
L.A.
Connecticut
L.A.
L.A.
L.A.
L.A.
L.A.
Connecticut
L.A.
L.A.
L.A.
right
right
right
right
right
right
left
left
left
right
left
right
left
right
right
left
right
right
right
right
right
right
right
right
yes
yes
yes
yes
no
yes
yes
no
yes
yes
no
no
female
male
male
female
male
male
male
male
male
female
female
male
Olivia
Matt
Ben
James
Susannah
Rae
Will
Connecticut
L.A.
L.A.
Connecticut
Connecticut
L.A.
L.A.
left
left
left
left
right
left
left
right
right
right
left
right
left
right
yes
yes
yes
no
no
yes
yes
female
female
male
male
female
female
male
Answer the following questions about Katrina’s data. You may want to draw a two-way table
to help you.
a. What percent of students from Connecticut were left-handed?
b. What percent of students from Los Angeles were left-handed?
c. Do you think there is relationship between handedness and location? What might you
do to investigate this further?
Math 2 Week 5 Packet Page 10
Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Do Now 15
Name:
Date:
Do Now 15 – Association and Independence Body Mass Index (BMI) is a number calculated from a person's weight and height. BMI provides a reliable indicator of body fatness for most people and is used to screen for weight categories that may lead to health problems. 1. Do you think that Body Mass Index is related to whether someone is active or inactive? Explain why or why not. Body Mass Index Above Healthy Healthy Total Weight Weight Inactive 52 119 171 Physical Active 48 81 129 Activity Level Total 100 200 300 2. Looking at the two way table above, do you think that the table shows that Body Mass Index and Physical Activity Level are related? Explain why or why not, making specific reference to the table. Math 2 Week 5 Packet Page 11
Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Name:
Date:
Association with Categorical Data
Let’s look at data about Body Mass Index (which calculated using height and weight) and the
amount of physical activity.
Body Mass Index
Above
Healthy
Total
Healthy
Weight
Weight
Inactive
Physical
Activity
Level
Active
Total
52
119
171
48
81
129
100
200
300
Vocabulary:
Joint Frequency:
Conditional Distribution:
Marginal Distribution:
Look at your two-way table from the last class. Write out the conditional distributions for each
column below.
Also, write the column marginal distribution for your table.
What do you notice about these distributions? How do they compare?
Math 2 Week 5 Packet Page 12
Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Name:
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Looking back at the example from earlier, how can we display the conditional and marginal
distributions more easily?
What can these displays tell us?
Another example:
Go to bed before 10:00pm
Yes
No
Total
Yes
Have less
than a 10
minute
commute
No
Total
2
4
6
7
14
21
9
18
27
Make segmented bar graphs for the example above:
What do you notice?
More Vocabulary:
Segmented Bar Graph:
Independence:
Association:
Math 2 Week 5 Packet Page 13
Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Name:
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Again, look at your two-way table from last class. Create the segmented bar graphs for the
distributions you already calculated.
Are your categories independent or do they have an association? Explain.
Math 2 Week 5 Packet Page 14
Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Name:
Date:
Homework 11 - Associations
Directions: for exercises 1 – 3 use the table below. It shows the results of a survey of students
that was conducted to learn more about whether eye dominance is associated with other traits,
such as handedness, gender, or being an athlete.
Name
Elham
Michael
Danielle
Location
Connecticut
Connecticut
L.A.
Eyedness
right
right
right
Handedness
right
right
right
Athlete
yes
yes
yes
Gender
female
male
female
Frederick
Jessica
Kaily
Anmol
Aaron
Sahar
Sam
Alex S
Mitchell
Alex L
Christian
Mariana
Connecticut
L.A.
Connecticut
L.A.
Connecticut
L.A.
L.A.
L.A.
L.A.
L.A.
Connecticut
L.A.
right
left
right
right
right
right
right
right
left
left
left
right
left
right
left
right
right
left
right
right
right
right
right
right
yes
no
yes
yes
yes
yes
no
yes
yes
no
yes
yes
male
female
female
male
male
female
male
male
male
male
male
female
Anna
Nicolai
Olivia
Matt
Ben
James
Susannah
Rae
Will
L.A.
L.A.
Connecticut
L.A.
L.A.
Connecticut
Connecticut
L.A.
L.A.
left
right
left
left
left
left
right
left
left
right
right
right
right
right
left
right
left
right
no
no
yes
yes
yes
no
no
yes
yes
female
male
female
female
male
male
female
female
male
1. Build a two-way table and segmented bar graphs to determine whether there is an
association between location and eye dominance.
Math 2 Week 5 Packet Page 15
Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Name:
Date:
2. Build a two-way table and segmented bar graphs to determine whether there is an
association between eye dominance and being an athlete.
3. The following two-way frequency table came from a larger survey than the one on the
previous page.
Left Eyed
Right Eyed
Total
Athlete
11
41
52
Non-Athlete
16
17
33
Total
27
58
85
a. In this survey, which group of students was more likely to be left-eyed: athlete or
non-athletes? Describe the calculations you used.
b. Are the categorical variables of eye dominance and athletic status associated?
Explain how you know.
4. Suggest two categorical variables you expect to be associated, and explain why you
expect this.
5. Suggest two categorical variables you expect to be independent, and explain why you
expect this.
Math 2 Week 5 Packet Page 16
Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Do Now 16
Name:
Date:
Do Now 16 – Quantitative Data Quantitative Data is numerical data where the number is related to a measurement of some sort. For each of the questions below, list as many ideas as you can think of. 1. Think of some numerical data you could gather about a person. 2. Think of some numerical data you could gather about a place. 3. Think of some numerical data you could gather about an event. Math 2 Week 5 Packet Page 17
Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Name:
Date:
Quantitative Data
Here is data on fat and sodium content in 7 fast-food burgers that were tested.
Fat (g)
19
31
34
35
39
39
43
Sodium (mg)
920
1500
1310
860
1180
940
1260
How might we summarize and display this data? Is a two-way table helpful here? How does this
data compare to data we have been working with so far?
Definition:
What are some examples of quantitative data?
Now, we work in Excel to create scatterplots in order to display quantitative data.
You will work in pairs to create scatterplots for your assigned data. Describe the shape of your
graph. Then, explain if your variables are correlated or not. How do you know?
Math 2 Week 5 Packet Page 18
Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Name:
Date:
Homework 12 – Quantitative Data
Height (cm)
185.9
172.0
155.0
191.5
162.0
164.3
177.5
180.0
179.5
Forearm (cm)
48.5
44.5
41.0
50.5
43.0
42.5
47.0
48.0
47.5
1. Use height as the independent variable and length of forearm as the dependent variable for
the data collected from nine students (above).
a. Set up a plot and label your axes. Explain how you scaled them and why you chose to
scale them that way.
b. Does this relationship appear to be linear?
c. Does there seem to be a correlation between the two variables? If yes, how are they
correlated? If no, how can you tell that they are not correlated?
d. Can you assume that height causes length of forearm? Explain why or why not.
e. Could you have used forearm as the independent variable and height as the dependent
variable? Why or why not?
Math 2 Week 5 Packet Page 19
Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Name:
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2. This data set was collected by a college psychology class to determine the effects of sleep
deprivation on students’ ability to solve problems. Ten participants went 8, 12, 16, 20, or 24
hours without sleep and then completed a set of simple addition problems. The number of
addition errors was recorded.
Hours without
Sleep
Number of Errors
8
8
12
12
16
16
20
20
24
24
8
6
6
10
8
14
14
12
16
12
a. Define your variables and create and label a scatterplot.
b. How did you choose which variable to put on the x-axis and which to put on the y-axis?
c. Does this relationship appear to be linear?
d. Does there seem to be a correlation between the two variables? If yes, how are they
correlated? If no, how can you tell that they are not correlated?
e. Can you assume that hours without sleep causes number of arithmetic errors? Explain
why or why not.
Math 2 Week 5 Packet Page 20