1. Two-Way Frequency Tables
Lesson 4.2
Two-Way Frequency Tables
S.ID.5
Summarize categorical data for two categories in two-way frequency tables. Interpret frequencies in context of given data.
4.2.1: Summarizing Data Using Two-Way Frequency Tables

2. Introduction to Two-Way Frequency Tables
4.2.1: Summarizing Data Using Two-Way Frequency Tables

3. Type of characteristic
Introduction
Information about people who are surveyed can be captured in two-way frequency tables. A two-way frequency table is a table of data that separates responses by a characteristic of the respondents.
Type of characteristic
Type of response
Response 1
Response 2
Characteristic 1 a b c d
4.2.1: Summarizing Data Using Two-Way Frequency Tables

4. Type of characteristic
Vocabulary
A joint frequency is the number of responses for a given characteristic.
The entries in the cells of a two-way frequency table are joint frequencies.
In the sample table, a, b, c, and d are each joint frequencies.
Type of characteristic
Type of response
Response 1
Response 2
Characteristic 1 a b c d
4.2.1: Summarizing Data Using Two-Way Frequency Tables

5. Type of characteristic
Vocabulary
A marginal frequency is the total number of times a response was given, or the total number of respondents with a given characteristic.
This is the sum of either a row or a column in a two-way frequency table.
In the sample table, a + b would be the marginal frequency of people with Characteristic 1.
Type of characteristic
Type of response
Response 1
Response 2
Characteristic 1 a b c d
a + b
4.2.1: Summarizing Data Using Two-Way Frequency Tables

6. Guided Practice Example 1a
Create a Two-Way Frequency Table given the following information:
Heather is a hairdresser. She is making a record of all the customers she has had in the last month.
Identify your characteristics:
Design a table that will show the number of male and female customers who are blond or brunette.
Hair Color
Gender
Blonde
Brunette
Female
Male
4.2.1: Summarizing Data Using Two-Way Frequency Tables

7. Guided Practice Example 1a
Create a Two-Way Frequency Table given the following information:
Heather is a hairdresser. She is making a record of all the customers she has had in the last month.
Fill in the values for the given characteristic.
In one month she has 40 blond females and only 5 blond males. Put these values in the table.
Hair Color
Gender
Blonde
Brunette
Female 40
Male 5
4.2.1: Summarizing Data Using Two-Way Frequency Tables

8. Guided Practice Example 1a
Create a Two-Way Frequency Table given the following information:
Heather is a hairdresser. She is making a record of all the customers she has had in the last month.
Fill in the values for the next characteristic.
In the same month, she had 25 brunette females and 20 brunette males. Put these values in the table.
Hair Color
Gender
Blonde
Brunette
Female 40 25
Male 5 20
4.2.1: Summarizing Data Using Two-Way Frequency Tables

9. Example 1b
Create a Two-Way Frequency Table given the following information:
Steven is trying to decide on players for a soccer team for a big competition. He decides to look at the strike rate for three of his attackers.
Design a table for Steven, showing the number of goals scored and the number of appearances for three players; Jermain, Wayne and Peter.
Strike Rate
Player
Appearances
Goals Scored
Jermain
Wayne
Peter
4.2.1: Summarizing Data Using Two-Way Frequency Tables

10. Guided Practice Example 1b
Create a Two-Way Frequency Table given the following information:
Steven is trying to decide on players for a soccer team for a big competition. He decides to look at the strike rate for three of his attackers.
Wayne has scored 11 goals in 28 appearances, Put these values in your table.
Strike Rate
Player
Appearances
Goals Scored
Jermain
Wayne 28 11
Peter
4.2.1: Summarizing Data Using Two-Way Frequency Tables

11. Guided Practice Example 1b
Create a Two-Way Frequency Table given the following information:
Steven is trying to decide on players for a soccer team for a big competition. He decides to look at the strike rate for three of his attackers.
Peter has scored no goals in just 4 appearances, and Put these values in your table.
Strike Rate
Player
Appearances
Goals Scored
Jermain
Wayne 28 11
Peter 4
4.2.1: Summarizing Data Using Two-Way Frequency Tables

12. Guided Practice Example 1b
Create a Two-Way Frequency Table given the following information:
Steven is trying to decide on players for a soccer team for a big competition. He decides to look at the strike rate for three of his attackers.
Jermain has scored 1 goal in 15 appearances. Put these values in your table.
Strike Rate
Player
Appearances
Goals Scored
Jermain 15 1
Wayne 28 11
Peter 4
4.2.1: Summarizing Data Using Two-Way Frequency Tables

13. Guided Practice Example 1b
Create a Two-Way Frequency Table given the following information:
Steven is trying to decide on players for a soccer team for a big competition. He decides to look at the strike rate for three of his attackers.
If you were Sven who would be your 1st choice striker?
Strike Rate
Player
Appearances
Goals Scored
Jermain 15 1
Wayne 28 11
Peter 4
4.2.1: Summarizing Data Using Two-Way Frequency Tables

14. You Try!
Create a two-way frequency table given the following information:
Sarah is worried about how much rubbish she creates each week. She decides to look at how many items she could recycle over three weeks which she ends up throwing in to the normal rubbish bin.
Design Sarah a table to show for the number of cans, glass bottles and newspapers she throws away over the next three weeks.
Sarah throws away 5 cans in the 1st week, 3 in the second and 4 in the last week.
She throws away 6 glass bottles every week
1 newspaper in the last week. In the 1st two weeks she throws away 2 and then 3 newspapers.
4.2.1: Summarizing Data Using Two-Way Frequency Tables

15. What is the marginal frequency of each type of pet?
Guided Practice
Example 2a
Abigail surveys students in different grades, and asks each student which pet they prefer. The responses are in the table below.
What is the marginal frequency of each type of pet?
Grade
Preferred pet
Bird
Cat
Dog
Fish 9 3 49 53 22 10 7 36 64
4.2.1: Summarizing Data Using Two-Way Frequency Tables

16. Guided Practice: Example 2a, continued
Sum the responses of people with each characteristic for the first pet type, “bird.”
3 people in grade 9 preferred birds,
7 people in grade 10 preferred birds.
3 + 7 = 10 people who preferred birds
4.2.1: Summarizing Data Using Two-Way Frequency Tables

17. Guided Practice: Example 2a, continued
Sum the responses of people with each characteristic for the second pet type, “cat.”
49 people in grade 9 preferred cats,
36 people in grade 10 preferred cats.
= 85 people who preferred cats
4.2.1: Summarizing Data Using Two-Way Frequency Tables

18. Guided Practice: Example 2a, continued
Sum the responses of people with each characteristic for the third pet type, “dog.”
53 people in grade 9 preferred dogs,
64 people in grade 10 preferred dogs.
= 117 people who preferred dogs
4.2.1: Summarizing Data Using Two-Way Frequency Tables

19. Guided Practice: Example 2a, continued
Sum the responses of people with each characteristic for the fourth pet type, “fish.”
22 people in grade 9 preferred fish,
10 people in grade 10 preferred fish.
= 32 people who preferred fish
4.2.1: Summarizing Data Using Two-Way Frequency Tables

20. ✔ Guided Practice: Example 2, continued
Organize the marginal frequencies in a two-way frequency table.
Create a row and include the marginal frequencies of each response under the name of each response.
Grade
Preferred pet
Bird
Cat
Dog
Fish 9 3 49 53 22 10 7 36 64
Total ✔ 10 85
117 32
4.2.1: Summarizing Data Using Two-Way Frequency Tables

21. Find the marginal frequency for each test score interval.
You Try!
Ms. Scanlon surveys her students about the time they spend studying. She creates a table showing the amount of time students studied and the score each students earned on a recent test.
Find the marginal frequency for each test score interval.
Time spent studying
in hours
Test score
0–25
26–50
51–75
76–100
0–2 2 8 12
2–4 10 24
4–6 1 9 6+ 4
TOTAL
4.2.1: Summarizing Data Using Two-Way Frequency Tables

22. You Try!
Ms. Scanlon surveys her students about the time they spend studying. She creates a table showing the amount of time students studied and the score each students earned on a recent test.
Find the conditional relative frequency for each.
[Hint: There are a total of 83 students]
Time spent studying
in hours
Test score
0–25
26–50
51–75
76–100
0–2 2 8 12
2–4 10 24
4–6 1 9 6+ 4
4.2.1: Summarizing Data Using Two-Way Frequency Tables

23. Guided Practice Example 3
Analyze the following two-way frequency table.
How many females “eat breakfast regularly”? (This is a joint frequency)
How many females were included in the survey? (This is a marginal frequency)
Male
Female
Totals
Eat Breakfast regularly
190
110
300
Do not Eat Breakfast regularly
130
165
295
320
275
595
4.2.1: Summarizing Data Using Two-Way Frequency Tables

24. Guided Practice Example 3
Analyze the following two-way frequency table.
How many people were included in this survey? (This is a marginal frequency)
Male
Female
Totals
Eat Breakfast regularly
190
110
300
Do not Eat Breakfast regularly
130
165
295
320
275
595
4.2.1: Summarizing Data Using Two-Way Frequency Tables

25. Guided Practice Example 3
Analyze the following two-way frequency table.
How many males “do not eat breakfast regularly”? (this is a joint frequency)
How many males and females do not eat breakfast regularly? (this is a marginal frequency)
Male
Female
Totals
Eat Breakfast regularly
190
110
300
Do not Eat Breakfast regularly
130
165
295
320
275
595
4.2.1: Summarizing Data Using Two-Way Frequency Tables

26. You Try! .
Looking at the joint frequencies we see that women show a strong preference for which activity?
Looking at the joint frequencies we see that men show a strong preference for which activity?
Looking at just the total columns (marginal frequencies) what can we conclude about the 3 activities?
Dance is way more interesting.
They have roughly equal appeal.
Sports is the least chosen activity.
TV is the preferred activity.
4.2.1: Summarizing Data Using Two-Way Frequency Tables