lesson 4.2 two-way frequency tables s.id.5

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.

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4.2.1: Summarizing Data Using Two-Way Frequency Tables

Introduction to Two-Way Frequency Tables

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http://walch.com/rr/CAU4L2TwoWayFrequencies

IntroductionInformation 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.

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Type of characteristic

Type of responseResponse 1 Response 2

Characteristic 1 a bCharacteristic 1 c d

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.

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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.

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a + b

Guided PracticeExample 1aCreate 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. 1. Identify your characteristics:

• Design a table that will show the number of male and female customers who are blond or

brunette.

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Gender Hair Color

FemaleMale

Blonde Brunette

Guided PracticeExample 1aCreate 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. 2. 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.

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Gender Hair Color

FemaleMale

Blonde Brunette405

Guided PracticeExample 1aCreate 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.

3. 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.

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Gender Hair Color

FemaleMale

Blonde Brunette405

2520

Example 1bCreate 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.

1. Design a table for Steven, showing the number of goals scored and the number of appearances for three players; Jermain, Wayne and Peter.

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PlayerStrike Rate

JermainWayne

Appearances Goals Scored

Peter

Guided PracticeExample 1bCreate a Two-Way Frequency Table given the following information:Steven is trying to decide on players for a soccer team for a


2. Wayne has scored 11 goals in 28 appearances, Put these values in your table.

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PlayerStrike Rate

JermainWayne


Peter1128



3. Peter has scored no goals in just 4 appearances, and Put these values in your table.

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PlayerStrike Rate

JermainWayne


Peter112804



4. Jermain has scored 1 goal in 15 appearances. Put these values in your table.

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PlayerStrike Rate

JermainWayne


Peter112804

115

Guided PracticeExample 1bCreate 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?

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PlayerStrike Rate

JermainWayne


Peter112804

115

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.1. Design Sarah a table to show for the number of cans, glass

bottles and newspapers she throws away over the next three weeks.

2. Sarah throws away 5 cans in the 1st week, 3 in the second and 4 in the last week.

3. She throws away 6 glass bottles every week 4. 1 newspaper in the last week. In the 1st two weeks she

throws away 2 and then 3 newspapers. 14


Guided PracticeExample 2aAbigail 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?

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GradePreferred pet

Bird Cat Dog Fish9 3 49 53 2210 7 36 64 10

Guided Practice: Example 2a, continued1. 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

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characteristic for the second pet type, “cat.”• 49 people in grade 9 preferred cats,

• 36 people in grade 10 preferred cats. • 49 + 36 = 85 people who preferred cats

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characteristic for the third pet type, “dog.”• 53 people in grade 9 preferred dogs,

• 64 people in grade 10 preferred dogs. • 53 + 64 = 117 people who preferred

dogs

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characteristic for the fourth pet type, “fish.”• 22 people in grade 9 preferred fish,

• 10 people in grade 10 preferred fish. • 22 + 10 = 32 people who preferred fish

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Guided Practice: Example 2, continued5. 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.

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GradePreferred pet

Bird Cat Dog Fish9 3 49 53 2210 7 36 64 10

Total ✔10 85 117 32

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.

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Time spent studyingin hours

Test score0–25 26–50 51–75 76–100

0–2 2 8 12 22–4 0 10 8 244–6 1 0 2 96+ 0 0 1 4

TOTAL

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]

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Time spent studyingin hours

Test score0–25 26–50 51–75 76–100

0–2 2 8 12 22–4 0 10 8 244–6 1 0 2 96+ 0 0 1 4

Guided PracticeExample 3Analyze 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)

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Male Female TotalsEat Breakfast

regularly 190 110 300Do not Eat Breakfast

regularly 130 165 295Totals 320 275 595


How many people were included in this survey? (This is a marginal frequency)

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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)

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You Try!.

2. Looking at the joint frequencies we see that women show a strong preference for which activity?

3. Looking at the joint frequencies we see that men show a strong preference for which activity? 26


1. 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.

lesson 4.2 two-way frequency tables s.id.5

Documents

twoway frequency tables24

table of data

summarizing data

given characteristic

marginal frequency of

sample table

context of given data

categorical data