Lesson 4.2 Two-Way Frequency Tables S.ID.5
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Transcript of 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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4.2.1: Summarizing Data Using Two-Way Frequency Tables
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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4.2.1: Summarizing Data Using Two-Way Frequency Tables
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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4.2.1: Summarizing Data Using Two-Way Frequency Tables
Type of characteristic
Type of responseResponse 1 Response 2
Characteristic 1 a bCharacteristic 1 c d
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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4.2.1: Summarizing Data Using Two-Way Frequency Tables
Type of characteristic
Type of responseResponse 1 Response 2
Characteristic 1 a bCharacteristic 1 c d
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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4.2.1: Summarizing Data Using Two-Way Frequency Tables
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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4.2.1: Summarizing Data Using Two-Way Frequency Tables
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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4.2.1: Summarizing Data Using Two-Way Frequency Tables
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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4.2.1: Summarizing Data Using Two-Way Frequency Tables
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
big competition. He decides to look at the strike rate for three of his attackers.
2. Wayne has scored 11 goals in 28 appearances, Put these values in your table.
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4.2.1: Summarizing Data Using Two-Way Frequency Tables
PlayerStrike Rate
JermainWayne
Appearances Goals Scored
Peter1128
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.
3. Peter has scored no goals in just 4 appearances, and Put these values in your table.
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4.2.1: Summarizing Data Using Two-Way Frequency Tables
PlayerStrike Rate
JermainWayne
Appearances Goals Scored
Peter112804
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.
4. Jermain has scored 1 goal in 15 appearances. Put these values in your table.
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4.2.1: Summarizing Data Using Two-Way Frequency Tables
PlayerStrike Rate
JermainWayne
Appearances Goals Scored
Peter112804
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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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4.2.1: Summarizing Data Using Two-Way Frequency Tables
PlayerStrike Rate
JermainWayne
Appearances Goals Scored
Peter112804
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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
4.2.1: Summarizing Data Using Two-Way Frequency Tables
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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4.2.1: Summarizing Data Using Two-Way Frequency Tables
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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4.2.1: Summarizing Data Using Two-Way Frequency Tables
Guided Practice: Example 2a, continued2. 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. • 49 + 36 = 85 people who preferred cats
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4.2.1: Summarizing Data Using Two-Way Frequency Tables
Guided Practice: Example 2a, continued3. 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. • 53 + 64 = 117 people who preferred
dogs
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4.2.1: Summarizing Data Using Two-Way Frequency Tables
Guided Practice: Example 2a, continued4. 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. • 22 + 10 = 32 people who preferred fish
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4.2.1: Summarizing Data Using Two-Way Frequency Tables
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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4.2.1: Summarizing Data Using Two-Way Frequency Tables
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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4.2.1: Summarizing Data Using Two-Way Frequency Tables
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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4.2.1: Summarizing Data Using Two-Way Frequency Tables
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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4.2.1: Summarizing Data Using Two-Way Frequency Tables
Male Female TotalsEat Breakfast
regularly 190 110 300Do not Eat Breakfast
regularly 130 165 295Totals 320 275 595
Guided PracticeExample 3Analyze the following two-way frequency table.
How many people were included in this survey? (This is a marginal frequency)
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4.2.1: Summarizing Data Using Two-Way Frequency Tables
Male Female TotalsEat Breakfast
regularly 190 110 300Do not Eat Breakfast
regularly 130 165 295Totals 320 275 595
Guided PracticeExample 3Analyze 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)
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4.2.1: Summarizing Data Using Two-Way Frequency Tables
Male Female TotalsEat Breakfast
regularly 190 110 300Do not Eat Breakfast
regularly 130 165 295Totals 320 275 595
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
4.2.1: Summarizing Data Using Two-Way Frequency Tables
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.