Warm Up
workbook page 689
Real World Link
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Day 7: Two­Way Frequency Tables
When do you use a two­way table?
Check:
Why do you use a two­way table?
Check:
When you have 2 different types of data you are comparing.
Organize data - Can look for patterns and/or trends.
Information about people who are surveyed can be captured in two­way frequency tables. A two­way frequency table is a table of data that separates responses by a characteristic of the respondents.
Read pg 690 in your workbook. Try Got It Question a, on top of pg 691. 2
Type of Characteristic
Type of Response
Response 1
Response 2
Characteristic 1
a
b
Characteristic 2
c
d
Joint Frequency: The cell value (each individual cell)
Marginal Frequency: An entry in the "Total" row or "Total" column of a two­way relative frequency table
Relative Frequency: The cell value over the grand total
Conditional Relative Frequency: Compares a joint frequency to the marginal total that is being used
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Ex. 1) Cameron surveys students in his school who play sports, and asks them which sport they prefer. He records the responses in the table below.
Fade In to check answers
a) How many students play sports?
237
b) What is the joint frequency of male students who prefer soccer? 52
c) What is the marginal frequency for each type of sport?
Baseball
72
erase to reveal
Soccer
Basketball
116
49
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d) What is the marginal frequency for each gender?
Check Answer:
Male: 117
Female: 120
e) Calculate the relative frequency of males who play soccer. erase
52
= 0.22
237
f) Complete the table by finding the row conditional relative frequencies. Round your answer to the nearest hundredth.
erase to reveal
Baseball
Soccer
Basketball
Male
0.42
0.44
0.14
Female
0.19
0.53
0.28
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Ex. 2) Abigail surveys students in different grades, and asks each student which pet they prefer. The responses are in the table below.
a) What is the joint frequency of 9th grade students who prefer fish?
22
b) What is the marginal frequency of each type of pet?
Bird
Cat
Dog
Fish
10
85
117
32
c) Calculate the relative frequency of 10 graders who prefer cats.
36
244
th
= 0.15
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d) Calculate the relative frequency of 9th graders who prefer dogs.
53
244
= 0.22
e) Complete the table by finding the column conditional relative frequencies. Round your answer to the nearest hundredth.
Bird
Cat
Dog
Fish
9
0.30
0.58
0.45
0.69
10
0.70
0.42
0.55
0.31
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Ex. 3) Juniors and seniors were asked if they plan to attend college right after graduation, seek full­time employment, or some other option. A random sample of 100 students was selected from those who completed the survey. Scott started to calculate the relative frequencies to the nearest hundredth.
Plan to attend college
Seniors
Juniors
Totals
.25
0.35
.60
Plan to seek full time employment
Other options
Totals
.10
0.20
0.55
0.05
.15
0.05
.25
.45
1.00
a) Complete the calculations of the relative frequencies for each of the blank cells. Round your answers to the nearest hundredth.
b) Find the joint frequency for seniors who plan to attend college.
25
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c) Find the joint relative frequency for seniors who plan to seek full time employment.
0.10
d) The school website article indicated that “A Vast Majority of Students from our School Plan to Attend College.” Do you agree or disagree with that article. Explain why agree or disagree.
Agree because the data shows that 60% of
students plan to attend college
e) Do you think juniors and seniors differ regarding after graduation options? Explain.
Yes, while the majority of juniors and seniors
plan to attend college, 20% of seniors have
other options compared to 5% of juniors
having other options.
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In your workbook: pg 693­694
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Warm Up
The eighth grade class went to a water park. Out of the 65 students who went to the park, 17 swam in the wave pool. There were a total of 46 students who rode down the water slide and 16 of those also swam in the wave pool. Construct a two­way table to summarize the data.
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Homework Answers!
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FunZone America Survey Activity
FunZone America, an amusement park, collects information from park visitors. The park uses this information to determine how to attract certain guests to the park. For example, one summer FunZone America learned that 12–17­year­olds were most interested in roller coasters. When FunZone America wanted to try to get more 12–17­year­olds to visit the park, the park ran advertisements about roller coasters. The park surveyed recent visitors and recorded the information below. The three main attractions were roller coasters, shows, and the water park.
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At the end of this activity, you should be able to answer the following:
Are there any trends in the type of attractions preferred by each age group? Use your findings to support your answer.
Using the chart sheet provided complete these steps:
a. Create a two­way frequency table showing the joint frequencies of visitors with the following age ranges: 5–15, 16–25, 26–35, 36–45, 46–55. Include in the table the marginal frequency for the type of attractions and for the age range of the visitors. b. Use your table to tally the number of attractions selected for each given age range. Be sure to write the tally as a joint frequency. For example, to fill in the first joint frequency, tally the number of people aged 5 through 15 who selected roller coasters. Count the number of tallies and write this number in the cell also. Fill in a two­way frequency table with this information.
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b. Find the marginal frequencies. c. Complete the calculations of the row conditional relative frequencies. Round your answers to the nearest thousandth.
d. Complete questions e – j on the activity sheet. e. Complete the column conditional frequency (chart k) and answer questions l – n on the activity sheet.
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Ticket Out!
Turn it in when complete
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