Extend 12-7: Algebra Lab Two-Way Frequency Tables
1. How many students responded to the survey?
ANSWER: 150
2. How many of the students that were surveyed are attending the dance?
ANSWER: 78
3. How many of the surveyed sophomores are not attending the dance?
ANSWER: 38
4. What does each of the joint frequencies represent?
ANSWER: The joint frequencies represent every viable combination of subcategories. These include the frequency of freshmen
attending, freshmen not attending, sophomores attending, and sophomores not attending.
5. What does each of the marginal frequencies represent?
ANSWER: The marginal frequencies represent the total frequency of every subcategory. In other words, they indicate how
many times that particular subcategory occurred.
6. WORK Heather sent out a survey asking who was working during the holiday. Of the 50 boys who responded, 34
said yes. Of the 45 girls who responded, 21 said no. Create a two-way frequency table of the results.
ANSWER: 7. SOCCER Pamela asked if anyone would be interested in a co-ed soccer team. Of the 28 boys who responded, 18
said that they would play and 4 were undecided. Of the 22 girls who responded, 6 said they did not want to play and
3 were undecided. Create a two-way frequency table of the results.
ANSWER: 8. Given that a respondent was a sophomore, what is the probability that he or she said no?
ANSWER: 45%
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ANSWER: relative frequencies represent?
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8. Given that a respondent was a sophomore, what is the probability that he or she said no?
Extend
12-7: Algebra Lab Two-Way Frequency Tables
ANSWER: 45%
9. What does each of the conditional relative frequencies represent?
ANSWER: Each conditional relative frequency represents the probability that one subcategory occurred given the knowledge
that another
subcategory already is known. For example, the probability that a person is not attending if you already know she is a
freshman.
10. Why do you think that the columns do not sum to 100%?
ANSWER: The sums of the columns (for attending) do not equal 100% because the conditional relative frequency table is
organized by class. The probability of freshmen attending and the probability of sophomores attending are not
mutually exclusive. The sums of the rows equal 100% because those events are mutually exclusive.
11. Create a two-way conditional relative frequency table for the category attendance.
ANSWER: 12. Given that a respondent was not attending, what is the probability that he or she is a freshman?
ANSWER: 47%
13. ACTIVITIES The managers, staff, and assistants were given three options for the holiday activity: a potluck, a
dinner at a restaurant, and a gift exchange. Five of the 11 managers want a dinner, while 3 want a potluck. Eleven of
the 45 staff members want a gift exchange, while 18 want a dinner. Ten of the 32 assistants want a dinner, while 8
of them want a gift exchange.
a. Create a two-way frequency table. b. Convert the two-way frequency table into a relative frequency table.
c. Create two conditional relative frequency tables: one for the activities and one for the employees.
ANSWER: a. b.
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c.
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12. Given that a respondent was not attending, what is the probability that he or she is a freshman?
ANSWER: Extend
12-7: Algebra Lab Two-Way Frequency Tables
47%
13. ACTIVITIES The managers, staff, and assistants were given three options for the holiday activity: a potluck, a
dinner at a restaurant, and a gift exchange. Five of the 11 managers want a dinner, while 3 want a potluck. Eleven of
the 45 staff members want a gift exchange, while 18 want a dinner. Ten of the 32 assistants want a dinner, while 8
of them want a gift exchange.
a. Create a two-way frequency table. b. Convert the two-way frequency table into a relative frequency table.
c. Create two conditional relative frequency tables: one for the activities and one for the employees.
ANSWER: a. b.
c.
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