Two-Way Frequency Tables

AlgebraQuestion 1 (Multiple Choice Worth 1 points)

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The table shows music preferences:

What type of music do you prefer? PopClassicalRapJazzRockRow totalsMale student80608070100390Female student200150207050490Column totals280210100140150880

Which of the following are possible positive associations or observations?

 Pop music is the most popular music for each category of students. The largest difference in conditional relative frequency between males and females is for pop music. Male and female students have the same conditional relative frequency for jazz music. The largest difference in conditional relative frequency between males and females is for rap music.

Question 2 (Multiple Choice Worth 1 points)

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The table shows preferences of dancing or playing sports for male and female students:

Do you prefer dancing or playing sports? Playing sportsDancingRow totalsMale students321244Female students325284Column totals6464128

Which of the following are possible positive associations or observations?

 Male and female students have the same conditional relative frequency of 32 for playing sports. The conditional relative frequencies for dancing and playing sports are the same: 64 out of 128 = 50%. For the condition of female students, there is a high positive association for dancing of 81%. For the condition of dancing, there is a high positive association for female students of 81%.

Question 3 (Multiple Choice Worth 1 points)

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The table shows vacation preferences of families with children under 16 and over 16:

Summer vacation CampingTraveling out of stateActivities in local areaRow totalsAt least one child under 1622123670All children 16 or older17452082Column totals395756152

Sharon mistakenly calculated the marginal relative frequency for traveling out of state to be 57 out of 100 or 57%. What should Sharon have done, and what is the correct answer?

 She should have divided 57 by 152: 37.5% She should have divided 12 by 57: 21% She should have divided 45 by 57: 79% She should have divided 45 by 82: 55%

Question 4 (Multiple Choice Worth 2 points)

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Male and female students were asked at which location they would most want to vacation. They had the following preferences:

Which location would you most like to visit? Aspen, ColoradoNew York,

New YorkRow totals

Male students0.220.280.50Female students0.160.340.50Column totals0.380.621

Which of the following is a two-way conditional frequency table for gender?

Which location would you most like to visit? Aspen, ColoradoNew York,

New York

Male students0.580.45Female students0.420.55Column totals11Which location would you most like to visit? Aspen, ColoradoNew York,

New YorkRow totals

Male students22%28%50%Female students16%34%50%Column totals38%62%100%Which location would you most like to visit? Aspen, ColoradoNew York,

New YorkRow totals

Male students4456100Female students3268100Column totals76124200Which location would you most like to visit? Aspen, ColoradoNew York, New YorkRow totalsMale students0.440.561Female students0.320.681Question 5 (Multiple Choice Worth 2 points)

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High school students from grades 9-10 and 11-12 were asked to choose the kind of band to have play at a school dance: rap, rock, or country.

Their choices were as follows:

Grades 9-10—Rap: 40; Rock: 30; Country: 55

Grades 11-12—Rap: 60; Rock: 25; Country: 35

Which of the following is a correct two-way frequency table for the data?

Band preference for school dance RapRockCountryRow totalsGrades 9-100.280.210.380.86Grades 11-120.410.170.240.83Column totals0.690.380.621Band preference for school dance RapRockCountryRow totalsGrades 9-100.400.550.610.86Grades 11-120.600.450.390.83Column totals1111Band preference for school dance RapRockCountryRow totalsGrades 9-10403055125Grades 11-12602535120Column totals1005590245Band preference for school dance RapRockCountryRow totalsGrades 9-100.320.240.441Grades 11-120.500.210.291Column totals0.690.380.621Question 6 (Multiple Choice Worth 2 points)

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High school students and college students were surveyed to see what type of movies they prefer. The results are as follows:

High school—Action: 26; Drama: 14; Comedy: 22

College—Action: 20; Drama: 28; Comedy: 18

Which of the following is a correct two-way relative frequency table for the data?

Movie Preference ActionDramaComedyRow totalsHigh School26142262College20281866Column totals464240128Movie Preference ActionDramaComedyRow totalsHigh School0.570.330.550.48College0.430.670.450.52Column totals1111Movie Preference ActionDramaComedyRow totalsHigh School0.420.230.351College0.300.420.271Column totals0.360.330.311Movie Preference ActionDramaComedyRow totalsHigh School0.200.110.170.48College0.160.220.140.52Column totals0.360.330.311Question 7 (Multiple Choice Worth 1 points)

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Using the following table, what term best describes the entry of 62%?

Which location would you most like to visit? Aspen, ColoradoNew York,

New YorkRow totals

Male students22%28%50%Female students16%34%50%Column totals38%62%100%

 Joint frequency Joint relative frequency Marginal frequency Marginal relative frequency