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Flashcards: Summarize Interpret Categorical Data in Two-Way Frequency Tables: CCSS.Math.Content.HSS-ID.B.5

Suppose a social scientist wants to know the effects of gender upon film preferences. She samples fifty men and women and asks them to mark their preference between to genres: documentaries and dramas. She then constructs a two-way frequency table as shown:

2 way

What is the relative probability of men who prefer dramas?

0.15 $\displaystyle 0.15$

0.11 $\displaystyle 0.11$

0.22 $\displaystyle 0.22$

0.35 $\displaystyle 0.35$

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Flashcards: Summarize Interpret Categorical Data in Two-Way Frequency Tables: CCSS.Math.Content.HSS-ID.B.5

2 way

What is the relative probability of men who prefer dramas?

0.15 $\displaystyle 0.15$

0.11 $\displaystyle 0.11$

0.22 $\displaystyle 0.22$

0.35 $\displaystyle 0.35$

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Flashcards: Summarize Interpret Categorical Data in Two-Way Frequency Tables: CCSS.Math.Content.HSS-ID.B.5

2 way

What is the relative probability of men who prefer dramas?

Your answer:

0.11 $\displaystyle 0.11$

Your answer:

0.22 $\displaystyle 0.22$

Your answer:

0.35 $\displaystyle 0.35$

Correct answer:

0.15 $\displaystyle 0.15$

Explanation:

This question requires us to calculate a relative probability from a two-way frequency chart. Before we can calculate this probability, we need to consider the composition of these tables. The numbers located within the table are not quantitative (i.e. they simply represent the number of times a particular phenomenon occurs). These tables are made up of marginal and joint frequencies. Marginal frequencies occur in the columns and rows labeled as “titles,’” while the joint frequencies are embedded in the table. Let’s observe the frequency table given in the question:

2 way

Relative probabilities are calculated by dividing the marginal and joint frequencies by the total in the table. If we divide each frequency by the total frequency, then we can create the following table:

Relative frequency

In this table we can see that the relative probability of men who like dramas is:

$\textup{Relative probability}=\frac{\textup{joint frequency}}{\textup{total}}$ $\displaystyle \textup{Relative probability}=\frac{\textup{joint frequency}}{\textup{total}}$

$\textup{Relative probability=}\frac{15}{100}$ $\displaystyle \textup{Relative probability=}\frac{15}{100}$

$\textup{Relative probability}=0.15$ $\displaystyle \textup{Relative probability}=0.15$

This can also be solved by graphing the relative probabilities on a stacked bar chart such as the one shown below:

Stacked bar

Flashcards: Summarize Interpret Categorical Data in Two-Way Frequency Tables: CCSS.Math.Content.HSS-ID.B.5

2 way

What is the conditional probability of men who like documentaries?

0.35 $\displaystyle 0.35$

0.22 $\displaystyle 0.22$

0.70 $\displaystyle 0.70$

0.50 $\displaystyle 0.50$

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Flashcards: Summarize Interpret Categorical Data in Two-Way Frequency Tables: CCSS.Math.Content.HSS-ID.B.5

2 way

What is the conditional probability of men who like documentaries?

Your answer:

0.35 $\displaystyle 0.35$

Your answer:

0.22 $\displaystyle 0.22$

Your answer:

0.50 $\displaystyle 0.50$

Correct answer:

0.70 $\displaystyle 0.70$

Explanation:

This question requires us to calculate a conditional probability from a two-way frequency chart. Before we can calculate this probability, we need to consider the composition of these tables. The numbers located within the table are not quantitative (i.e. they simply represent the number of times a particular phenomenon occurs). These tables are made up of marginal and joint frequencies. Marginal frequencies occur in the columns and rows labeled as “titles,’” while the joint frequencies are embedded in the table. Let’s observe the frequency table given in the question:

2 way

Conditional probabilities are calculated by dividing a joint frequency by a marginal frequency. In this case we need to divide the number of men who like documentaries by the total number of men in the study (i.e. the two conditions we know).

$\textup{Conditional probability}=\frac{\textup{joint frequency}}{\textup{marginal frequency}}$ $\displaystyle \textup{Conditional probability}=\frac{\textup{joint frequency}}{\textup{marginal frequency}}$

$\textup{Conditional probability}=\frac{35}{50}$ $\displaystyle \textup{Conditional probability}=\frac{35}{50}$

$\textup{Conditional probability}=0.70$ $\displaystyle \textup{Conditional probability}=0.70$

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Flashcards: Summarize Interpret Categorical Data in Two-Way Frequency Tables: CCSS.Math.Content.HSS-ID.B.5

All Common Core: High School - Statistics and Probability Resources

Flashcards: Summarize Interpret Categorical Data in Two-Way Frequency Tables: CCSS.Math.Content.HSS-ID.B.5

Flashcards: Summarize Interpret Categorical Data in Two-Way Frequency Tables: CCSS.Math.Content.HSS-ID.B.5

Flashcards: Summarize Interpret Categorical Data in Two-Way Frequency Tables: CCSS.Math.Content.HSS-ID.B.5

Flashcards: Summarize Interpret Categorical Data in Two-Way Frequency Tables: CCSS.Math.Content.HSS-ID.B.5

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