Questions: A national survey asked people, "How often do you eat out for dinner, instead of at home?" The frequencies were as follows. Response Frequency Never 211 Rarely 642 Sometimes 981 Most of the time 244 Always 21 Construct a relative frequency distribution of the data. Response Relative Frequency Never Rarely Sometimes Most of the time Always (Round to three decimal place as needed.)

A national survey asked people, "How often do you eat out for dinner, instead of at home?" The frequencies were as follows.

Response Frequency
Never 211
Rarely 642
Sometimes 981
Most of the time 244
Always 21

Construct a relative frequency distribution of the data.

Response Relative Frequency
Never
Rarely
Sometimes
Most of the time
Always

(Round to three decimal place as needed.)

Transcript text: A national survey asked people, "How often do you eat out for dinner, instead of at home?" The frequencies were as follows. \begin{tabular}{|l|c|} \hline \multicolumn{1}{|c|}{ Response } & Frequency \\ \hline Never & 211 \\ Rarely & 642 \\ Sometimes & 981 \\ Most of the time & 244 \\ Always & 21 \\ \hline \end{tabular} Construct a relative frequency distribution of the data. \begin{tabular}{|l|c|} \hline \multicolumn{1}{|c|}{ Response } & \begin{tabular}{c} Relative \\ Frequency \end{tabular} \\ \hline Never & $\square$ \\ Rarely & $\square$ \\ Sometimes & $\square$ \\ Most of the time & $\square$ \\ Always & $\square$ \\ \hline \end{tabular} (Round to three decimal place as needed.)

Solution

Solution Steps

To construct a relative frequency distribution, first calculate the total number of responses. Then, for each response category, divide the frequency by the total number of responses to get the relative frequency. Finally, round each relative frequency to three decimal places.

Step 1: Calculate Total Responses

The total number of responses is calculated by summing the frequencies of all response categories: \[ \text{Total Responses} = 211 + 642 + 981 + 244 + 21 = 2099 \]

Step 2: Calculate Relative Frequencies

The relative frequency for each response category is determined by dividing the frequency of each category by the total number of responses: \[ \text{Relative Frequency} = \frac{\text{Frequency}}{\text{Total Responses}} \] Calculating for each category:

For "Never": \[ \text{Relative Frequency}_{\text{Never}} = \frac{211}{2099} \approx 0.101 \]
For "Rarely": \[ \text{Relative Frequency}_{\text{Rarely}} = \frac{642}{2099} \approx 0.306 \]
For "Sometimes": \[ \text{Relative Frequency}_{\text{Sometimes}} = \frac{981}{2099} \approx 0.467 \]
For "Most of the time": \[ \text{Relative Frequency}_{\text{Most of the time}} = \frac{244}{2099} \approx 0.116 \]
For "Always": \[ \text{Relative Frequency}_{\text{Always}} = \frac{21}{2099} \approx 0.010 \]

Step 3: Present Relative Frequencies

The relative frequencies rounded to three decimal places are:

Never: $0.101$
Rarely: $0.306$
Sometimes: $0.467$
Most of the time: $0.116$
Always: $0.010$

Final Answer

The relative frequency distribution is as follows: \[ \begin{array}{|l|c|} \hline \text{Response} & \text{Relative Frequency} \\ \hline \text{Never} & 0.101 \\ \text{Rarely} & 0.306 \\ \text{Sometimes} & 0.467 \\ \text{Most of the time} & 0.116 \\ \text{Always} & 0.010 \\ \hline \end{array} \] Thus, the final answer is: \[ \boxed{\text{Relative Frequencies: } 0.101, 0.306, 0.467, 0.116, 0.010} \]

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