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A national survey asked people, "How often do you eat out for dinner instead of at home?" The frequencies were as follows. Complete parts (a) through (b).

\begin{tabular}{|l|c|}
\hline \multicolumn{1}{|c|}{ Response } & Frequency \\
\hline Never & 305 \\
Rarely & 428 \\
Sometimes & 927 \\
Most of the time & 468 \\
Always & 80 \\
\hline
\end{tabular}

(a) 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 & [tex]$\square$[/tex] \\
Rarely & [tex]$\square$[/tex] \\
Sometimes & [tex]$\square$[/tex] \\
Most of the time & [tex]$\square$[/tex] \\
Always & [tex]$\square$[/tex] \\
\hline
\end{tabular}
(Round to three decimal places as needed.)



Answer :

GinnyAnswer
To construct a relative frequency distribution of the data, follow these steps:

1. Determine the total frequency: Sum up the frequencies of each response.
[tex]\[ \text{Total frequency} = 305 + 428 + 927 + 468 + 80 = 2208 \][/tex]

2. Calculate the relative frequency for each response: Divide the frequency of each response by the total frequency and round the result to three decimal places.

- Never:
[tex]\[ \text{Relative Frequency (Never)} = \frac{305}{2208} \approx 0.138 \][/tex]

- Rarely:
[tex]\[ \text{Relative Frequency (Rarely)} = \frac{428}{2208} \approx 0.194 \][/tex]

- Sometimes:
[tex]\[ \text{Relative Frequency (Sometimes)} = \frac{927}{2208} \approx 0.420 \][/tex]

- Most of the time:
[tex]\[ \text{Relative Frequency (Most of the time)} = \frac{468}{2208} \approx 0.212 \][/tex]

- Always:
[tex]\[ \text{Relative Frequency (Always)} = \frac{80}{2208} \approx 0.036 \][/tex]

3. Construct the relative frequency distribution:

\begin{tabular}{|l|c|}
\hline \multicolumn{1}{|c|}{ Response } & \begin{tabular}{c}
Relative \\
Frequency
\end{tabular} \\
\hline
Never & 0.138 \\
Rarely & 0.194 \\
Sometimes & 0.420 \\
Most of the time & 0.212 \\
Always & 0.036 \\
\hline
\end{tabular}

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