Problem

Here are the shopping times (in minutes) for each of eighteen shoppers at a local grocery store.
\begin{tabular}{|llllll|}
\hline \multicolumn{6}{|c|}{\begin{tabular}{c}
Shopping times \\
(in minutes)
\end{tabular}} \\
\hline 33 & 20 & 23 & 28 & 26 & 22 \\
32 & 38 & 19 & 21 & 31 & 15 \\
30 & 30 & 24 & 17 & 27 & 34 \\
\hline
\end{tabular}
(a) Complete the grouped frequency distribution for the data. (Note that the class width is 6 .)
\begin{tabular}{|c|c|}
\hline \begin{tabular}{c}
Shopping times \\
(in minutes)
\end{tabular} & Frequency \\
\hline 15 to 20 & \\
21 to 26 & \\
27 to 32 & \\
33 to 38 & $\square$ \\
\hline
\end{tabular}
(b) Construct a histogram for the data.

Answer

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Answer

\(\boxed{\text{Final Answer:}}\) The grouped frequency distribution for the data is: \begin{tabular}{|c|c|} \hline \begin{tabular}{c} Shopping times \(in minutes) \end{tabular} & Frequency \\ \hline 15 to 20 & 4 \\ 21 to 26 & 5 \\ 27 to 32 & 6 \\ 33 to 38 & 3 \\ \hline \end{tabular} The histogram for the data is a bar graph with the shopping times on the x-axis and the frequency on the y-axis. The bars represent the class intervals 15 to 20, 21 to 26, 27 to 32, and 33 to 38, with heights of 4, 5, 6, and 3, respectively.

Steps

Step 1 :Given the shopping times for eighteen shoppers at a local grocery store, we are asked to create a grouped frequency distribution and a histogram. The class width for the grouped frequency distribution is given as 6.

Step 2 :To create the grouped frequency distribution, we count the number of data points that fall within each class interval. The class intervals are given as 15 to 20, 21 to 26, 27 to 32, and 33 to 38.

Step 3 :The grouped frequency distribution for the data is: \begin{tabular}{|c|c|} \hline \begin{tabular}{c} Shopping times \(in minutes) \end{tabular} & Frequency \\ \hline 15 to 20 & 4 \\ 21 to 26 & 5 \\ 27 to 32 & 6 \\ 33 to 38 & 3 \\ \hline \end{tabular}

Step 4 :To construct a histogram, we use the class intervals as the x-axis and the frequency as the y-axis. The height of each bar corresponds to the frequency of each class interval.

Step 5 :The histogram for the data is a bar graph with the shopping times on the x-axis and the frequency on the y-axis. The bars represent the class intervals 15 to 20, 21 to 26, 27 to 32, and 33 to 38, with heights of 4, 5, 6, and 3, respectively.

Step 6 :\(\boxed{\text{Final Answer:}}\) The grouped frequency distribution for the data is: \begin{tabular}{|c|c|} \hline \begin{tabular}{c} Shopping times \(in minutes) \end{tabular} & Frequency \\ \hline 15 to 20 & 4 \\ 21 to 26 & 5 \\ 27 to 32 & 6 \\ 33 to 38 & 3 \\ \hline \end{tabular} The histogram for the data is a bar graph with the shopping times on the x-axis and the frequency on the y-axis. The bars represent the class intervals 15 to 20, 21 to 26, 27 to 32, and 33 to 38, with heights of 4, 5, 6, and 3, respectively.

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