Problem

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A small startup company wishes to know how many hours, per week, that its employees spend commuting to and from work. The number of hours for each employee are shown below. Construct a frequency table for grouped data using four classes.
$17,2,19,14,13,21,21,9,17,10,3,12,15,10,15,8,5,21,17,13$

Provide your answer below:
\begin{tabular}{|l|l|l|}
\hline Lower Class Limit & Upper Class Limit & Frequency \\
\hline$\square$ & $\square$ \\
\hline$\square$ & $\square$ & $\square$ \\
\hline
\end{tabular}

Answer

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Answer

\begin{tabular}{|l|l|l|} \hline Lower Class Limit & Upper Class Limit & Frequency \ \hline 2.0 & 7.0 & 3 \ \hline 7.0 & 12.0 & 4 \ \hline 12.0 & 17.0 & 6 \ \hline 17.0 & 22.0 & 7 \ \hline \end{tabular}

Steps

Step 1 :First, we need to find the range of the data, which is the difference between the maximum and minimum values. In this case, the maximum value is 21 and the minimum value is 2, so the range is \(21 - 2 = 19\).

Step 2 :Next, we divide this range by the number of classes to find the class width. Since we want to use four classes, the class width is \(19 / 4 = 4.75\). However, to make the classes more understandable, we round this up to 5.

Step 3 :Now, we can construct the frequency table by counting the number of data points in each class. The classes are [2.0, 7.0), [7.0, 12.0), [12.0, 17.0), and [17.0, 22.0).

Step 4 :Counting the data points, we find that there are 3 points in the first class, 4 points in the second class, 6 points in the third class, and 7 points in the fourth class.

Step 5 :\(\boxed{\text{Final Answer: The frequency table for the given data using four classes is:}}\)

Step 6 :\begin{tabular}{|l|l|l|} \hline Lower Class Limit & Upper Class Limit & Frequency \ \hline 2.0 & 7.0 & 3 \ \hline 7.0 & 12.0 & 4 \ \hline 12.0 & 17.0 & 6 \ \hline 17.0 & 22.0 & 7 \ \hline \end{tabular}

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