$=1$ $=2$ $\equiv 3$ $\equiv 4$ $=5$ $=6$ 7 8 9 10 Internet radio: The following table presents the number of hours a sample of 40 subscribers listened to Pandora Radio in a given week. \begin{tabular}{|c|c|c|c|c|c|c|c|} \hline 0 & 5 & 10 & 15 & 20 & 25 & 30 & 35 \\ \hline 50 & 1 & 11 & 16 & 21 & 26 & 31 & 36 \\ \hline 3 & 13 & 18 & 23 & 0 & 10 & 15 & 20 \\ \hline 3 & 13 & 23 & 3 & 13 & 23 & 1 & 11 \\ \hline 0 & 10 & 2 & 12 & 14 & 12 & 10 & 11 \\ \hline \end{tabular} Send data to Excel Part: 0 / 3 Part 1 of 3 (a) Construct a frequency distribution with eleven classes. Start the first class with 0 and use a class width of 5 .
Solution
Step 1 ：Given the data of the number of hours a sample of 40 subscribers listened to Pandora Radio in a given week, we are asked to construct a frequency distribution with eleven classes, starting from 0 and with a class width of 5. This means we need to count how many times each number in the range of 0 to 50 (with a step of 5) appears in the given data.
Step 2 ：First, we organize the data into the following classes: [0, 5), [5, 10), [10, 15), [15, 20), [20, 25), [25, 30), [30, 35), [35, 40), [40, 45), [45, 50), [50, 55).
Step 3 ：Then, we count the number of data points that fall into each class. The results are as follows: [0, 5) has 9 data points, [5, 10) has 1 data point, [10, 15) has 13 data points, [15, 20) has 4 data points, [20, 25) has 6 data points, [25, 30) has 2 data points, [30, 35) has 2 data points, [35, 40) has 2 data points, [40, 45) has 0 data points, [45, 50) has 0 data points, and [50, 55) has 1 data point.
Step 4 ：Finally, we can conclude that the frequency distribution with eleven classes is as follows: \[\begin{align*} [0, 5) & : 9 \\ [5, 10) & : 1 \\ [10, 15) & : 13 \\ [15, 20) & : 4 \\ [20, 25) & : 6 \\ [25, 30) & : 2 \\ [30, 35) & : 2 \\ [35, 40) & : 2 \\ [40, 45) & : 0 \\ [45, 50) & : 0 \\ [50, 55) & : 1 \\ \end{align*}\]
