Problem

A random sample of 40 college professors is selected from all professors at a university. The following list gives their ages. \[ \begin{array}{l} 60,48,43,46,37,53,42,44,48,23,50,63,54,47,64, \\ 69,59,44,58,27,36,69,47,42,38,35,44,35,23,43 \\ 68,39,37,47,28,33,40,39,37,59 . \end{array} \] Construct a stem-and-leaf plot for the data. Complete parts $\mathbf{a}$. and $\mathbf{b}$. a. Determine the leaves for each corresponding stem. Complete the table below. (Use ascending order.) Stem Leaves \begin{tabular}{c|l} Stem \\ \hline 2 & $\square$ \end{tabular}

Solution

Step 1 :Sort the given data in ascending order: 23, 23, 27, 28, 33, 35, 35, 36, 37, 37, 37, 38, 39, 39, 40, 42, 42, 43, 43, 44, 44, 44, 46, 47, 47, 47, 48, 48, 50, 53, 54, 58, 59, 59, 60, 63, 64, 68, 69, 69.

Step 2 :Construct the stem-and-leaf plot using the sorted data. The stem is the first digit or digits, and the leaf is the last digit. For example, in the number 53, 5 would be the stem and 3 would be the leaf.

Step 3 :The stem-and-leaf plot is as follows: \[\begin{array}{c|l} \text{Stem} & \text{Leaves} \\ \hline 2 & 3, 3, 7, 8 \\ 3 & 3, 5, 5, 6, 7, 7, 7, 8, 9, 9 \\ 4 & 0, 2, 2, 3, 3, 4, 4, 4, 6, 7, 7, 7, 8, 8 \\ 5 & 0, 3, 4, 8, 9, 9 \\ 6 & 0, 3, 4, 8, 9, 9 \end{array}\]

Step 4 :So, the leaves for the stem 2 are 3, 3, 7, 8. \(\boxed{\text{Leaves for stem 2: } 3, 3, 7, 8}\)

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Source: https://solvelyapp.com/problems/ytr38inpDC/

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