Question

Make a stem-and-leaf plot for the data. Use the result to list the data in increasing order. $$\begin{aligned}&87,61,54,77,79,86,30,76,52\\\&44,48,76,87,68,82,61,84\\\&33,39,68,37,80,62,81,76\end{aligned}$$

Short answer

The stem-and-leaf plot of the given data is intermediate with stems as tens digits and leaves as ones digits. Further, data arranged in ascending order as follows: 30, 33, 37, 39, 44, 48, 52, 54, 61, 61, 62, 68, 68, 76, 76, 76, 77, 79, 80, 81, 82, 84, 86, 87, 87.

Step-by-step solution

Sorting the data

The data is initially unsorted. To make a stem-and-leaf plot, the data should be sorted in increasing order. So, the sorted data will be: 30, 33, 37, 39, 44, 48, 52, 54, 61, 61, 62, 68, 68, 76, 76, 76, 77, 79, 80, 81, 82, 84, 86, 87, 87.

Determining the stems and leaves

Now that the numbers are sorted, divide each number into a stem and a leaf. The stem will be the first digit and the leaf will be the second digit. For example, for the number 30, 3 will be the stem, 0 will be the leaf.

Creating the stem-and-leaf plot

Draw a vertical line. Write the stem values to the left and the leaf values to the right. For each stem value, match the leaf value. For instance, the stem 3 has the leaves 0, 3, 7, and 9. Repeat this for all stems.

Listing the data in increasing order

The stem-and-leaf plot conveniently lists the data in increasing order, so just write down your list from lowest to highest: 30, 33, 37, 39, 44, 48, 52, 54, 61, 61, 62, 68, 68, 76, 76, 76, 77, 79, 80, 81, 82, 84, 86, 87, 87.