Question

Make a stem-and-leaf plot for the data. Use the result to list the data in increasing order. $$\begin{aligned}&24,29,17,50,39,51,19,22\\\&40,45,20,18,23,30\end{aligned}$$

Short answer

The stem-and-leaf plot for the given data is: \[ \begin{array}{ll} 1 & 7, 9, 8 \ 2 & 4, 9, 2, 0, 3 \ 3 & 9, 0 \ 4 & 0, 5 \ 5 & 0, 1 \end{array} \] and the list in increasing order is: 17, 18, 19, 20, 22, 23, 24, 29, 30, 39, 40, 45, 50, 51.

Step-by-step solution

Understand the Concept of Stem-and-Leaf Plot

A stem-and-leaf plot is a method used to organize statistical data. In the plot, each number is separated into two parts: the stem, which consists of the first digit, and the leaf, which consists of the second digit. For example, in the number 24, 2 would be the stem and 4 would be the leaf.

Develop the Stem-and-Leaf Plot

Given the data: 24, 29, 17, 50, 39, 51, 19, 22, 40, 45, 20, 18, 23, 30. First, identify the stems (the first digit) and list these in a column. The digits are: 1, 2, 3, 4, 5. Then for each of these stems, write the corresponding leaves (the second digit) in order. The draws the following chart: \[ \begin{array}{ll} 1 & 7, 9, 8 \ 2 & 4, 9, 2, 0, 3 \ 3 & 9, 0 \ 4 & 0, 5 \ 5 & 0, 1 \end{array} \]

List the Data in Increasing Order

Finally, determining the increasing order from the stem-and-leaf plot involves reading the plot from top to bottom and left to right, combining the stem with each of its leaves. This gives the ordered list: 17, 18, 19, 20, 22, 23, 24, 29, 30, 39, 40, 45, 50, 51.