12.2 Frequency Distributions and Statistical Graphs 777 Stem-and-Leaf Displays Frequency distributions and histograms provide very useful tools to organize and summarize data. However, if the data are grouped, we cannot identify specific data values in a frequency distribution and in a histogram. For example, in Example 7, we know that there are eight pieces of luggage in the class of 1 to 5 pounds, but we don’t know the specific weights of those eight pieces of luggage. A stem-and-leaf display is a tool that organizes and groups the data while allowing us to see the actual values that make up the data. To construct a stem-and-leaf display, each value is represented with two different groups of digits. The left group of digits is called the stem. The remaining group of digits on the right is called the leaf. There is no rule for the number of digits to be included in the stem. Usually the units digit is the leaf and the remaining digits are the stem. For example, the number 53 would be broken up into 5 and 3. The 5 would be the stem and the 3 would be the leaf. The number 417 would be broken up into 41 and 7. The 41 would be the stem and the 7 would be the leaf. The number 6, which can be represented as 06, would be broken up into 0 and 6. The stem would be the 0 and the leaf would be the 6. With a stem-and-leaf display, the stems are listed, in ascending order, to the left of a vertical line. Then we place each leaf to the right of its corresponding stem, to the right of the vertical line. In stem-and-leaf displays, the leaves are sometimes listed from lowest digit to greatest digit, but that is not necessary. Example 8 illustrates this procedure. Solution There are five units between class midpoints, so each class width must also be five units. Since three is the midpoint of the first class, there must be two units below and two units above it. The first class must be 1–5. The second class must therefore be 6–10. The frequency distribution is given in Table 12.3. Table 12.3 Weight (pounds) Number of Pieces of Luggage 1–5 8 6–10 10 11–15 7 16–20 5 21–25 6 26–30 3 31–35 1 36 – 40 2 Now try Exercise 37 7 m Acadia National Park Example 8 Stem-and-Leaf Display The table below indicates the ages of a sample of 20 visitors to Acadia National Park. Construct a stem-and-leaf display. 29 31 39 43 56 60 62 59 58 32 47 27 50 28 71 72 44 45 44 68 Pat & Chuck Blackley/ Alamy Stock Photo
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