More Graphs and Displays 2.2 SECTION 2.2 More Graphs and Displays 55 Graphing Quantitative Data Sets Graphing Qualitative Data Sets Graphing Paired Data Sets What You Should Learn How to graph and interpret quantitative data sets using stem-and-leaf plots and dot plots How to graph and interpret qualitative data sets using pie charts and Pareto charts How to graph and interpret paired data sets using scatter plots and time series charts Graphing Quantitative Data Sets In Section 2.1, you learned several ways to display quantitative data graphically. In this section, you will learn more ways to display quantitative data, beginning with stem-and-leaf plots. Stem-and-leaf plots are examples of exploratory data analysis (EDA), which was developed by John Tukey in 1977. In a stem-and-leaf plot, each number is separated into a stem (for instance, the entry’s leftmost digits) and a leaf (for instance, the rightmost digit). You should have as many leaves as there are entries in the original data set and the leaves should be single digits. A stem-and-leaf plot is similar to a histogram but has the advantage that the graph still contains the original data. Another advantage of a stem-and-leaf plot is that it provides an easy way to sort data. Constructing a Stem-and-Leaf Plot The data set at the left lists the number of text messages sent in one day by 50 U.S. adults. Display the data in a stem-and-leaf plot. Describe any patterns. SOLUTION Because the data entries go from a low of 17 to a high of 148, you should use stem values from 1 to 14. To construct the plot, list these stems to the left of a vertical line. For each data entry, list a leaf to the right of its stem. For instance, the entry 104 has a stem of 10 and a leaf of 4. Make the plot with the leaves in increasing order from left to right. Be sure to include a key. Number of Text Messages Sent 1 7 8 Key: 100 4 = 104 2 0345556799 3 002233568 4 0 1 2 3 6 9 9 5 2 4 5 9 6 6 8 9 7 3 5 5 6 8 8 0 1 4 8 9 8 10 4 9 11 4 12 3 13 14 8 Interpretation From the display, you can see that more than 50% of the cell phone users sent between 20 and 50 text messages. EXAMPLE 1 Study Tip It is important to include a key for a stem-and-leaf plot to identify the data entries. This is done by showing an entry represented by a stem and one leaf. Number of Text Messages Sent 75 49 104 59 88 123 75 109 68 81 66 80 78 69 55 76 114 98 73 18 42 84 46 52 25 25 26 33 25 20 32 24 43 17 49 27 32 29 29 40 23 33 30 41 35 38 36 54 30 148
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