774 CHAPTER 12 Statistics Note in Example 3 that the class width is 6.2, the modal class is 43.9–50.0, and the class mark of the first class is 31.5 37.6 2 , + or 34.55. We have discussed how to organize and summarize data. Now we will introduce graphs that can be used to display information. We will consider four types of graphs: the histogram, the frequency polygon, the stem-and-leaf graph, and the circle graph. Histograms and Frequency Polygons Histograms and frequency polygons are statistical graphs used to illustrate frequency distributions. A histogram is a graph with observed values on its horizontal scale and frequencies on its vertical scale. A bar is constructed above each observed value (or class when classes are used), indicating the frequency of that value (or class). The horizontal scale need not start at zero, and the calibrations on the horizontal and vertical scales do not have to be the same. The vertical scale must start at zero. It may be necessary to break the vertical scale, as was done in displaying Stock B in Fig. 12.2, to accommodate large frequencies on the vertical scale. Because histograms and other bar graphs are easy to interpret visually, they are used a great deal in newspapers and magazines. Solution First rearrange the data from lowest to highest so that the data will be easier to categorize. 31.8 40.3 44.7 48.8 53.7 35.5 40.9 45.8 50.7 56.3 39.8 44.6 46.5 52.4 65.2 The first class goes from 31.5 to 37.6. Since the data are in tenths, the class limits will also be given in tenths. The first class ends with 37.6; therefore, the second class must start with 37.7. The class width of the first class is 37.7 31.5, − or 6.2. The upper class limit of the second class must therefore be 37.6 6.2, + or 43.8. The frequency distribution is given below. Income ($1000) Number of Families 31.5–37.6 2 37.7– 43.8 3 43.9–50.0 5 50.1–56.2 3 56.3– 62.4 1 62.5– 68.6 1 15 7 Now try Exercise 17 Learning Catalytics Keyword: Angel-SOM-12.2 (See Preface for additional information.) Example 4 Construct a Histogram The frequency distribution developed in Example 1, is repeated below. Construct a histogram of this frequency distribution. Number of Children (Observed Values) Number of Families (Frequency) 0 8 1 11 2 18 3 11 4 6 5 4 6 2 7 1 8 2 9 1
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