2-2 Histograms 55 35.Interpreting Effects of Outliers Refer to Data Set 41 “Aluminum Cans” in Appendix B for the axial loads of aluminum cans that are 0.0111 in. thick. An axial load is the force at which the top of a can collapses. The load of 504 lb is an outlier because it is very far away from all of the other values. Construct a frequency distribution that includes the value of 504 lb, and then construct another frequency distribution with the value of 504 lb excluded. In both cases, start the first class at 200 lb and use a class width of 20 lb. State a generalization about the effect of an outlier on a frequency distribution. 2-1 Beyond the Basics 2-2 Histograms PART 1 Basic Concepts of Histograms Key Concept While a frequency distribution is a useful tool for summarizing data and investigating the distribution of data, an even better tool is a histogram, which is a graph that is easier to understand and interpret than a table of numbers. DEFINITION A histogram is a graph consisting of bars of equal width drawn adjacent to each other (unless there are gaps in the data). The horizontal scale represents classes of quantitative data values, and the vertical scale represents frequencies. The heights of the bars correspond to frequency values. Important Uses of a Histogram ■ Visually displays the shape of the distribution of the data ■ Shows the location of the center of the data ■ Shows the spread of the data ■ Identifies outliers A histogram is basically a graph of a frequency distribution. For example, Figure 2-2 on the next page shows the Minitab-generated histogram corresponding to the frequency distribution given in Table 2-2 on page 45. Class frequencies should be used for the vertical scale and that scale should be labeled as in Figure 2-2. There is no universal agreement on the procedure for selecting which values are used for the bar locations along the horizontal scale, but it is common to use class midpoints (as shown in Figure 2-2) or class boundaries or class limits or something else. It is often easier for us mere mortals to use class midpoints for the horizontal scale. Histograms can usually be generated using technology. Relative Frequency Histogram A relative frequency histogram has the same shape and horizontal scale as a histogram, but the vertical scale uses relative frequencies (as percentages or proportions) instead of actual frequencies. Figure 2-3 on the next page is the relative frequency histogram corresponding to Figure 2-2.
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