Bluman A.G. Elementary Statistics- A Step By Step Approach

Section 6–2 Applications of the Normal Distribution 323Since the histogram is approximately bell-shaped, we can say that the distribution isapproximately normal.Step 2 Check for skewness. For these data, X 79.5, median 77.5, and s 40.5.Using the Pearson coefficient of skewness givesStep 3379.5 77.5PC 40.5 0.148In this case, the PC is not greater than 1 or less than 1, so it can beconcluded that the distribution is not significantly skewed.Check for outliers. Recall that an outlier is a data value that lies more than1.5(IQR) units below Q 1 or 1.5(IQR) units above Q 3 . In this case, Q 1 45and Q 3 98; hence, IQR Q 3 Q 1 98 45 53. An outlier would bea data value less than 45 1.5(53) 34.5 or a data value larger than98 1.5(53) 177.5. In this case, there are no outliers.Since the histogram is approximately bell-shaped, the data are not significantlyskewed, and there are no outliers, it can be concluded that the distribution isapproximately normally distributed.Example 6–12Number of Baseball Games PlayedThe data shown consist of the number of games played each year in the career ofBaseball Hall of Famer Bill Mazeroski. Determine if the data are approximatelynormally distributed.81 148 152 135 151 152159 142 34 162 130 162163 143 67 112 70Source: Greensburg Tribune Review.SolutionStep 1 Construct a frequency distribution and draw a histogram for the data. SeeFigure 6–28.Figure 6–28Histogram forExample 6–12Frequency876543ClassFrequency34–58 159–83 384–108 0109–133 2134–158 7159–183 42133.558.5 83.5 108.5 133.5 158.5 183.5Games6–25