chapter 1

Chapter 1: Overview and Descriptive Statistics83.a. When there is perfect symmetry, the smallest observation y 1 and the largestobservation y n will be equidistant from the median, so y n− x = x − y1.Similarly, the second smallest and second largest will be equidistant fromy n 1− x = x − ythe median, so−2and so on. Thus, the first and second numbers in each pair will be equal, so thateach point in the plot will fall exactly on the 45 degree line. When the data ispositively skewed, y n will be much further from the median than is y 1 , so~ x − y and the point~ , ~ )y n− ~ xwill considerably exceed1( y n− x x − y1will fallconsiderably below the 45 degree line. A similar comment aplies to other points inthe plot.b. The first point in the plot is (2745.6 – 221.6, 221.6 0- 4.1) = (2524.0, 217.5). Theothers are: (1476.2, 213.9), (1434.4, 204.1), ( 756.4, 190.2), ( 481.8, 188.9), ( 267.5,181.0), ( 208.4, 129.2), ( 112.5, 106.3), ( 81.2, 103.3), ( 53.1, 102.6), ( 53.1, 92.0),(33.4, 23.0), and (20.9, 20.9). The first number in each of the first seven pairsgreatly exceed the second number, so each point falls well below the 45 degree line.A substantial positive skew (stretched upper tail) is indicated.46