Answered: Karl Pearson developed a measure that…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.2: Arithmetic Sequences

Problem 51E

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Question

Karl Pearson developed a measure that describes the skewness of a distribution, called the coefficient of skewness. The formula is Skewness = 3 (mean-median)/standard deviation.

The value of this measure generally lies between -3 and +3. The closer the value lies to -3, the more the distribution is skewed left. The closer the value lies to +3, the more the distribution is skewed right. A value close to 0 indicates a symmetric distribution. Find the coefficient of skewness of the following distributions and comment on the skewness.

Compute the coefficient of skewness for this data (See photo):

The following data represent the length of eruption for a random sample of eruptions at the Old Faithful geyser in Calistoga, California.

108
108
99
105
103
103
94
102
99
106
90 104
110
110
103
109
109
111
101
101
110
102
105
110
106
104
104
100
103 102
120
90
113
116
95 105
103 101
100
101
107 110
92
108
Source: Ladonna Hansen, Park Curator.

Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

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