A sample of five clerks revised the following number of tax records in the last hour: 73, 98, 60, 92 and 84. Compute the coefficient of skewness using the Pearson method. What is your conclusion regarding the shape of the distribution?
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The formula to calculate the coefficient of skewness using the Pearson method is:
Coefficient of Skewness = 3 * (Mean - Median) / Standard Deviation
To find the mean, median, and standard deviation, we first need to arrange the data in ascending order: 60, 73, 84, 92, 98.
Mean = (60 + 73 + 84 + 92 + 98) / 5 = 407 / 5 = 81.4
Median = (84 + 84) / 2 = 168 / 2 = 84
To find the standard deviation, we need to find the variance first.
Variance = [(60 - 81.4)^2 + (73 - 81.4)^2 + (84 - 81.4)^2 + (92 - 81.4)^2 + (98 - 81.4)^2] / 5
= [441.96 + 85.96 + 6.76 + 113.56 + 267.96] / 5
= 917.2 / 5
= 183.44
Standard Deviation = √(Variance) = √(183.44) = 13.54
Now, we can calculate the coefficient of skewness:
Coefficient of Skewness = 3 * (81.4 - 84) / 13.54
= (-2.6) / 13.54
= -0.19
The coefficient of skewness is -0.19. Since it is negative, it means the distribution is negatively skewed, or left-skewed. This indicates that the tail of the distribution is longer on the left side and there are more values on the right side of the median.
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