Question

For a group of 20 items, sum of X = 1452, sum of x ² = 144800 and mode = 67,

find the Karl Pearson’s coefficient of skewness and interpret the results.

Answer 1

$\bar{x}=\frac{\sum{x_i}}{n}=\frac{1452}{20}=72.6\\s=\sqrt{\frac{\sum{{x_i}^2}-n\bar{x}^2}{n}}=\sqrt{\frac{144800-20\cdot 72.6^2}{20}}=44.3761\\K=\frac{\bar{x}-Mo}{s}=\frac{72.6-67}{44.3761}=0.126194\\The\,\,distribution\,\,is\,\,positively\,\,skewed$