Interpretaton and Implementation of the Coefficient of Skewness

Question

Direction:
Achieve the result based on the table and its data by using Coefficient of skewness (CS).

Obstacle:
I have difficult to make a calculation step by step based on the equation below. I need to learn how to do it from beginning and all the way to the end based formula with support of data below. I have difficulty to interpret the equation and then implement it to gain a value of Coefficient of skewness.

$$CS = \frac{\frac{1}{N} \sum_{i=1}^N (x_i - \mu)^3}{\sigma^3}$$

Hours
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Answer 1

First, as @Glen_b implies, you've got the formula for population skewness, not sample skewness; in a sample, the formula (from Wikipedia) is

$ g_1 = \frac{m_3}{m_2^{3/2}} = \frac{\tfrac{1}{n} \sum_{i=1}^n (x_i-\overline{x})^3}{\left(\tfrac{1}{n} \sum_{i=1}^n (x_i-\overline{x})^2\right)^{3/2}}$

Second, in this formula, all the calculations are routine, if tedious; which are giving you trouble. Did someone assign you to calculate these by hand? If not, why not use a program (there are many)?

Third, interpretation is best done by example here. You can plot the density of various distributions with different skewness and see what it means; essentially, it's a measure of how long one tail of the distribution is vs. the other tail. E.g. income is (nearly always) right skew: There are a few people who make a great deal of money (much more than the mean or median) but none who make that much less.