Certainly! Let's analyze the given formulas one by one to determine which one represents the Software Coefficient of Skewness.
1. [tex]\(sk = \frac{3(\bar{x} - \text{Median})}{s}\)[/tex]
In this formula:
- [tex]\(\bar{x}\)[/tex] represents the mean of the dataset.
- [tex]\(\text{Median}\)[/tex] is the median of the dataset.
- [tex]\(s\)[/tex] is the standard deviation of the dataset.
This formula calculates a measure of skewness based on the relationship between the mean and median. However, it is not the Software Coefficient of Skewness.
2. [tex]\(sk = \frac{n}{(n-1)(n-2)} \left[ \sum \left( \frac{x - \bar{x}}{s} \right)^3 \right]\)[/tex]
In this formula:
- [tex]\(n\)[/tex] is the number of observations in the dataset.
- [tex]\(x\)[/tex] represents each individual observation.
- [tex]\(\bar{x}\)[/tex] is the mean of the dataset.
- [tex]\(s\)[/tex] is the standard deviation of the dataset.
This formula is a well-known definition of the Software Coefficient of Skewness (also referred to as the Pearson’s moment coefficient of skewness).
3. [tex]\(s = \sqrt{\frac{\sum (X - \bar{X})^2}{n-1}}\)[/tex]
In this formula:
- [tex]\(X\)[/tex] is each individual observation.
- [tex]\(\bar{X}\)[/tex] is the mean of the dataset.
- [tex]\(n\)[/tex] is the number of observations in the dataset.
This formula calculates the sample standard deviation of the dataset, which is not related to skewness but is a measure of the spread or dispersion of the dataset.
Given the analysis, it is clear that the correct formula for the Software Coefficient of Skewness is:
[tex]\[sk = \frac{n}{(n-1)(n-2)} \left[ \sum \left( \frac{x - \bar{x}}{s} \right)^3 \right]\][/tex]
So, the correct answer is the second formula, associated with the given formula and analysis:
[tex]\[ \boxed{2} \][/tex]
