Certainly! Let's analyze each of the given formulas to identify Pearson's Coefficient of Skewness.
1. The first formula is:
[tex]\[ sk = \frac{n}{(n-1)(n-2)} \sum \left( \frac{x - \bar{X}}{s} \right)^3 \][/tex]
This formula represents the sample skewness, but it is not the Pearson's Coefficient of Skewness. Sample skewness measures the asymmetry of the probability distribution of a real-valued random variable about its mean.
2. The second formula is:
[tex]\[ sk = \frac{3(\bar{x} - \text{Median})}{s} \][/tex]
This is the correct formula for Pearson's Coefficient of Skewness. Pearson's Coefficient of Skewness is used to measure the skewness of a distribution based on the mean, median, and standard deviation.
3. The third formula is:
[tex]\[ S = \frac{\Sigma(x - \bar{x})^2}{n-1} \sqrt{ } \][/tex]
This formula is the sample standard deviation formula with an additional square root symbol incorrectly placed. Standard deviation measures the amount of variation or dispersion of a set of values, but it is not the formula for Pearson's Coefficient of Skewness.
Therefore, the correct formula for Pearson's Coefficient of Skewness is the second option:
[tex]\[ sk = \frac{3(\bar{x} - \text{Median})}{s} \][/tex]
Hence, the answer is:
[tex]\[ 2 \][/tex]
