Skewness is a measure of the asymmetry of a probability distribution about its mean. In simple terms, it tells us how much a dataset deviates from the normal distribution. A positive skewness indicates that the distribution is stretched towards the right tail, while a negative skewness suggests that it is stretched towards the left tail. Skewness can be an important parameter in statistical analysis, helping to understand the nature of data and make better decisions.

In this article, we will provide a step-by-step guide on how to calculate skewness using different methods and explain its implications in data analysis.

1. Calculating Skewness Using The Empirical Formula

The most common way to calculate skewness is by using the empirical formula:

Skewness = (Mean – Median) / Standard Deviation

To compute skewness using this formula, follow these steps:

a) Calculate the mean.

b) Calculate the median.

c) Compute the standard deviation.

d) Subtract the median from the mean and divide the result by the standard deviation.

2. Calculating Skewness Using Pearson’s First Coefficient of Skewness

Pearson’s first coefficient of skewness formula is given as follows:

Pearson_Skewness_1 = (3 * (Mean – Median)) / Standard Deviation

a) Compute the mean.

b) Calculate the median.

c) Compute the standard deviation.

d) Apply Pearson’s first coefficient of skewness formula.

3. Calculating Skewness Using The Moment Form

Skew_X = (Σ(X-Mean)^3 * fx)/((Σ(X-Mean)^2 * fx)^1.5)

a) Calculate the mean.

b) Subtract each data value from its respective mean, cube each difference, and multiply it by its respective frequency.

c) Sum all the values from step 2.

d) Calculate the variance: (Σ(X-Mean)^2 * fx) / N

e) Take the square root of the variance to find the standard deviation.

f) Cube the standard deviation and multiply it by N.

g) Divide step 3 by step 6 to find skewness.

4. Calculating Skewness Using Excel

In Excel, the skewness can be easily calculated using the “SKEW” function:

=SKEW(array_of_data)

Conclusion

Skewness is an important parameter that helps us understand the distribution of data, detect outliers, and make informed decisions based on insights gained. Various methods can be used to calculate skewness, such as empirical formula, Pearson’s coefficient, moment form, and Excel functions. Learning these techniques will enhance your data analysis skills and help you to comprehensively analyze large datasets.