Coefficient of Skewness
2026-02-28 13:08 Diff
https://brightchamps.com/en-us/math/data/coefficient-of-skewness

Skewness indicates how data points are spread in a dataset. We can classify skewness into two main types:

Positive Skewness: In a positively skewed distribution, the mean will be greater than the median, which is greater than the mode. This implies that the distribution has a longer tail towards the right side, where the extreme values pull the mean towards the right.

Negative Skewness: In a negative skewed distribution, the mean will be less than the median, which is less than the mode. This means that the distribution has a longer tail towards the left side, with a few extreme values pulling the mean towards the left. There are several measures that we use to quantify the skewness in a distribution. Some of the most commonly used measures are:

Pearson’s First Coefficient: Pearson’s First Coefficient, also known as the moment coefficient of skewness, measures the skewness of a distribution. It is a measure of skewness used to compare the mean and mode of a data distribution. It determines the direction and the extent of the skewness in the data. The formula we use for Pearson’s first coefficient is: Pearson’s first coefficient formula = (Mean - Mode) / Standard Deviation

Where:

Mean is the average of the values in the dataset

Mode is the most frequently occurring value in the dataset

Standard Deviation is a measure of the amount of variation in the dataset.

If mean > mode, the skewness is positive (right-skewed)

If mean < mode, the skewness is negative (left-skewed)

If mean ≈ mode, the skewness is symmetric

Pearson’s Second Coefficient of Skewness: Compared to Pearson’s first coefficient, it is less influenced by outliers or any extreme values in the distributions. We use Pearson’s second coefficient if the mode is not well-defined. The formula we use is:

Pearson’s Second Coefficient Formula = 3  × (Mean - Median) / Standard Deviation

Where:

Mean is the average of the values in the dataset

Median is the central value in the dataset

Standard Deviation is a measure of the amount of variation in the dataset.

If mean > median, the skewness is positive (right-skewed)

If mean < median, the skewness is negative (left-skewed)

If mean ≈ median, the skewness is symmetric

These are the two formulas used to calculate Pearson’s coefficient of skewness.