Enter the mean, median, and (sample) standard deviation into the calculator to determine Pearson’s coefficient of skewness.
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Skewness Coefficient Formula
The following formula is used to calculate Pearson’s coefficient of skewness (based on the mean and median) for a set of data.
SK = 3 * (M - MD) / s
- Where SK is the coefficient of skewness
- M is the mean of the data set
- MD is the median of the data set
- s is the (sample) standard deviation of the data set
To calculate the coefficient of skewness, subtract the median of the data set from the mean of the set, multiply the result by 3, then divide by the (sample) standard deviation.
What is the coefficient of skewness?
Definition:
Pearson’s coefficient of skewness (using the median) is a measure of the asymmetry of a distribution based on the mean, median, and standard deviation.
Skewness itself is a measure of the shape of a data set. In this context, it measures how far the mean is from the median relative to the standard deviation (the data’s variability). Positive values indicate right skew (a longer right tail), and negative values indicate left skew (a longer left tail).
How to calculate a coefficient of skewness?
Example Problem:
The following example problem outlines the steps and information needed to calculate a coefficient of skewness.
First, determine the mean of the sample. For this example, the mean will be 6.
Next, determine the median of the sample. In this case, the median is measured to be 4.
Next, determine the (sample) standard deviation. The standard deviation in this example is 5.
Finally, calculate the coefficient of skewness using the formula above:
SK = 3 * (M – MD) / s
SK = 3 * (6 – 4) / 5
SK = 1.2
