Skewness Calculator Formula

Understand the math behind the skewness calculator. Each variable explained with a worked example.

Use the Skewness Calculator

Formulas Used

Pearson Skewness Coefficient

skewness = 3 * (mean_val - median_val) / std_dev

Mean - Median Difference

direction = mean_val - median_val

Variables

VariableDescriptionDefault
mean_valMean55
median_valMedian50
std_devStandard Deviation10

How It Works

How to Estimate Skewness

Pearson's Second Coefficient of Skewness

Skewness = 3 * (Mean - Median) / Standard Deviation

  • Positive skewness: The right tail is longer; the mean exceeds the median.
  • Negative skewness: The left tail is longer; the mean is below the median.
  • Zero skewness: The distribution is symmetric.

    • This is an approximation. The exact moment-based skewness requires raw data.

    Worked Example

    A dataset has mean 55, median 50, and SD 10. Estimate the skewness.

    mean_val = 55median_val = 50std_dev = 10
    1. 01Skewness = 3 * (55 - 50) / 10
    2. 02= 3 * 5 / 10
    3. 03= 15 / 10 = 1.5
    4. 04Positive value indicates right skew

    Ready to run the numbers?

    Open Skewness Calculator