Skewness Calculator Formula

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

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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

    Frequently Asked Questions

    What does positive skewness mean?

    The distribution has a longer right tail. Most values cluster to the left, with some high outliers pulling the mean above the median. Income distributions are typically positively skewed.

    What skewness value is considered significant?

    A rough guideline: |skewness| < 0.5 is approximately symmetric, 0.5-1 is moderately skewed, and > 1 is highly skewed.

    Why use Pearson's approximation?

    It requires only three summary statistics (mean, median, SD) rather than the entire raw dataset. It works well for unimodal, moderately skewed distributions.

    Ready to run the numbers?

    Open Skewness Calculator