SKEWNESS

This function measures distribution asymmetry using sample skewness.

Using central moments m_2 and m_3, the Fisher-Pearson skewness coefficient is:

g_1 = \frac{m_3}{m_2^{3/2}}

Positive skewness indicates a longer right tail, negative skewness indicates a longer left tail, and values near zero suggest approximate symmetry.

Excel Usage

=SKEWNESS(data, bias)

data (list[list], required): 2D array of numeric values. Non-numeric values are ignored.
bias (bool, optional, default: true): If True, calculations are not corrected for statistical bias.

Returns (float): Skewness value (float), or error message string.

Example 1: Right skewed data returns positive skewness

Inputs:

data	bias
1	true
2
3
4
10

Excel formula:

=SKEWNESS({1;2;3;4;10}, TRUE)

Expected output:

1.13842

Example 2: Left skewed data returns negative skewness

Inputs:

data	bias
1	true
7
8
9
10

Excel formula:

=SKEWNESS({1;7;8;9;10}, TRUE)

Expected output:

-1.13842

Example 3: Symmetric data returns zero skewness (biased)

Inputs:

data	bias
1	true
2
3
4
5

Excel formula:

=SKEWNESS({1;2;3;4;5}, TRUE)

Expected output:

0

Example 4: Symmetric data returns zero skewness (unbiased)

Inputs:

data	bias
1	false
2
3
4
5

Excel formula:

=SKEWNESS({1;2;3;4;5}, FALSE)

Expected output:

0

Python Code

import math
from scipy.stats import skew as scipy_skew

def skewness(data, bias=True):
    """
    Calculate the skewness of a dataset.

    See: https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.skew.html

    This example function is provided as-is without any representation of accuracy.

    Args:
        data (list[list]): 2D array of numeric values. Non-numeric values are ignored.
        bias (bool, optional): If True, calculations are not corrected for statistical bias. Default is True.

    Returns:
        float: Skewness value (float), or error message string.
    """
    def to2d(x):
        return [[x]] if not isinstance(x, list) else x

    try:
      data = to2d(data)

      if not isinstance(data, list) or not all(isinstance(row, list) for row in data) or not data:
        return "Error: Invalid input: data must be a non-empty 2D list."

      if not isinstance(bias, bool):
        return "Error: Invalid input: bias must be a boolean."

      flat_data = []
      for row in data:
        for item in row:
          try:
            val = float(item)
            if math.isfinite(val):
              flat_data.append(val)
          except (ValueError, TypeError):
            continue

      if len(flat_data) < 3 and not bias:
        return "Error: Invalid input: At least 3 data points are required for unbiased skewness calculation."
      if len(flat_data) < 2:
        return "Error: Invalid input: At least 2 data points are required for skewness calculation."

      result = scipy_skew(flat_data, bias=bias)

      return float(result)
    except Exception as e:
      return f"Error: {str(e)}"

Online Calculator

data *

2D array of numeric values. Non-numeric values are ignored.

bias

If True, calculations are not corrected for statistical bias.