PMEAN

This function computes the generalized (power) mean of positive numeric data for exponent p.

For values x_1, x_2, \ldots, x_n, the power mean is:

M_p = \left(\frac{1}{n}\sum_{i=1}^{n} x_i^p\right)^{1/p}

Special cases include arithmetic mean (p=1), geometric mean as the limit at p \to 0, and harmonic mean (p=-1).

Excel Usage

=PMEAN(data, p)

data (list[list], required): 2D array of numeric values. Non-numeric values are ignored.
p (float, required): The power exponent for the generalized mean (e.g., 1 for arithmetic, 0 for geometric, -1 for harmonic).

Returns (float): Power mean (float), or error message string.

Example 1: Arithmetic mean (p=1)

Inputs:

data		p
1	2	1
3	4

Excel formula:

=PMEAN({1,2;3,4}, 1)

Expected output:

2.5

Example 2: Geometric mean (p=0)

Inputs:

data		p
1	2	0
3	4

Excel formula:

=PMEAN({1,2;3,4}, 0)

Expected output:

2.21336

Example 3: Harmonic mean (p=-1)

Inputs:

data		p
1	2	-1
3	4

Excel formula:

=PMEAN({1,2;3,4}, -1)

Expected output:

1.92

Example 4: Quadratic mean (p=2)

Inputs:

data		p
1	2	2
3	4

Excel formula:

=PMEAN({1,2;3,4}, 2)

Expected output:

2.73861

Python Code

import math
from scipy.stats import pmean as scipy_pmean

def pmean(data, p):
    """
    Computes the power mean (generalized mean) of the input data for a given power p.

    See: https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.pmean.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.
        p (float): The power exponent for the generalized mean (e.g., 1 for arithmetic, 0 for geometric, -1 for harmonic).

    Returns:
        float: Power mean (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):
        return "Error: Invalid input: data must be a 2D list."

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

      if not flat:
        return "Error: Invalid input: data must contain at least one numeric value."

      if not isinstance(p, (int, float)):
        return "Error: Invalid input: p must be a number."

      p = float(p)
      if not math.isfinite(p):
        return "Error: Invalid input: p must be a finite number."

      for v in flat:
        if v <= 0:
          return "Error: Invalid input: all values must be positive."

      result = scipy_pmean(flat, p, axis=None, nan_policy='omit', keepdims=False)
      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.

p *

The power exponent for the generalized mean (e.g., 1 for arithmetic, 0 for geometric, -1 for harmonic).