PMEAN

Overview

The PMEAN function calculates the power mean (also known as the generalized mean) of the input data for a given power p. The power mean is a generalization of the arithmetic, geometric, and harmonic means, and is defined as:

M_p(x_1, ..., x_n) = \left(\frac{1}{n} \sum_{i=1}^n x_i^p\right)^{1/p}

where $p$ is the power parameter, and $x_i$ are the data values. For $p=1$ , the power mean is the arithmetic mean; for $p=0$ , it is the geometric mean; and for $p=-1$ , it is the harmonic mean. This function flattens the input, ignores non-numeric values, and does not support weights or axis arguments, unlike scipy.stats.pmean. Excel does not have a direct equivalent; this function is a custom implementation for 2D lists.

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

Usage

To use the function in Excel:


=PMEAN(data, p)

data (2D list, required): The input data as a 2D list (column or matrix). Non-numeric values are ignored.
p (float, required): The power parameter for the mean. Common values: 1 (arithmetic), 0 (geometric), -1 (harmonic).

The function returns a single value (float): the power mean of the input data, or an error message (string) if the input is invalid.

Examples

Example 1: Arithmetic Mean (p=1)

Inputs:

data		p
1	2	1
3	4

Excel formula:


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

Expected output:

Result
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:

Result
2.2134

Example 3: Harmonic Mean (p=-1)

Inputs:

data		p
1	2	-1
3	4

Excel formula:


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

Expected output:

Result
1.9200

Example 4: Power Mean (p=2)

Inputs:

data		p
1	2	2
3	4

Excel formula:


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

Expected output:

Result
2.7386

Python Code


import math
 
def pmean(data, p):
    """
    Computes the power mean (generalized mean) of the input data for a given power p.
    Flattens the input, ignores non-numeric values, and does not support weights or axis arguments.
    This example function is provided as-is without any representation of accuracy.
    """
    # Flatten and filter numeric values
    flat = []
    if isinstance(data, (int, float)):
        return "Two or more data elements are needed"
    for row in data:
        for val in row:
            try:
                v = float(val)
                flat.append(v)
            except (ValueError, TypeError):
                continue
    if len(flat) < 2:
        return "Two or more data elements are needed"
    n = len(flat)
    if p == 0:
        # Geometric mean
        prod = 1.0
        for v in flat:
            if v <= 0:
                return "All values must be positive for geometric mean"
            prod *= v
        return round(prod ** (1.0 / n), 4)
    else:
        try:
            mean = sum(v ** p for v in flat) / n
            return round(mean ** (1.0 / p), 4)
        except Exception as e:
            return str(e)

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PMEAN

Overview

Usage

Examples

Python Code

Live Notebook

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