SKEW.P function

The SKEW.P function in Excel calculates the population skewness of a dataset, which measures the degree of asymmetry in the population distribution of values around the mean. This function is similar to SKEW, but it assumes the data represents the entire population, rather than a sample.

Syntax

=SKEW.P(number1, [number2], ...)

Parameters

1. number1 (required): The first value or range of the dataset.
2. number2, … (optional): Additional values or ranges (up to 254).

Key Points

• Positive Skewness: A positive value indicates the distribution has a longer tail on the right side.
• Negative Skewness: A negative value indicates the distribution has a longer tail on the left side.
• Zero Skewness: A value of zero indicates a symmetric distribution.
• Minimum Data Points: At least 3 numeric values are required to calculate skewness.
• Non-numeric values, logical values, or empty cells in the input range are ignored.

Calculation Formula

The population skewness formula is:

$$S = \frac{\frac{1}{n} \sum \left(\frac{x_i – \bar{x}}{s}\right)^3}{\left(\frac{1}{n} \sum \left(\frac{x_i – \bar{x}}{s}\right)^2\right)^{\frac{3}{2}}}$$

Where:

• $n$: Number of data points.
• $x_i$: Individual data value.
• $\bar{x}$: Mean of the data.
• $s$: Standard deviation of the data.

Examples

1. Basic Population Skewness Calculation

Suppose the dataset is {3, 5, 7, 8, 12} in A1:A5.

To calculate population skewness:

=SKEW.P(A1:A5)

Result: 0.341351

• The positive value indicates a slight right-skew.

2. Negative Skewness

For a dataset {12, 8, 7, 5, 3} in B1:B5:

=SKEW.P(B1:B5)

Result: -0.341351

• The negative value indicates a slight left-skew.

3. Symmetric Population

For a symmetric dataset {10, 15, 20, 25, 30} in C1:C5:

=SKEW.P(C1:C5)

Result: 0

• The result of zero indicates perfect symmetry.

4. Using Multiple Ranges

If the dataset spans two ranges, such as D1:D3 and E1:E3, containing {2, 4, 6} and {8, 10, 12} respectively:

=SKEW.P(D1:D3, E1:E3)

Result: A value reflecting the skewness of the combined population dataset.

Notes

• Error Handling:
  • If fewer than 3 numeric values are provided, Excel returns a #DIV/0! error.
  • Logical values (e.g., TRUE, FALSE) and text in ranges are ignored.
• Population vs. Sample:
  • Use SKEW for sample data skewness.
  • Use SKEW.P for population data skewness.
• Symmetry Insight: Like SKEW, this function does not measure kurtosis.

Related Functions

• SKEW: Calculates skewness for a sample dataset.
• KURT.P: Measures the kurtosis of a population dataset.
• AVERAGE: Calculates the mean of a dataset.
• STDEV.P: Calculates the standard deviation of a population dataset.
• VAR.P: Calculates the variance of a population dataset.

The SKEW.P function is useful in statistical analysis and modeling when analyzing the symmetry of a dataset that represents the entire population, helping to identify outliers and understand the overall shape of the data distribution.