SKEW function

The SKEW function in Excel calculates the skewness of a dataset, which measures the degree of asymmetry in the distribution of values around the dataset’s mean. Skewness indicates whether the data is skewed to the left (negative skew), right (positive skew), or approximately symmetric (near zero).

Syntax

=SKEW(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: Indicates a distribution with a longer tail on the right (more values below the mean).
• Negative Skewness: Indicates a distribution with a longer tail on the left (more values above the mean).
• Zero Skewness: Indicates a symmetric distribution (e.g., normal distribution).
• Minimum Data Points: At least 3 numeric data points are required to calculate skewness.
• Non-numeric values, logical values, or empty cells in the input range are ignored.

Calculation Formula

The formula for skewness is:

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

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 Skewness Calculation

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

To calculate skewness:

=SKEW(A1:A5)

Result: 0.420084

• The positive value indicates a slight right-skew.

2. Negative Skewness

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

=SKEW(B1:B5)

Result: -0.420084

• The negative value indicates a slight left-skew.

3. Symmetric Dataset

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

=SKEW(C1:C5)

Result: 0

• The result of zero indicates perfect symmetry.

4. Using Multiple Ranges

If data is spread across two ranges, such as D1:D3 and E1:E3, containing {4, 8, 12} and {6, 10, 14}, respectively:

=SKEW(D1:D3, E1:E3)

Result: A value reflecting the skewness of the combined 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.
• Symmetry Insight: The function does not indicate the kurtosis (peakness or flatness) of the distribution; it only measures skewness.
• Visualization: Pair with histogram charts to visually analyze the skewness.

Related Functions

• KURT: Measures the kurtosis (tailedness) of a dataset.
• AVERAGE: Calculates the mean of a dataset.
• STDEV.S: Calculates the standard deviation of a sample dataset.
• VAR.S: Calculates the variance of a sample dataset.
• MEDIAN: Returns the median of a dataset.

The SKEW function is especially useful in statistical and financial analysis for understanding the shape and characteristics of a dataset, helping to assess whether data meets normality assumptions or shows significant asymmetry.