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Skew

SKEW Function

The SKEW function in Excel is used to return the skewness of a distribution. Skewness is a statistical measure that indicates the asymmetry of a dataset's distribution around its mean. It helps you understand whether the data is more concentrated on one side of the mean or evenly distributed.

Key Features of SKEW:

  • Positive Skew: If the result is greater than 0, the distribution has a longer tail on the right side (towards higher values).
  • Negative Skew: If the result is less than 0, the distribution has a longer tail on the left side (towards lower values).
  • Symmetry: A result of 0 indicates a perfectly symmetrical distribution.

Syntax:

SKEW(number1, [number2], ...)
  • number1, number2, ...: Required. One or more numbers or ranges to calculate the skewness. At least three data points are required for the calculation.

How It Works:

The SKEW function evaluates the shape of a distribution by comparing the mean, median, and individual data points. It calculates skewness using the following formula:

SKEW = (n / [(n-1)(n-2)]) * Σ((xi - x̄)³ / s³)

Where:

  • n: Number of data points.
  • xi: Each individual data point.
  • x̄: The mean (average) of the dataset.

  • s: The standard deviation of the dataset.

  • Positive skew: Indicates more data is concentrated below the mean, with outliers pulling the tail to the right.

  • Negative skew: Indicates more data is concentrated above the mean, with outliers pulling the tail to the left.

Examples:

  1. Positive Skew: If the numbers {2, 4, 6, 8, 100} are provided: 

    =SKEW(2, 4, 6, 8, 100)
    Result: 1.5926 (A strongly positively skewed distribution as 100 is an outlier on the right).

  2. Negative Skew: For the numbers {50, 51, 52, 53, 10}: 

    =SKEW(50, 51, 52, 53, 10)
    Result: -1.3093 (This indicates a negatively skewed distribution with 10 as a left-side outlier).

  3. Near Symmetry: For a more symmetrical dataset like {10, 20, 30, 40, 50}: 

    =SKEW(10, 20, 30, 40, 50)
    Result: 0 (The distribution is symmetrical, with no skew).

Notes:

  • Minimum Requirements:
    • The dataset must include at least three data points. Otherwise, the function returns a #DIV/0! error.
  • Non-Numeric Data:
    • Text, logical values, or empty cells within the data range are ignored in the calculation.
  • Outliers' Impact:
    • Skewness is highly sensitive to outliers. A few extreme values can strongly influence the result.
  • Symmetry Indicator:
    • Although a result of 0 implies symmetry, it does not guarantee a normal distribution.

Applications:

  • Descriptive Statistics: Analyze data's asymmetry in research and reports.
  • Financial Analysis: Assess risk in returns distributions (e.g., stock performance often shows skewness).
  • Quality Control: Identify biases in processes or measurements.
  • Data Science: Evaluate data distribution to choose appropriate statistical models or transformations.

Tip: Complement the SKEW function with the KURT function to explore both skewness and kurtosis (the " tailedness" of the distribution).