How to Calculate Kurtosis & Skew

When you have a continuous variable (such as age, height, weight or IQ), collected on a sample, there are various ways of describing the distribution. A distribution is simply a statistical term for how common various possibilities are. The mean, or average, is a measure of central tendency, the standard deviation is a measure of spread. But there are also measures of shape.

Skewness measures whether the tail of the distribution is longer to the right or left. Income, for example is right-skew, because it has a long right tail.

Kurtosis is a measure of peakedness of the distribution. For example, the uniform distribution is very platykurtic (flat).

Instructions

1. Enter the data. In Excel, enter each value in a cell in column A.

2. Go to an empty cell. Click on Formulas, then More functions, then Statistical, and then Kurt. In the first box, highlight the cells containing your data, then hit "Enter." This is the kurtosis.

3. Go to an empty cell. Click on Formulas, then More functions, then Statistical, and then Skew. In the first box, highlight the cells containing your data, then hit "Enter." This is the skewness.

Tips & Warnings

• Skewness of more than 0 indicates right skew, or a longer tail to the right. Skewness of less than 0 indicates left skew, or a longer tail to the left.

• Kurtosis less than 0 indicates playkurtosis (flat distribution), kurtosis of more than 0 indicates leptokurtosis (highly peaked distribution).

• Kurtosis in Excel is actually kurtosis - 3. This is done in Excel (and some other programs) so that a normal distribution (the bell shaped curve) will have kurtosis of 0.

References

• Wolfram Mathworld: Kurtosis
• Wolfram Mathworld: Skewness