Kurtosis is a descriptive statistic that is not as well known as other descriptive statistics such as the mean and standard deviation. Descriptive statistics give some sort of summary information about a data set or distribution. As the mean is a measurement of the center of a data set and the standard deviation how spread out the data set is, kurtosis is a measurement of the thickness of the fails of a distribution.

The formula for kurtosis can be somewhat tedious to use, as it involves several intermediate calculations. However, statistical software greatly speeds up the process of calculating kurtosis. We will see how to calculate kurtosis with Excel.

## Types of Kurtosis

Before seeing how to calculate kurtosis with Excel, we will examine a few key definitions. If the kurtosis of a distribution is greater than that of a normal distribution, then it has positive excess kurtosis and is said to be leptokurtic. If a distribution has kurtosis that is less than a normal distribution, then it has negative excess kurtosis and is said to be platykurtic. Sometimes the words kurtosis and excess kurtosis are used interchangeably, so be sure to know which one of these calculations you want.

## Kurtosis in Excel

With Excel it is very straightforward to calculate kurtosis. Performing the following steps streamlines the process of using the formula displayed above. Excel's kurtosis function calculates excess kurtosis.

- Enter the data values into cells.
- In a new cell type =KURT(
- Highlight the cells where the data are at. Or type the range of cells containing the data.
- Make sure to close the parentheses by typing )
- Then press the enter key.

The value in the cell is the excess kurtosis of the data set.

For smaller data sets, there is an alternate strategy that will work:

- In an empty cell type =KURT(
- Enter the data values, each separated by a comma.
- Close the parentheses with )
- Press the enter key.

This method is not as preferable because the data are hidden within the function, and we cannot do other calculations, such as a standard deviation or mean, with the data that we have entered.

## Limitations

It is also important to note that Excel is limited by the amount of data that the kurtosis function, KURT, can handle. The maximum number of data values that can be used with this function is 255.

Due to the fact that the function contains the quantities (*n* - 1), (*n* - 2) and (*n* - 3) in the denominator of a fraction, we must have a data set of at least four values in order to use this Excel function. For data sets of size 1, 2 or 3, we would have a division by zero error. We also must have a nonzero standard deviation in order to avoid a division by zero error.