Syntax. KURT(number1,number2,...)
Definition. This function returns the kurtosis of a data set. The kurtosis characterizes the relative peakedness or flatness of a distribution compared with the normal distribution. A positive kurtosis indicates a relatively peaked distribution, and a negative kurtosis indicates a relatively flat distribution.
Arguments
number1 (required) and number2 (optional). At least one and up to 255 arguments (30 in Excel 2003 and earlier versions) for which you want to calculate the kurtosis. You can also use an array or a reference to an array instead of arguments separated by commas.
Note
Arguments can be numbers, names, arrays, or references containing numbers. If an array or a reference argument contains text, logical values, or empty cells, those values are ignored. However, cells with the value 0 are included.
If there are fewer than four data points or the sample standard deviation is 0, KURT() returns the #DIV/0! error.
Background. The kurtosis indicates whether the distribution (curve) of observed values is peaked or flat compared with a normal distribution. A normal distribution has the kurtosis 0.
See Also
You will find more information about normal distributions in the description of NORM.DIST().
The kurtosis indicates whether the empirical distribution is more peaked than the normal distribution. In this case, the kurtosis is positive. A kurtosis is defined as follows:
s is the standard deviation of the sample.
The kurtosis and the skewness characterize the form and the degree of symmetry of a distribution. Both calculations are important for finding the correct distribution to be used to further evaluate the data.
The kurtosis of a statistical distribution is defined as follows:
m4(μ) is the fourth central moment, and σ is the standard deviation. As already mentioned, the kurtosis describes the deviation of the given probability distribution compared with the normal distribution.
Example. We will use the example of the software company to explain the KURT() function. The marketing department wants to evaluate the download area as well as the entire website and to calculate the kurtosis of the website clicks in the download area.
To illustrate the probability distribution compared to the normal distribution for the download area as well as for the entire website, you create charts (see Figure 12-81 and Figure 12-82).
Figure 12-81. Calculating the kurtosis for the download area and the average clicks of the entire website.
Statements. The negative kurtosis of –1.27 for the download area (as shown in Figure 12-81) indicates a relative flat distribution compared to the normal distribution. The values for the empirical distribution are dispersed further around the mean than for the normal distribution.
The positive kurtosis of 0.42 for the entire website indicates the relative peaked distribution compared to the normal distribution. The values for the empirical distribution are dispersed closer around the mean than for the normal distribution.