## How to use the KURT function

*What is the KURT function?*

The KURT function lets you calculate the kurtosis in Excel. The kurtosis shows the tailedness of a probability distribution, in other words, how often outliers (extreme values) occur. This number is **not** related to the peak of the distribution but to it's tails.

A high kurtosis number tend to indicate large outliers in a distribution, whereas a small kurtosis value indicate smaller tails. A distribution with a higher kurtosis than three is called leptokurtic, meaning that it has fatter tails than a normal distribution. A distribution with a lower kurtosis than three is called platykurtic, meaning that it has thinner tails than a normal distribution.

*How is the kurtosis calculated in Excel?*

The math formula Excel uses to calculate the kurtosis is:

Xi is each value in the data set.

xÂ Ì… is the average of all values.

n is the number of values.

s is the standard deviation. It is a measure of how spread out the values are.

Using the values 2, 4, 1, and 6 shown in the image above:

Average: 13/4 equals 3.25

n: 4

Standard deviation: 2.21735578260835

(How to use the STDEV.S function)

#### Step 1 - First part of the math formula

4*(4+1)/((4-1)*(4-2)*(4-3))

becomes

20/(3*2*1)

becomes

20/6 equals approx. 3.33333

#### Step 2 - Second part of the math formula

SUM(((B3:B6-AVERAGE(B3:B6))/H2)^4)

becomes

SUM((({2;4;1;6}-3.25)/2.21735578260835)^4)

becomes

SUM({-1.25;0.75;-2.25;2.75}/2.21735578260835)^4)

becomes

SUM(({-0.563734521002122;0.338240712601273;-1.01472213780382;1.24021594620467})^4)

becomes

SUM({0.10099468543522;0.0130889112324045;1.06020180982477;2.3658611031313})

and returns

3.54014650962367

#### Step 3 - Third part of the math formula

becomes

3*(4-1)^2/((4-2)*(4-3))

becomes

3*3^2/(2*1)

becomes

27/2 equals 13.5

#### Step 4 - Multiply and subtract

becomes

3.33333*3.54014650962367)-13.5

becomes

11.8004883654122-13.5

equals

-1.69951

This value matches the value calculated by the KURT function in cell D3, see the image below.

*What is the difference between kurtosis and skewness?*

Skewness measures the symmetry of a distribution whereas kurtosis measures outliers or the tails of the distribution relative to a normal distribution.

A symmetric distribution has zero skewness, meaning that the data values are evenly distributed on both sides of the mean. An asymmetric distribution has either positive or negative skewness, meaning that the data values are more concentrated on one side of the mean than the other.

### Table of contents

## 1. KURT Function Syntax

KURT(*number1*, *number2*, ...)

## 2. KURT Function Arguments

Argument |
Description |

number1 |
Required. A single numerical value or a cell reference to multiple numerical values. |

number2 |
Optional. Up to 30 additional arguments. |

Text, logical values and empty cells are ignored.

The KURT function returns

- #DIV/0! error value if the number of values is less than 4.

## 3. KURT Function example

The image above shows two distributions, the first one is a normal distribution and the second one has random values.

The second one has a higher kurtosis than the normal distribution meaning it has at least one larger outlier.

A normal distribution has a kurtosis of 3, however, Excel returns approx. -0.6196 for this normal distribution.

### Useful resources

KURT function - Microsoft

Excel's KURT(Â ) function computes the excess kurtosis, not the kurtosis

How to Interpret Excess Kurtosis and Skewness

### Functions in 'Statistical' category

The KURT function function is one of many functions in the 'Statistical' category.

### Excel function categories

### Excel categories

### 3 Responses to “How to use the KURT function”

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Great explanation on how to use the KURT function in Excel to calculate kurtosis and its relation to outliers. One question I have is, how can we use the kurtosis value to make meaningful interpretations about our data?

Since kurtosis measures outliers (i.e., rare extreme values), high kurtosis alerts you to the problem.

There are erroneous statements in the document concerning relation of the kurtosis to the shape/height of the peak; these should be ignored, or better yet, corrected by the author.

Ana Carol,

thank you.

Peter Westfall,

thank you for your comment, I appreciate it.

https://en.wikipedia.org/wiki/Kurtosis

I have corrected these statements.