## Formula to Calculate Kurtosis

Despite having a biased estimation if you do not have the full-scale data of a given phenomenon, we will calculate the Kurtosis using the **Population Kurtosis Formula** in this article. It is denoted mathematically by the following formula:

`Kurtosis =Fourth Moment value/Square of second Moment value`

Where,

and,

Here,

- n= Sample size
- X
_{i}= sample value - X
_{avaerage}= mean value of the sample values.

We take into account a random variable x and a data collection of size n, S = {x_{1}, x_{2},…, x_{n}} that contains all possible x values. The dataset may reflect the entire population under study or a sample from it. Below is our dataset, **“States-wise Sales Report of Fruits: March”. **

### Method 1 – Applying an Arithmetic Formula

** Steps**:

- Enter the following formula in the
**C17**cell:

`=COUNT(B5:B15)`

- To calculate the mean value,
- Enter the following formula in cell
**C18**:

`=COUNT(B5:B15)`

Here,** B5:B15 **refers to the **numerical values of each data **and** C17 **represents the** sample size.**

- To calculate the
**deviation**of each value from the**mean value,** - Enter the following formula in cell
**C5:**

`=B5-$C$18`

We have locked cell **C18** because we have to use it to get the other value.

- Drag the
**Fill Handle**tool to get the other values.

- Enter the following formula in cell
**D5**to calculate the squared value of the deviation.

`=C5^2`

- Press
**OK**to see the output.

- Drag the
**Fill Handle**tool to get the other values.

- Enter the following formula in cell
**E5:**

`=C5^4`

- Lower the cursor to cell
**E15**to use the**AutoFill**tool.

- To calculate the second moment,
- Enter the following formula in cell
**E17:**

`=SUM(D5:D15)/C17`

- Press the
**Enter**button to see the output below.

- To calculate the fourth moment,
- Enter the formula in cell
**E18:**

`=SUM(E5:E15)/C17`

- Enter the following formula in cell
**E19:**

`=E18/E17^2`

Here, E17 refers to the second-moment value, and E18 refers to the fourth-moment value.

- Press
**Enter**to see the output as below.

**Read More: **How to Calculate Skewness in Excel

### Method 2 – Using the KURT Function

** Steps**:

- Enter the following function in cell
**D16:**

`=KURT(D5:D15)`

- Press the
**Enter**key to see the output.

**Read More: **How to Calculate Coefficient of Skewness in Excel

## Things to Remember

- The maximum argument the
**KURT**function can hold is**30**. If your dataset is larger than**30**, you will face trouble using this function. - Similarly, the minimum number of arguments to get the output from the
**KURT**function is**4**. So if your sample size is less than**4**, then an error will occur. To avoid such a situation, input a value, even zero, as your argument to fulfill the minimum requirement.

## Practice Section

We have provided a** Practice** section on the right side of each sheet so you can practice yourself.

**Download the Practice Workbook**

You can download the dataset to practice.

## Related Articles

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