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# Skewness Calculator

**Skewness** is defined as a statistical measure to help reveal the asymmetry of a probability distribution.

## What is Skewness Calculator?

'**Skewness Calculator**' is an online tool that helps to calculate the value of skewness for a given dataset. Online Skewness Calculator helps you to calculate the value of skewness for a given dataset in a few seconds.

### Skewness Calculator

**NOTE:** Enter values, separated by a comma.

## How to Use Skewness Calculator?

Please follow the steps below on how to use the calculator:

**Step 1:**Enter the numbers separated by a comma in the given input box.**Step 2:**Click on the**"Calculate"**button to find the value of skewness for a given dataset.**Step 3:**Click on the**"Reset"**button to clear the field and enter the new values.

## How to Find Skewness?

**Skewness** is defined as the measure of the asymmetry in a probability distribution where it measures the deviation of the normal distribution curve for data. The formula to calculate the skewness is given by:

**Skewness = ∑(x _{i} - x)^{3} / (n - 1)s^{3}**

Where x_{i} is individual values in the sample, and x is the mean or an average of the sample, N is the number of terms in the sample, and 's' is the standard deviation.

The** mean **or average of a given data is defined as the sum of all observations divided by the number of observations. The mean is calculated using the formula:

**Mean or Average = (x _{1} + x_{2} + x_{3}...+ x_{n}) / n **

Where n = total number of terms, x_{1},_{ }x_{2},_{ }x_{3}, . . . , x_{n} = Different n terms

**Standard deviation** is** **commonly denoted as SD, and it tells about the value that how much it has deviated from the mean value.

**Standard deviation = √∑(x _{i} - x)^{2} / (N - 1)**

Where x_{i} is individual values in the sample, and x is the mean or an average of the sample, N is the number of terms in the sample.

**Solved Examples on Skewness Calculator**

**Example 1:**

Find the skewness for the following set of data: {51,38,79,46,57}

**Solution:**

Given n = 5

Standard deviation = √(∑(x_{i} - x)^{2} / (n - 1))

Mean(x) = 51 + 38 + 79 + 46 + 57 / 5 = 54.2

Standard deviation = √(51 − 54.2)^{2} + (38 − 54.2)^{2} + (79 − 54.2)^{2} + (46 − 54.2)^{2} + (57 − 54.2)^{2} / (5 - 1)

= 15.51

Skewness = ∑(x_{i} - x)^{3} / (n - 1)s^{3}

Skewness = (51 − 54.2)^{3} + (38 − 54.2)^{3} + (79 − 54.2)^{3} + (46 − 54.2)^{3} + (57 − 54.2)^{3} / (5 - 1)(15.5)^{3}

= 10439.28 / 14895.5

= 0.7

**Example 2:**

Find the skewness for the following set of data: {1, 5, 9, 4, 6}

**Solution:**

Given n = 5

Standard deviation = √(∑(x_{i} - x)^{2} / (n - 1))

Mean(x) = 1 + 5 + 9 + 4 + 6 / 5 = 5

Standard deviation = √(1 - 5)^{2} + (5 - 5)^{2} + (9 - 5)^{2} + (4 - 5)^{2} + (6 - 5)^{2} / (5 - 1)

= 2.91

Skewness = ∑(x_{i} - x)^{3} / (n - 1)s^{3}

Skewness = (1 - 5)^{3} + (5 - 5)^{3} + (9 - 5)^{3} + (4 - 5)^{3} + (6 - 5)^{3 }/ (5 - 1)(2.91)^{3}

= 0

Similarly, you can try the calculator to find the skewness for the following dataset:

- 21,14,16,8,2,4,15,8
- 25,1,7,15,6,14,14,25,7

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