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 = ∑(xi - x)3 / (n - 1)s3
Where xi 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 = (x1 + x2 + x3...+ xn) / n
Where n = total number of terms, x1, x2, x3, . . . , xn = 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 = √∑(xi - x)2 / (N - 1)
Where xi 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 = √(∑(xi - 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 = ∑(xi - x)3 / (n - 1)s3
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 = √(∑(xi - 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 = ∑(xi - x)3 / (n - 1)s3
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