Table of Contents
Formula and Calculation of Standard Deviation
Standard deviation- Introduction: Standard deviation of a set of data is a measure of how spread out the data is. It is calculated by taking the square root of the average of the squared differences between each data point and the mean of the data.
For example, if you have the following data set:
1, 2, 3, 4, 5
The mean is 3 and the squared differences are:
1-3 = -2
2-3 = -1
3-3 = 0
4-3 = 1
5-3 = 2
The standard deviation is the square root of the average of the squared differences, or 1.4.
What are the Variance and Standard Deviation?
The variance is a measure of how spread out a set of data is. It is calculated by taking the sum of the squared differences between each data point and the mean, divided by the number of data points. The standard deviation is the square root of the variance. It is a measure of how spread out the data is around the mean.
Standard Deviation v/s Variance
- Standard deviation is a measure of how dispersed the values in a set of data are from the mean. It is calculated by taking the square root of the variance.
- Variance is a measure of how spread out the values in a set of data are. It is calculated by taking the sum of the squared differences between each value and the mean, divided by the number of data points.
Variance and Standard Deviation Formula
As discussed, the variance of the data set is the average square distance between the mean value and each data value. And standard deviation defines the spread of data values around the mean.
How to Calculate the Standard Deviation?
The standard deviation is calculated by taking the average of the squared differences of each number from the mean, then dividing by the number of data points.
Steps to Calculate the Standard Deviation
1. Add up the numbers in the data set.
2. Square each number in the data set.
3. Add up the squares of the numbers in the data set.
4. Divide the sum of the squares by the number of data points in the set.
5. Take the square root of the number you obtained in step four.
