How to Calculate Standard Deviation with Formulas

Updated: Aug 29

Introduction to Standard Deviation and When It's Used

Standard deviation is a statistical measure that tells you how spread out the data points are around the mean. The higher the standard deviation, the more spread out the data points are.

The most common use of standard deviation is to determine if a set of scores is normally distributed. If you have a set of scores that have a high degree of variability, it may be difficult to tell if they are normally distributed or not. A high degree of variability usually indicates that there's something different about those scores, such as outliers or skewness.



Sr No

Height (x)

x - x̅

(x-x̅)²

1

160

-8.29

68.7

2

170

​1.71

2.9

3

167

​-1.29

1.7

4

164

​-4.29

18.4

5

172

​3.71

13.8

6

174

5.71

32.7

7

169

0.71

0.5

8

173

4.71

22.2

9

175

6.71

45.1

10

166

-2.29

5.2

11

158

​-10.29

105.8

12

177

8.71

75.9

13

161

-7.29

53.1

14

170

1.71

2.9

N = 14 (Total Count)

x̅ = 168.29 (mean/average)

​∑(x-x̅)²=448.9



What is a Normal Distribution?

A normal distribution is a type of distribution that is bell shaped. This means that the data has a symmetrical and peaked shape. The mean, median, and mode are all equal to each other.

How Does Standard Deviation Work? What Makes it Different from Mean or Variance?

Standard deviation is a statistical measure that tells us how much the data in a set of numbers deviate from the average.

It is different from mean and variance because it measures how dispersed the data in a set of numbers is around an average, rather than just telling us what that average is.





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