CK-12 Basic Probability and Statistics - A Short Course

5.2. Calculating the Standard Deviation http://www.ck12.org

Example 2:

Calculate the variance and the standard deviation of the following values:

Solution:

5 , 14 , 16 , 17 , 18

TABLE5.2:

x (x−x ̄) (x−x ̄)^2

5 -9 81

14 0 0

16 2 4

17 3 9

18 4 16

Work space for completing the table

∑x=^70 (x−x ̄)→^5 −^14 =−9; 14−^14 =0; 16−^14 =2; 17−^14 =3; 18−^14 =^4

x ̄=

70

5

(x−x ̄)^2 →(− 9 )^2 =81;( 0 )^2 =0;( 2 )^2 = 4 ( 3 )^2 =9;( 4 )^2 = 16

x ̄= 14

Variance:∑(x−x ̄)^2 = 100

σ^2 =

∑(x−x ̄)^2

n

σ^2 =

110

5

σ^2 = 22

Standard Deviation:∑(x−x ̄)^2 = 110

x ̄=

110

5

x ̄= 22

SD=

√

22

SD= 4. 7

The symbol(σ)is used to represent standard deviation. Using this symbol and the steps that were followed to
calculate the standard deviation, we can write the following formula:

σ=

√

∑(x−x ̄)^2

n