Question

12.4. Measure of Dispersion
2076 Q.No. 15 Find the standard deviation of: 4, 6, 8, 10, 12.​

Answer 1

Standard deviation of given data = 3.16227

Explanation:

Step(i):-

Given sample size 'n' = 5

Given data 4, 6,8,10,12

`Mean = (4+6+8+10+12)/(5) = 8`

Mean of the sample x⁻ = 8

Standard deviation of the sample

`S.D = \sqrt{(Sum(x-x^(-) )^(2) )/(n-1)}`

Step(ii):-

Given data

x : 4 6 8 10 12

x-x⁻ : 4 - 8 6-8 8-8 10-8 12-8

(x-x⁻) : -4 -2 0 2 4

(x-x⁻)² : 16 4 0 4 16

`S.D = \sqrt{(Sum(x-x^(-) )^(2) )/(n-1)}`

`S.D = \sqrt{(16+4+0+4+16)/(4)}`

S.D = √10 = 3.16227

Final answer:-

The standard deviation = 3.16227