Answer:
Standard deviation of given data = 3.16227
Step-by-step explanation:
Step(i):-
Given sample size 'n' = 5
Given data 4, 6,8,10,12
[tex]Mean = \frac{4+6+8+10+12}{5} = 8[/tex]
Mean of the sample x⁻ = 8
Standard deviation of the sample
[tex]S.D = \sqrt{\frac{Sum(x-x^{-} )^{2} }{n-1}}[/tex]
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
[tex]S.D = \sqrt{\frac{Sum(x-x^{-} )^{2} }{n-1}}[/tex]
[tex]S.D = \sqrt{\frac{16+4+0+4+16}{4}}[/tex]
S.D = √10 = 3.16227
Final answer:-
The standard deviation = 3.16227
