)Compute variance and standard deviation of the following data observations. 9,12,15,18,21,24,27
Answers
Variance of the observations= 42
Standard deviation of the observations = √42
Observations - 9,12,15,18,21,24,27
No. Of observations = 7
Mean = sum of observations / no. of observations
Mean = X = 126/7 = 18
Using the formula for variance -
Variance = Σ (xi - X)²/(n-1)
xi is the observations , n is the no. of observations
=> ( (9-18)² + (12-18)² + ------------- + (27-18)² ) / 6
=> 252/6
=> 42
Variance of the observations = 42
Standard deviation of the observations= √variance
= √42
Given : 9,12,15,18,21,24,27
To Find : standard deviation
Solution:
First Find Mean :
( 9+12+15+18+21+24+27) =126/7 =18
x x-Mean (x-Mean)^2
9 -9 81
12 -6 36
15 -3 9
18 0 0
21 3 9
24 6 36
27 9 81
252
Variance = ∑(xi-Mean)² / N
= 252/7
= 36
SD = √Variance
SD = √36 = 6
standard deviation, 6
Variance = 36
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