The mean of 100 observations is 40 and their standard deviation is 3. The sum of squares of all deviations is a. 40000 b. 160900 c. 160000 d. 30000

Answers (1)

Given 
Mean,overlinex=40
Number of observation.n=100
Standard deviation,sigma=3
Given variance=sigma^2=3^2=9
Now we know that,
Variance is given as,
sigma^2=fracSigma x_i^2n-(overlinex)^2
9=fracSigma x_i^2100-(40)^2
9=fracSigma x_i^2100-1600
fracSigma x_i^2100=9+1600
fracSigma x_i^2100=1609
Sigma x_i^2=1609*100=160900
Therefore, the sum of squares of all deviations is160900

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