sum of 5 observations is 25 and their sum of squares is 145 so what is the standard deviationof these observation

Question

sum of 5 observations is 25 and sum of their squares is 145 so what is the stardard deviation observation

 

Answer 1

There is a handy shortcut formula for standard deviations:

 

S = √[ (n∑(X²) - (∑X)²) / (n*(n-1)) ]

In your case, 

n = 5

∑X = 25

∑X² = 145

If you plug all of these into the formula, you should get:

S = √ [ (725 - 625) / 20]

S = √ [100/20]

S = √5 ≈ 2.236