Q30 of 46 Page 278

The mean of 100 observations is 50 and their standard deviation is 5. The sum of all squares of all the observations is

As per given criteria,

Number of observations, n=100


Mean of the given observations,


But we know,



Substituting the corresponding values, we get



⇒ ∑xi=50× 100=5000


Hence the sum of all the 100 observations = 5000


Also given the standard deviation of the 100 observations is 5


i.e., σ=5


But we know



Substituting the corresponding values, we get



Now taking square on both sides, we get








And the sum of the squares of all the 100 observations is 252500.

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