Q13 of 46 Page 278

Mean and standard deviation of 100 items are 50 and 4, respectively. Find the sum of all items and the sum of the squares of the items.

Given: Mean and standard deviation of 100 items are 50 and 4, respectively


To find: the sum of all items and the sum of the squares of the items


As per given criteria,


Number of items, n=100


Mean of the given items,


But we know,



Substituting the corresponding values, we get



⇒ ∑xi=50× 100=5000


Hence the sum of all the 100 items = 5000


Also given the standard deviation of the 100 items is 4


i.e., σ=4


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 items is 251600.


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