Answer :

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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