Mean and standard

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

⇒ ∑x_i=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.