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Question
Mean and standard deviation of 100 items are 50 and 4, respectively. Find the sum of all the item and the sum of the squares of the items.
Solution
Given that `barx = 50, n = 100` and S.D. `(sigma) = 4`
`barx = (sumx_i)/N`
⇒ 50 = `(sumx_i)/100`
⇒ `sumx_i` = 5000
And variance `sigma^2 = (sumf_ix_i^2)/N - ((sumf_ix_i)/N)^2`
`(4)^2 = (sumf_ix_i^2)/100 - (50)^2`
⇒ 16 = `(sumf_ix_i^2)/100 - 2500`
∴ `sumf_ix_i^2 = (2500 + 16) xx 100`
⇒ `sumf_ix_i^2 = 2516 xx 100` = 251600
Hence, the required sum are 5000 and 251600.
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