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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.
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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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