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Question
The mean of 100 observations is 50 and their standard deviation is 5. The sum of all squares of all the observations is ______.
Options
50000
250000
252500
255000
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Solution
The mean of 100 observations is 50 and their standard deviation is 5. The sum of all squares of all the observations is 252500.
Explanation:
Here `barx = (sumx_i)/n`
50 = `(sumx_i)/100`
⇒ `sumx_i` = 5000
∴ S.D. = `sqrt((sumx_i^2)/n - ((sumx_i^2)/n)^2`
5 = `sqrt((sumx_i^2)/100 - (5000/100)^2`
⇒ 25 = `(sumx_i^2)/100 - 2500`
⇒ `(sumx_i^2)/100 = 2500 + 25`
⇒ `(sumx_i^2)/00` = 2525
∴ `sumx_i^2 = 255 xx 100` = 252500
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