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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
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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