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Question

The mean of 30 scores is 18 and their standard deviation is 3. Find the sum of all the scores and also the sum of the squares of all the scores

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Solution

The number of scores =n=30
The mean of scores =¯¯¯x=18
We know that, sum of scores =x=18×30=540(¯¯¯x=xn)
Sum of all scores =540
Standard deviation of 30 scores =σ=3
σ2=x2n(xn)2x230182=9
x230=9+324
x2=333×30=9990
sum of squares of all the scores =9990.

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