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Use mean and variance to find the sum of squares or the number of observations

This type of question, asked 2 times: May 2021 S1, 2 May 2023 S1. All 2 questions below, oldest first.

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  1. Question 1

    May 2021 S1

    110
    The mean and variance of nn observations x1,x2,…,xnx_1, x_2, \ldots, x_n are 5 and 0, respectively. If ∑i=1nxi2=400\sum_{i=1}^n x_i^2 = 400, then the value of nn is equal to

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  2. Question 2

    2 May 2023 S1

    145
    The mean of 100 observations is 50 and their standard deviation is 5, then the sum of all squares of all the observations is

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