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Q62Section DA (Data Science and Artificial Intelligence (Q11–Q65))62 of 65

Recovering the sample variance from a sum of squared pairwise differences

For a given data set {x1,x2,…,xn}\{x_1, x_2, … , x_n\}, where n=100n = 100, it is known that 12000∑i=1n∑j=1n(xi−xj)2=99\frac{1}{2000}\sum_{i=1}^{n}\sum_{j=1}^{n}(x_i - x_j)^2 = 99 Let us denote xˉ=1n∑i=1nxi\bar{x} = \frac{1}{n}\sum_{i=1}^{n} x_i The value of 199∑i=1n(xi−xˉ)2\frac{1}{99}\sum_{i=1}^{n}(x_i - \bar{x})^2 is __________ . (Answer in integer)

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