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Descriptive Statisticshard
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Let X={x1,x2,…,xn}X = \{x_1, x_2, \dots, x_n\}X={x1​,x2​,…,xn​} be a dataset. A statistician defines a measure of overall pairwise variance as D=1n2∑i=1n∑j=1n(xi−xj)2D = \frac{1}{n^2} \sum_{i=1}^n \sum_{j=1}^n (x_i - x_j)^2D=n21​∑i=1n​∑j=1n​(xi​−xj​)2. Which of the following is the correct relationship between DDD and the standard population variance σ2=1n∑i=1n(xi−xˉ)2\sigma^2 = \frac{1}{n} \sum_{i=1}^n (x_i - \bar{x})^2σ2=n1​∑i=1n​(xi​−xˉ)2?