Descriptive Statisticshard
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For any dataset X={x1,x2,,xn}X = \{x_1, x_2, \dots, x_n\} of size n2n \geq 2 with an unbiased sample standard deviation s>0s > 0 and a mean absolute deviation from the mean MAD=1ni=1nxixˉ\text{MAD} = \frac{1}{n} \sum_{i=1}^n |x_i - \bar{x}|, which of the following inequalities represents the sharpest upper bound for the ratio MADs\frac{\text{MAD}}{s}?