Ononot — A researcher wishes to minimize the Mean Absolute Deviation

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Descriptive Statisticshard

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A researcher wishes to minimize the Mean Absolute Deviation from a constant $c$ , defined as $f(c) = \frac{1}{n}\sum_{i=1}^n |x_i - c|$ . If the dataset is $\{1, 2, 100\}$ , which value of $c$ minimizes this function?