Mean deviation is least if it is taken about | vedclass

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(B) The mean deviation of a set of observations $x_1, x_2, ..., x_n$ about a value $a$ is defined as $\frac{1}{n} \sum_{i=1}^{n} |x_i - a|$.It is a we

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Median

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(B) The mean deviation of a set of observations $x_1, x_2, ..., x_n$ about a value $a$ is defined as $\frac{1}{n} \sum_{i=1}^{n} |x_i - a|$.It is a well-known mathematical property that the sum of absolute deviations $\sum |x_i - a|$ is minimized when $a$ is the median of the data set.Therefore,the mean deviation is least when it is calculated about the median.

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