Multiple choice

If the mean deviation about the median of the numbers $\mathrm{a},\ 2\mathrm{a},\ \ldots$ , $50\mathrm{a}$ is $50$, then $|\mathrm{a}|$ is equal

  1. $2$
  2. $3$
  3. $4$
  4. $5$
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C Correct answer
Explanation

The median of the 50 numbers a, 2a, ..., 50a is 25.5a. The sum of the absolute deviations from the median is |a| * (|1 - 25.5| + |2 - 25.5| + ... + |50 - 25.5|) = 625 * |a|. Dividing this sum by 50 gives the mean deviation, 12.5 * |a| = 50, which yields |a| = 4.

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