If the mean deviation about the median of the numbers a,2a,3a,…,50a,is 50, then a equals

If the mean deviation about the median of the numbers a,2a,3a,,50a,is 50, then a equals

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    Solution:

    The numbers are a,2a,3a,,50a. The median of these numbers is 25a+26a2=255a.

     Mean deviation about median

    =|a25.5a|+|2a25.5a|++|0.5a|+|0.5a|++|50a25.5a|50

    =|a|25(0.5+1.5+2.5++24.5)=|a|25×252(0.5+24.5)=25|a|2

     50=25|a|2|a|=4

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