If the mean deviation about the median of the numbers a,2a,3a,…,50a,is 50, then a equals
The numbers are a,2a,3a,…,50a. The median of these numbers is 25a+26a2=255a.
∴ Mean deviation about median
=|a−25.5a|+|2a−25.5a|+…+|−0.5a|+|0.5a|+…+|50a−25.5a|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