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Question

If the mean deviation about the median of the numbers a,2a,....,50a is 50, then |a| equals:-

A
4
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B
5
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C
2
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D
3
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Solution

The correct option is A 4
Given series:- a,2a,3a,.....,50a
Median =25a+26a2=25.5a
Mean deviation about median =50(Given)
Mean deviation =50i=1|xi25.5a|50
24.5a+23.5a+22.5a+.....+23.5a+24.5a50=50
a+3a+5a+.....+47a+49a=2500
252(2a+(251)2a)=2500
2a×25=200
a=20050=4

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