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Question

The mean deviation about median of varieties 13,14,15,....,99,100 is?

A
1936
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B
21.5
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C
23.5
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D
22
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Solution

The correct option is A 1936
Here, n=88
Median=44thobs+45thobs2
Median=56+572
Median=56.5
MD=88i=1|xi56.5|88

=43.5+42.5+......+0.5+0.5+..+43.588
=1+3+5+...+8788
=22
Now, 1,3,5,..,87 are in AP
a=1,d=2
ax=a+(n1)d
87=1+(n1)2
86=(n1)2
n1=43
n=44
Sn=n2[2a+(n1)d]

=442[2(1)+(441)2]

=22[2+86]
=22[88]
=1936



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