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Question

Let x1,x2,,x100 be 100 observations such that 100i=1xi=0, 1i<j100|xixj|=80000 and mean deviation from their mean be 5. Then their standard deviation is

A
10
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B
30
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C
40
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D
50
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Solution

The correct option is B 30
Given that xi=0
¯¯¯x=xi100=0
Now, |xi¯¯¯x|100=5
|xi|=500
Squaring both the sides
(|xi|)2=(500)2
x2i+21ij100|xixj|=(500)2
[(|xi|)2=x2i+2|xixj|]
x2i100=(500)22|xixj|100
x2i100=(500)22×80000100
x2i100=25001600=900
Standard deviation =(xi¯¯¯x)2100
=900=30

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