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Question

If mean and variance for the following series of numbers:
15,30,a,25,27,b,13,20 is 20 and 39.5 then the value of 3ab is

A
216
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B
36
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C
6
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D
9
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Solution

The correct option is B 6
Mean =xin=15+30+a+25+27+b+13+208
¯¯¯¯¯X=130+a+b8=20
a+b=30...(i)
Variance =ni=1(xi¯¯¯¯¯X)2n=39.5
σ2=(20a)2+(20b)2+2488
σ2=a2+b240(a+b)+10488
39.5×8=a2+b240×30+1048
a2+b2=468 ...(ii)
(a+b)2=(a2+b2+2ab)2ab=302468ab=4322=216
3ab=3216=6

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