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Question

The means of five observations is 4 and their variance is 5.2. If three of these observations are 1,2 and 6, then the other two observations are
  1. 2 and 9
  2. 4 and 7
  3. 3 and 8
  4. 5 and 6


Solution

The correct option is B 4 and 7
Let two observations be a and b.
Mean =1+2+6+a+b5=4
a+b=11   (i)

Variance =5.2
σ2=x2in(¯¯¯x)25.22=1+4+36+a2+b254226=41+a2+b280a2+b2=65   (ii)

From (i) and (ii)
a2+(11a)2=65
a2+12122a+a2=65
2a222a+56=0
a211a+28=0
(a4)(a7)=0
a=4 or 7
b=7 or 4

Hence, remaining two observations are 4 and 7.
 

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