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 are2 and 94 and 73 and 85 and 6

Solution

The correct option is B 4 and 7Let two observations be a and b. Mean =1+2+6+a+b5=4 ⇒a+b=11   …(i) Variance =5.2 ∵σ2=∑x2in−(¯¯¯x)2⇒5.22=1+4+36+a2+b25−42⇒26=41+a2+b2−80⇒a2+b2=65   …(ii) From (i) and (ii) a2+(11−a)2=65 ⇒a2+121−22a+a2=65 ⇒2a2−22a+56=0 ⇒a2−11a+28=0 ⇒(a−4)(a−7)=0 ⇒a=4 or 7 ⇒b=7 or 4 Hence, remaining two observations are 4 and 7.

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