The mean and variance of 8 observations are 10 and 13.5, respectively. If 6 of these observations are 5,7,10,12,14,15, then the absolute difference of the remaining two observations is :

Question

The mean and variance of 8 observations are 10 and 13.5, respectively. If 6 of these observations are 5,7,10,12,14,15, then the absolute difference of the remaining two observations is : (A) 7 (B) 3 (C) 5 (D) 9

Tardigrade Admin · Accepted Answer

barx=10 ⇒ barx-(63+a+b/8)=10 ⇒ a+b=17 dots(1) Since, variance is independent of origin. So, we subtract 10 from each observation. So, σ2=13.5=(79+(a-10)2+(b-10)2/8)-(10-10)2 ⇒ a2+b2-20(a+b)=-171 ⇒ a2+b2=169 dots(2) From (i) (ii); a=12 b=5

Q. The mean and variance of 8 observations are 10 and 13.5, respectively. If 6 of these observations are 5,7,10,12,14,15, then the absolute difference of the remaining two observations is :

7

3

5

9

xˉ=10 ⇒xˉ−863+a+b​=10 ⇒a+b=17…(1) Since, variance is independent of origin. So, we subtract 10 from each observation. So, σ2=13.5=879+(a−10)2+(b−10)2​−(10−10)2 ⇒a2+b2−20(a+b)=−171 ⇒a2+b2=169…(2) From (i) & (ii); a=12&b=5

Q. The mean and variance of $8$ observations are $10$ and $13.5,$ respectively. If $6$ of these observations are $5, 7, 10, 12, 14, 15,$ then the absolute difference of the remaining two observations is :