The mean and variance of 8 observations are 10 and 13.5, respectively.

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:

Accepted Answer

Let the two remaining observations be x and y.

$$ \because $$ $$\bar x = 10 = {{5 + 7 + 10 + 12 + 14 + 15 + x + y} \over 8}$$

$$ \Rightarrow x + y = 17$$ ....(1)

$$ \because $$ $${\mathop {\rm var}} (x) = 13.5 = {{25 + 49 + 100 + 144 + 196 + 225 + {x^2} + {y^2}} \over 8} - {(10)^2}$$

$$ \Rightarrow {x^2} + {y^2} = 169$$ ....(2)

From (1) and (2)

(x, y) = (12, 5) or (5, 12)

So $$\left| {x - y} \right| = 7$$

Solutions · 1