The mean and variance of seven& observations are 8 and 16...

The mean and variance of seven& observations are

8

and

16

respectively. If five of the observations are

2, 4, 10, 12

and

14

, then the remaining two& observations are

Options

A $5, 7$
B $3, 5$
C $6, 8$
D $4, 2$

Correct answer

C. $6, 8$

Step-by-step solution

Let $x$ and $y$ be remaining $2$ observations
Mean $= 8 = \dfrac{2 + 4 + 10 + 12 + 14 + x + y}{7}$
$⇒x + y = 14$ ...(i)
Variance $= 16 = \dfrac{1}{7}\left({2}^{2} + {4}^{2} + 1{0}^{2} + 1{2}^{2} + x^{2} + y^{2}\right) - \left(8\right)^{2}$
$⇒x^{2} + y^{2} = 100$ ...(ii)
now solving equation (i) and (ii),& we get,

$x = 8, y = 6$ or $x = 6, y = 8$

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