The mean and variance of 7 observations are 8 and 16, respectively. If five of the observations are 2, 4, 10, 12, 14. Find the remaining two observations.

Explanation

Let the two numbers be x and y. Then,

mean`=>(2+4+10+12+14+x+y)/7=8`

`=> 42 + x + y = 56`

`=> x + y = 14 . . . (i)`

Also, variance `=16

=> (1/7) (2^2+4^2+10^2+(12)^2+(14)^2+x^2+y^2)−8^2=16`

`=> ( 1/7) (460+x^2+y^2)=80`

`=> x2+y2=100 . . . (ii)`

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