Q. 205.0( 1 Vote )

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.

Answer :

Let us assume the remaining two observations be x and y

The given observations in the question are 2, 4, 10, 12, 14, x, y



x + y = 14 (i)


It is also given in the question that,


Variance = 16


We know that,






x2 + y2 = 112 - 12


x2 + y2 = 100 (ii)


Thus, by using (i) we have:


x2 + y2 + 2xy = 196 (iii)


Now, from equation (ii) and (iii) we have:


2xy = 196 – 100


2xy = 96 (iv)


Now subtracting equation (iv) from (ii), we get:


x2 + y2 – 2xy = 100 – 96


(x – y)2 = 4


x – y = 2 (v)


Hence, from equation (i) and (v) we have:


When x – y = 2 then x = 8 and y = 6


And, when x – y = - 2 then x = 6 and y = 8


The remaining observations are 6 and 8

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