The mean and variance of eight observations are 9 and 9.25, respectively. If six of the observations are 6, 7, 10, 12, 12 and 13, find the remaining two observations.


Let us assume the remaining two observations to be x and y respectively such that,

Observations: 6, 7, 10, 12, 12, 13, x, y.


Mean,



60 + x + y = 72


x + y = 12 (i)




By using (i)





So, from equation (i) we have:



Thus, from (ii) and (iii), we have


2xy = 64 (iv)


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


x2 + y2 – 2xy = 80 – 64


x – y = 4 (v)


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


When x – y = 4 then x = 8 and y = 4


And, when x – y = - 4 then x = 4 and y = 8


The remaining observations are 4 and 8


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