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The mean 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.

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Given,

The mean and variance of 7 observations are 8 and 16, respectively

Let the remaining two observations be x and y,

Observations: 2, 4, 10, 12, 14, x, y

∴ Mean, 

42 + x + y = 56

x  +  y  = 14     -(i)

Now, Variance,

Squaring (i), we get

Hence, From (i) and (v):

x – y = 2 ⇒ x = 8 and y = 6

x – y = -2 ⇒ x = 6 and y = 8

Therefore, The remaining observations are 6 and 8

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