The mean and variance of 8 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.
Given, Mean of 8 observation is 9 and variance is 9.25.
To Find: Find the other two observation
Assumption: Let x and y be the other two observation. And Mean is 9
Here, Mean =
60+x+y=72
X+y=12 ……(1)
Now, Let Variance (X) be the variance of this observation which is to be 9.25
If is the mean than we get,
9.25 =
9.25 =
642+x2+y2=722
X2+y2 =80 ---(2)
(x+y)2+(x-y)2=2(x2+y2)
By Subsititute the value we get,
122+(x-y)2=2×80
(x-y)2=160-144
(x-y)2=14
x-y =±4 ……(3)
On solving equations (1) and (3) we get,
X= 8, 4
And y = 4,8
Hence, The other two observations are 8 and 4.