The mean of 5 observations is 4.4 and their variance is 8.24. If three of the observations are 1, 2 and 6, find the other two observations.

Given, Mean of 5 observation is 4.4 and variance is 8.24.

To Find: Find the other two observation

Assumption: Let x and y be the other two observation. And Mean is 4.4

Here, Mean =

9+x+y=22

X+y=13 ……(1)

Now, Let Variance (X) be the variance of this observation which is to be 8.24

If is the mean than we get,

8.24 =

8.24 =

8.24 =

X²+y² =97 ……(2)

(x+y)²+(x-y)²=2(x²+y²)

By Subsititute the value we get,

13²+(x-y)²=2×97

(x-y)²=194-169

(x-y)²=25

x-y =±5 ……(3)

On solving equations (1) and (3) we get,

2x = 18

X = 9

And, y =4

Hence, The other two observations are 9 and 4.