Q. 44.5( 2 Votes )

# 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.

Answer :

**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 =

X^{2}+y^{2} =97 ……(2)

(x+y)^{2}+(x-y)^{2}=2(x^{2}+y^{2})

By Subsititute the value we get,

13^{2}+(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.**

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