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 =


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.


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