Q. 63.7( 3 Votes )

The mean and vari

Answer :

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.


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