Q. 55.0( 2 Votes )

The mean and vari

Answer :

Given: Mean of 5 observations = 4.4

and Variance of 5 observations = 8.24


Let the other two observations be x and y


, our observations are 1, 2, 6, x and y


Now, we know that,




5 × 4.4 = 9 + x + y


22 – 9= x + y


13 = x + y


or x + y = 13 …(i)


Also,


Variance = 8.24




So,




41.2 = 19.88 + (x2 + 19.36 – 8.8x) + (y2 + 19.36 – 8.8y)


41.2 – 19.88 = x2 + 19.36 – 8.8x + y2 + 19.36 – 8.8y


21.32 = x2 + y2 + 38.72 – 8.8(x + y)


x2 + y2 + 38.72 – 8.8(13) – 21.32 = 0 [from (i)]


x2 + y2 + 17.4 – 114.4 = 0


x2 + y2 – 97 = 0


x2 + y2 = 97 …(ii)


From eq. (i)


x + y = 17.4


Squaring both the sides, we get


(x + y)2 = (13)2


x2 + y2 + 2xy = 169


97 + 2xy = 169 [from (ii)]


2xy = 169 – 97


2xy = 72


xy = 36


…(iii)


Putting the value of x in eq. (i), we get


x + y = 13




y2 + 36 = 13y


y2 – 13y + 36 = 0


y2 – 4y – 9y + 36 = 0


y(y – 4) – 9(y – 4)= 0


(y – 4)(y – 9) = 0


y – 4 = 0 and y – 9 = 0


y = 4 and y = 9


For y = 4



Hence, x = 9, y = 4 are the remaining two observations


For y = 9



Hence, x = 4, y = 9 are the remaining two observations


Thus, remaining two observations are 4 and 9.


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