Home
Class 12
MATHS
The mean and variance of 7 observations ...

The mean and variance of 7 observations are 8 and 16, respectively. If five of the observations are 2, 4, 10, 12, 14. Find the remaining two observations.

A

48

B

40

C

45

D

49

Text Solution

Verified by Experts

The correct Answer is:
A
Mean `=(a+b+2+4=10+12+14)/(7)=8rArr(a+b+42)/(7)=8`
Variance = 16 `" " a+b+42=56`
`V=(sumx^2)/(N)-mu^2" "a+b=14`
`V=(a^2+b^2+2^2+4^2+10^2+12^2+14^2)/(7)-8^2`
`16=(a^2+b^2+460)/7-64`
`80=(a^2+b^2+460)/7`
`560=a^2+b^2+460`
`a^2+b^2=100`
`a^2+b^2=100`
`(a+b)^2-2ab=100`
`(14)^2-2ab=100`
`196-2ab=100`
`196-100=2ab`
`96/2=abimpliesab=48`
Promotional Banner

Similar Questions

Explore conceptually related problems

The mean and variance of 7 observations are 7 and 22 respectively. If 5 of the observations are 2, 4, 10, 12, 14, then the remaining 2 observations are

The mean and variance of eight observations are 9 and 9.25 ,respectively.If six of the observations are 6,7,10,12,12 and 13, find the remaining two observations.

The mean and variance of seven observations are 8 and 16 respectively. If five of these are 2,4,10,12,14, find the remaining two observations.

The mean and variance of 7 observations are 8 and 16 , respectively . If five observations are 2 , 4 , 10 , 12 , 14 , then the absolute difference of the remaining two observations is :

The mean and variance of 7 observations are 8 and 16 respectively. If two observations are 6 and 8, then the variance of the remaining 5 observations is :

The mean and variance of 5 observations are 4 and 5.2 respectively, out of them if three observation are 1, 2, 6 then remaining two observations will be

Mean and variance of 7 observation 2,4,10,12,14,x,y are 8 and 16 respectively. find xy is