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Let x(1),x(2)….x(n) be n obervations .Le...

Let `x_(1),x_(2)….x_(n)` be n obervations .Let `w_(i)=lx_(i) +k " for " i=1,2….n,`where `l` and `k` are constants. If the mean of `x_(i)` is `48` and their standard deviation is `12` the mean of `w_(i)` 's is `55` and standard deviation of `w_(i) ` is `15` then the value of `l` and `k` should be

A

`l=1.25,k=-5`

B

`l=-1.25,k=5`

C

`l=2.5,k= -5`

D

`l=2.5, k=5 `

Text Solution

Verified by Experts

The correct Answer is:
A
Given `w_(i)=x_(i)+k,` `bar x_i=48,sx =12 ,w_(i)=55 and sw_(i)=15`
then `barw_(i)=barx_(i)+k`
` [ " where " barw_(i) " is man " w_(i) " and " bar x_(i) " is mean of " x_(i)s]`
`rArr 55=48+K`
Now SD of `w_(i)=" SD of " x_(i)`
`rArr 15=12 `
`rArr l=15/12`
From Eqs.(i) and (ii) `k=55-1.25 xx 48 `
` =-5 `
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