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If the arithmetic mean of the observatio...

If the arithmetic mean of the observations `x_1,x_2,x_3,.............x_n` is `1`, then the arithmetic mean of `x_1/k,x_2/k,x_3/k,.............x_n/k , (k >0)` is

A

greater than 1

B

Less than 1

C

equal to 1

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
We have,
`(x_(1)+x_(2)+x_(3)+ ..+x_(n))/(n)=1 rArr x_(1)+x_(2)+x_(3)+ ... +x_(n)=n`
`therefore` Required arithmetic mean `((x_(1))/(k)+(x_(2))/(k)+ ...+ (x_(n))/(k))/(n)`
`=(1)/(k)((x_(1)+x_(2)+ ... +x_(n))/(n))=(1)/(k)`
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