If `barx` is the mean of `x_(1), x_(2), …………., x_(n)`, then for `a ne 0`, the mean of `ax_(1), ax_(2),…….., ax_(n), x_(1)/a, x_(2)/a, ……….., x_(n)/a` is

Options

A. `(a + 1/a)barx`
B. `(a +1/a)barx/2`
C. `(a+1/a)barx/n`
D. `((a+1/a)barx)/(2n)`

Answer

B

Explanation

Required mean = `(ax_(1) +ax_(2) +….+ax_(n))+((x_(1)/a+x_(2)/a +…..+x_(n)/a))/(2n)`
`=1/2{(a(x_(1)+x_(2)+......+x_(n)))/n+(1/a(x_(1)+x_(2)+......+x_(n)))/n}`
`1/2 { aoverlinex+1/aoverlinex} = (a+1/aoverlinex} = (a+1/a)overlinex/2`