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))bar(x)`
B. `(a+(1)/(a))(bar(x))/(2)`
C. `(a+(1)/(a))(bar(x))/(n)`
D. `((a+(1)/(a))bar(x))/(2n)`

Answer

B

Explanation

We know that, if x is the mean of `x_(1), x_(2),….., x_(n)` then
`bar(x) =(x_(1)+x_(2)+x_(3)+.....+ x_(n))/(n)`
`rArr x_(1)+x_(2)+x_(3)+.....+ x_(n) = nbar(x)`
Now, the mean of `ax_(1), ax_(2),…., ax_(n),(x_(1))/(a),(x_(2))/(a),....,(x_(n))/(a)` is
` " Mean "= ((ax_(1)+ax_(2)+ax_(3)+....+ax_(n))+ ((x_(1))/(a) +x_(2)/(a)+ ....+ x_(n)/(a)))/(n+n)`
`(nabar(x)+nbar(x)/(a))/(2n) = (nbar(x)(a+(1)/(a)))/(2n)=(bar(x)(a+(1)/(a)))/(2)=(a+(1)/(a))(bar(x))/(2)`
Hence, (b) is the correct answer.