If the arithmetic mean of the numbers `x_1, x_2, x_3, ..., x_n` is `barx,` then the arithmetic mean of the numbers `ax_1 +b, ax_2 +b, ax_3 +b, ....,ax_n +b,` where a, b are two constants, would be

Options

A. `overline (x)`
B. `na overline(x)+nb`
C. `a overline(x)`
D. `a overline(x)+b`

Answer

D

Explanation

Required mean
`=((ax_(1)+b)+(ax_(2)+b)+..+(ax_(n)+b))/(n)`
`=(a(x_(1)+x_(2) +..+x_(n)))/(n)+b=a overlinex+b`
`(because (x_(1)+x_(2)+..+x_(n))/(n)=overline(x))`