Question

There are 6 observations in a set of data and their mean is 12. If each observation is multiplied by 2, find the new mean.

Answer 1

Given:

Number of data (N) $=6$

Mean (m) $=12$

Let the 6 observations are given as: $x_1,x_2,x_3,x_4,x_5,x_6$

So, mean(m) $=\frac{x_1+x_2+x_3+x_4+x_5+x_6}{6}$

$12=\frac{x_1+x_2+x_3+x_4+x_5+x_6}{6}$.........(1)

Now, If each observation is multiplied by 2

New mean $=\frac{2x_1+2x_2+2x_3+2x_4+2x_5+2x_6}{6}$

New mean $=2\left(\frac{x_1+x_2+x_3+x_4+x_5+x_6}{6}\right)$

New mean $=2\times 12$ (from eq 1.)

New mean $=24$