Question

The mean of n observations is X. If each observation is multiplied by k, the mean of new observations is

(a) $k\overline{X}$

(b) $\frac{\overline{X}}{k}$

(c) $\overline{X}+k$

(d) $\overline{X}-k$

Answer 1

Let us take n observations.

Ifbe the mean of the n observations, then we have

Multiply a constant k to each of the observations. Then the observations becomes

Ifbe the mean of the new observations, then we have

Hence, the correct choice is (a).