Question

Consider the following statements:
$1.$ Variance is unaffected by change of origin and change of scale.
$2.$ Coefficient of variance is independent of the unit of observations.
Which of the statements given above is/ are correct?

• A. $1$ only
• B. $2$ only
• C. Both $1$ and $2$
• D. Neither $1$ nor $2$

Answer 1

Answer: (B)

$2$ only

Variance is independent of change of origin as the change in origin is uniformly added to all the values and hence the mean also and hence, when $(x-\overline{x}{)}^2$ is calculated, it remains unaffected. But, change of scale alters all values unevenly and hence, variation changes.

The coefficient of variance is standard deviation by mean which doesn't depend on the unit of observation.

So, Statement 1 is incorrect Statement 2 is correct