Coefficients of Dispersion - Practice Questions & MCQ

Coefficients of Dispersion

The measure of variability which is independent of units is called the coefficient of dispersion

We have three such measures

1. Coefficients of Range

It equals $\frac{x_{\max }+x_{\min }}{x_{\max }+x_{\min }}$
Where $x_{\max }$ is the highest observation, and $x_{\min }$ is the lowest observation
2. Coefficients of Standard Deviation

It equals $\frac{\sigma}{\bar{x}}$
where $\sigma$ and $\bar{x}$ are the standard deviation and mean of the data.
3. Coefficients of Variation (denoted as C.V.)

The coefficient of variation is defined as

$
\text { C.V. }=\frac{\sigma}{\bar{x}} \times 100, \bar{x} \neq 0
$

where $\sigma$ and $\bar{x}$ are the standard deviation and mean of the data.

For comparing the variability or dispersion of two series, we calculate the coefficient of variance for each series. The series having greater C.V. is said to be more variable than the other. The series having lesser C.V. is said to be more consistent than the other and thus is considered better.