Q.Calculate coefficient of variation of marks secured by a student in the exam, where the marks are: 85, 91, 96, 88, 98, 82

$CV=\dfrac{\sigma}{\bar{x}}\times100=\dfrac{3}{10}\times100=30\%$.

The coefficient of variation expresses the standard deviation as a percentage of the mean:

$CV=\frac{\sigma}{\bar{x}}\times100=\frac{3}{10}\times100=30\%.$

$\text{CV}=\dfrac{\sigma}{\bar{x}}\times 100=\dfrac{5}{20}\times 100=25\%$.

Step 1 — the coefficient of variation is the relative measure

$\text{CV}=\dfrac{\sigma}{\bar{x}}\times 100$

Step 2 — substitute $\sigma=5$ and $\bar{x}=20$:

$\text{CV}=\dfrac{5}{20}\times 100=0.25\times 100=25\%$

$C.V.=\dfrac{\sigma}{\bar{x}}\times100=\dfrac{15}{75}\times100=20\%$.

The coefficient of variation measures relative dispersion:

$C.V.=\frac{\sigma}{\bar{x}}\times100.$

Substituting $\sigma=\text{₹}15$ and $\bar{x}=\text{₹}75$:

$C.V.=\frac{15}{75}\times100=\frac{1}{5}\times100=20\%.$

A relative measure is dimensionless; ₹10 has units ⇒ not relative.

Relative measures of dispersion (coefficient of range, coefficient of quartile deviation, coefficient of mean deviation, coefficient of variation) are formed by dividing one quantity in the same units by another, so the units cancel and the result is a pure number such as $0.22$, $0.33$ or $0.44$.

The value ₹$10$ is expressed in rupees, i.e. it still carries units — that is the hallmark of an absolute measure, not a relative one.

The blank is Variation.

The coefficient of variation (C.V.) is a relative (unit-free) measure of dispersion defined as

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

where $\sigma$ is the standard deviation and $\bar{x}$ the arithmetic mean. It is used to compare the variability or consistency of two or more series; the series with the lower C.V. is more consistent.