Q.The marks obtained (out of 25) by 9 students in a class test are: 12, 18, 9, 22, 15, 20, 11, 17, 14. Find the Quartile Deviation and its Coefficient.

A quartile is a partition value, not a measure of dispersion.

Measures of dispersion quantify the spread of data: range, mean deviation and standard deviation all do this. A quartile by itself ($Q_1,Q_2,Q_3$) only locates a position in the data. (It is the quartile deviation $\tfrac{Q_3-Q_1}{2}$, not a lone quartile, that measures spread.)

Semi-interquartile range $=\dfrac{Q_3-Q_1}{2}$.

The interquartile range is $Q_3-Q_1$; its half is the semi-interquartile range, also called the quartile deviation:

$Q.D.=\frac{Q_3-Q_1}{2}.$

$Q_3-Q_1 = 2\times\dfrac{Q_3-Q_1}{2}=2\times$ Quartile deviation.

Quartile deviation (semi-interquartile range) is defined as

$Q.D.=\frac{Q_3-Q_1}{2}.$

Therefore the difference between the largest quartile $Q_3$ and the smallest quartile $Q_1$ is

$Q_3-Q_1 = 2\times Q.D.$

$\dfrac{62.63-31.75}{62.63+31.75}=\dfrac{30.88}{94.38}\approx0.33$.

The coefficient of quartile deviation is

$\frac{Q_3-Q_1}{Q_3+Q_1}.$

With $Q_1=\text{₹}31.75$ and $Q_3=\text{₹}62.63$:

$Q_3-Q_1=30.88,\qquad Q_3+Q_1=94.38,$

$\text{Coeff. of Q.D.}=\frac{30.88}{94.38}=0.327\approx0.33.$

The rupee units cancel, so the result is a pure number $0.33$ (not ₹0.33).

IQR $=Q_3-Q_1$ (half of it is the quartile deviation).

The interquartile range measures the range covered by the central half of the distribution:

$\text{IQR}=Q_3-Q_1.$

Halving it gives the quartile deviation $\dfrac{Q_3-Q_1}{2}$, but the interquartile range itself is the plain difference.

The correct term is Quartile deviation — $Q.D. = \dfrac{Q_3 - Q_1}{2}$.

The measure described, one-half of the gap between the upper and lower quartiles, is the quartile deviation, also called the semi-interquartile range:

$Q.D. = \frac{Q_3 - Q_1}{2}$

The standard deviation is an entirely different measure — it is the positive square root of the mean of the squared deviations taken from the arithmetic mean, $\sigma = \sqrt{\dfrac{\sum (x-\bar{x})^2}{N}}$. So "Standard" is the wrong word here.

The blank is Quartile.

The interquartile range is $Q_3 - Q_1$. Half of it, $\dfrac{Q_3 - Q_1}{2}$, is called the semi-interquartile range, and this is precisely the definition of the quartile deviation. Hence the two terms are synonyms.