Q.(m) Find the interquartile range and quartile deviation from the three quartiles 36, 54 and 72.

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

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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: …

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

Quartile deviation (semi-interquartile range) is defined as

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

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

The coefficient of quartile deviation is

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

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

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

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:

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

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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:

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

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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 tw …