What is quartile deviation ?

Please explain briefly with example.

quartile deviation is half the difference between upper quartile and lower quartile in a distribution.
it is a measure of the spread through the middle half of the distribution.
it can be useful because it is not influenced by extremely high or extremely low.
QD = $\frac{Q_3-Q_1}{2}$
now let us discuss the following example:
1. find the quartile deviation for the following data:
2,4,6,7,11,22,33
solution: since the given numbers are already arranged in increasing order.
and the number of terms = 7
lower quartile $Q_1=\frac{n+1}{4}th term=\frac{7+1}{4}i.e. 2nd term$
therefore $Q_1=4$
upper quartile $Q_3=\frac{3(n+1)}{4}th term = \frac{3*8}{4}=6th term$
$Q_3=22$
quartile deviation QD = $\frac{22-4}{2}=9$
now again consider the case when number of terms are 8.
find the QD for the given data; 2,4, 6, 7,11,22,28,30
solution: the number of terms = 8
lower quartile $Q_1=\frac{n+1}{4}th term =\frac{8+1}{4}=2.25th term$
$$\begin{gathered} Q_1=2nd value +0.25(3rd value - 2nd value) \\ =4+0.25(6-4) \\ =4+0.5 \\ {Q}_1=4.5 \end{gathered}$$
upper quartile $Q_3=\frac{3(n+1)}{4}th term =\frac{27}{4}=6.75th term$
$$\begin{gathered} Q_3=6th term +0.75(7th term - 6th term) \\ =22+0.75*(28-22) \\ =22+4.5 \\ =26.5 \end{gathered}$$
QD = $\frac{Q_3-Q_1}{2}=\frac{26.5-4.5}{2}=11$
hope this helps you.
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