Question

Find the Quartile deviation and Co-efficient of Quartile deviation of the following data.
$3,8,11,13,17,19,20,22,23,27,31$

Answer 1

$Q_1=\frac{n+1}{4}thterm=\frac{11+1}{4}thterm=3^{rd}term$

$3^{rd}term=11$

$\therefore$ $Q_1=11$

$Q_3=\frac{3(n+1)}{4}thterm=\frac{3(11+1)}{4}=9^{th}term$

$9^{th}term=23$

$\therefore$ $Q_3=23$

$\Rightarrow$ $Quartiledeviation=\frac{Q_3-Q_1}{2}$

$=\frac{23-11}{2}$

$=\frac{12}{2}$

$=6$

$\Rightarrow$ Coefficient of Quartile deviation $=\frac{Q_3-Q_1}{Q_3+Q_1}\times 100$

$=\frac{23-11}{23+11}\times 100$

$=\frac{12}{34}\times 100$

$=35.29$