Question

Compute quartile deviation for each of the following tables.

Class interval	frequency
$5-15$	$11$
$15-25$	$5$
$25-35$	$15$
$35-45$	$9$
$45-55$	$22$
$55-65$	$8$
$67-75$	$17$

Answer 1

Class Interval	Frequency	Cumulative Frequency
5-15 15-25 25-35 35-45 45-55 55-65 65-75	11 5 15 9 22 8 17	11 16 31 40 62 70 87
	$\sum f=87$

$N_3$ for $Q_3=\frac{3N}{4}=\frac{3\times 87}{4}=\mathrm{65.25.}$

$Q_1={\frac{n+1}{4}}^{th}term$

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

$Q_3=65+\frac{65.25-87}{17}\times 10=\mathrm{52.205.}$

$Q_1=h+\frac{N-C_f}{f}\times I$

$N_1$ for $Q_1=\frac{87}{4}=21.75$

Therefore, $Q_1=15+\frac{21.75-16}{5}\times 10\Rightarrow Q_1=15+11.5=26.5$

Therefore, Quartile deviation$=\frac{52.205-26.5}{2}=\mathrm{12.853.}$