Question

The quartile deviation for the data

x :	2	3	4	5	6
f :	3	4	8	4	1

is

• A. $\frac{1}{2}$
• B. $1$
• C. $\frac{1}{4}$
• D. $0$

Answer 1

Answer: (B)

$1$

$x$	$f$	Cumulative Frequency
2	3	3
3	4	7
4	8	15
5	4	19
6	1	20
Total	20

Here, $n=20$
$Q_1=(\frac{20+1}{4}{)}^{th}observation$
$=\frac{21}{4}={5.25}^{th}observation$
So, $Q_1=3$
$Q_3=\frac{3(n+1)}{4}{)}^{th}observation$
$=\frac{63}{4}={15.75}^{th}observation$
So, $Q_3=5$
Quartile deviation $=\frac{Q_3-Q_1}{2}$
$=\frac{5-3}{2}=1$