Question

Using raw data given below derive interquartile range, semiquartile range, and coefficient of quartile deviation. Choose the correct choice/s given below. Data given is $X=20,12,18,28,32,10$

• A. Interquartile range $=15.25$
• B. Coefficient of quartile deviation $=0.42$
• C. Coefficient of quartile deviation $=0.39$
• D. Semiquartile range $=7.01$

Answer 1

Answer: (A), (C)

Arrange the data in ascending order $X=10,12,18,20,25,32$
Number of items $=6$
$Q_1=(\frac{n+1}{4}{)}^{\frac{6}{n}}$ item $=(\frac{6+1}{4}{)}^{\text{th }}$ item
$Q_1=(1.75{)}^{\text{th }}$ item
So, $Q_1=I^{st}$ item $+0.75(2^{\text{nd }}.$ item $-{[}^{\text{st }}.$ item $)$
$=10+0.75(12-10)$
$=10+0.75(2)$
$=10+1.50=11.50$
$Q_3=3(\frac{N+1}{4}{)}^{\text{th }}$ item $=3(\frac{6+1}{4}{)}^{\text{th }}$ item
$Q_3=(5.25{)}^{\text{th }}$ item
$Q_3{=}^{\text{th }}$ item $+0.25(6^{\text{th }}.$ item $-5^{\text{th }}$ item $)$
$=25+0.25(32-25)$
$Q_3=25+0.25(7)=26.75$
Inter-quartile range $=Q_3-Q_1$
$=26.75-11.50=15.25$
Semi-quartile range
$=\frac{Q_3-Q_1}{2}=\frac{15.25}{2}=7.625$
Coefficient of quartile deviation
$=\frac{Q_3-Q_1}{Q_3+Q_1}=\frac{26.75-11.50}{26.75+11.50}$
$=\frac{15.25}{38.25}=0.39$