Question

The semi inter quartile range of the observations $9,12,14,6,23,36,20,7,42$ and $32$ is

• A. $12.75$
• B. $12.5$
• C. $11.5$
• D. $9.5$

Answer 1

Answer: (C)

$11.5$

The semi-interquartile range of a distribution is half the difference between the upper and lower quartiles, or half the interquartile range.
Arranging the observations in ascending order we get $6,7,9,12,14,20,23,32,36,42$

Median $=Q2=\frac{14+20}{2}=17$
The median of the numbers to the left of $Q2=Q1=9$
The median of the numbers to the right of $Q2=Q3=32.$
Semi interquartile range $=\frac{Q3-Q1}{2}=\frac{32-9}{2}=11.5$