Find the lower quartile, the upper quartile, the interquartile ra… - Vidyadip

Question

Find the lower quartile, the upper quartile, the interquartile range and the semi-interquartile range for the following frequency distributions:

Variate	10	11	12	13	14	15	16	17	18	19	20
Frequency	1	2	3	1	2	4	2	1	1	2	1

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Answer

Variate	Frequency (f)	Cumulative frequency
10	1	1
11	2	3
12	3	6
13	1	7
14	2	9
15	4	13
16	2	15
17	1	16
18	1	17
19	2	19
20	1	20

No. of terms $=20$
Lower Quartile $\left(Q_1\right)=\frac{n}{4}=\frac{20}{4}=5^{\text {th }}$ term $=12$
Upper Quartile $\left(Q_3\right)=\frac{n \times 3}{4}=\frac{20 \times 3}{4}=15^{\text {th }}$ term $=16$
Interquartile range $=Q_3-Q_1=16-12=4$
Semi-Interquartile range $=$$ \frac{Q_3-Q_1}{2}=\frac{16-12}{2}=2 $
Hence, Lower quartile $=12$, upper quartile $=16$, interquartile range $=4$, semi-interquartile range $=2$

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