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:

Marks	25	30	35	40	45	50
No. of students	6	15	12	10	18	9

✓

Answer

Marks	No. of students (f)	Cumulative frequency
25	6	6
30	15	21
35	12	33
40	10	43
45	18	61
50	9	70

No. of terms $=70$
Lower Quartile $\left( Q _1\right)=\frac{n}{4}=\frac{70}{4}=17.5^{\text {th }}$ term $=30$
Upper Quartile $\left( Q _3\right)=\frac{n \times 3}{4}=\frac{70 \times 3}{4}=52.5^{\text {th }}$ term $=45$
Interquartile range $=Q_3-Q_1=45-30=15$
Semi-Interquartile range $=$$ \frac{Q_3-Q_1}{2}=\frac{45-30}{2}=7.5 $
Hence, Lower quartile $=30$, upper quartile $=45$, interquartile range $=15$, semi -interquartile range $=$ 7.5

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