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Worked Examples · Example 8
Q.

For the continuous series below (the same data as Worked Example 3), find (i) the median, (ii) the lower quartile Q₁ and (iii) the upper quartile Q₃.

Class interval0–1010–2020–3030–4040–50
Frequency (f)5815166
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ClassfCumulative frequency (cf)
0–1055
10–20813
20–301528
30–401644
40–50650

N = 50.

Median. N2=25\dfrac{N}{2} = 25. The first cf ≥ 25 is 28, in class 20–30, so this is the median class: L=20L=20, cf=13cf=13 (previous class), f=15f=15, h=10h=10.

Median=L+N2−cff×h=20+25−1315×10=20+1215×10=20+8=28Median = L + \dfrac{\frac{N}{2}-cf}{f}\times h = 20 + \dfrac{25-13}{15}\times10 = 20+\dfrac{12}{15}\times10 = 20+8 = 28

Lower quartile Q₁. N4=12.5\dfrac{N}{4} = 12.5. The first cf ≥ 12.5 is 13, in class 10–20, so this is the Q₁ class: L=10L=10, cf=5cf=5, f=8f=8, h=10h=10.

Q1=10+12.5−58×10=10+7.58×10=10+9.375=19.375Q_1 = 10 + \dfrac{12.5-5}{8}\times10 = 10+\dfrac{7.5}{8}\times10 = 10+9.375 = 19.375 …

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