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Question

# 50 students of economics, secured the following marks in an examination: Marks 20−25 25−30 30−35 35−40 40−45 45−50 50−55 55−60 60−65 65−70 Students 6 3 7 4 6 4 2 8 3 7 Calculate median.

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Solution

## Marks Student (f) Cumulative Frequency (c.f.) 20 − 25 25 − 30 30 − 35 35 − 40 40 − 45 45 − 50 50 − 55 55 − 60 60 − 65 65 − 70 6 3 7 4 6(f) 4 2 8 3 7 6 9 16 20 (c.f.) 26 30 32 40 43 50 N = ∑f = 50 Median class is given by the size of ${\left(\frac{N}{2}\right)}^{th}$ item, i.e.${\left(\frac{50}{2}\right)}^{th}$ item, which is 25th item. This corresponds to the class interval of (40 − 45), so this is the median class. $\mathrm{Median}={l}_{1}+\frac{\frac{N}{2}-c.f.}{f}×i\phantom{\rule{0ex}{0ex}}\mathrm{so},\mathrm{Median}={l}_{1}+\frac{\frac{50}{2}-c.f.}{f}×i\phantom{\rule{0ex}{0ex}}\mathrm{or},\mathrm{Median}=40+\frac{25-20}{6}×5\phantom{\rule{0ex}{0ex}}\mathrm{or},\mathrm{Median}=40+\frac{25}{6}\phantom{\rule{0ex}{0ex}}\mathrm{Thus},\mathrm{Median}=40+4.16=44.16$

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