Question

# Calculate the median from the following data: Marks Frequency Less than 10 5 Less than 20 20 Less than 30 45 Less than 40 80 Less than 50 100 Less than 60 115 Less than 70 125 Less than 80 130

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Solution

## Marks Class Interval Frequency (f) Cumulative Frequency (c.f.) Less than 10 Less than 20 Less than 30 0 − 10 10 − 20 20 − 30 5 15 25 5 20 45 c.f Less than 40 30 − 40 (f) 35 80 Less than 50 Less than 60 Less than 70 Less than 80 40 − 50 50 − 60 60 − 70 70 − 80 20 15 10 5 100 115 125 130 $\underset{}{N=\sum }f=130$ Median class is given by the size of ${\left(\frac{N}{2}\right)}^{th}$ item, i.e.${\left(\frac{130}{2}\right)}^{\mathrm{th}}$ item, which is 65th item. This corresponds to the class interval of 30 − 40, so this is the median class. $\mathrm{Median}={l}_{1}+\frac{\frac{N}{2}-c.f.}{f}×i\phantom{\rule{0ex}{0ex}}\mathrm{so},\mathrm{Median}={l}_{1}+\frac{\frac{130}{2}-c.f.}{f}×i\phantom{\rule{0ex}{0ex}}\mathrm{or},\mathrm{Median}=30+\frac{65-45}{35}×10\phantom{\rule{0ex}{0ex}}\mathrm{or},\mathrm{Median}=30+5.71=35.71\phantom{\rule{0ex}{0ex}}\mathrm{Thus},\mathrm{Median}=35.71$

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