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Question

# Find the missing frequency form the following distribution, if median is 35 and N = 170. Variables 0−10 10−20 20−30 30−40 40−50 50−60 60−70 Frequency 10 20 ? 40 ? 25 15

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Solution

## Given, Median = 35 N=170 Let the missing frequencies be f1 & f2. Class Interval Frequency (f) Cumulative Frequency 0 − 10 10 − 20 20 − 30 10 20 f1 10 30 30 + f1 (c.f.) 30 − 40 40 (f) 70 + f1 40 − 50 50 − 60 60 − 70 f2 25 15 70 + f1 + f2 95 + f1 + f2 110 + f1 + f2 N = ∑f =170 Median class is given by the size of ${\left(\frac{N}{2}\right)}^{\mathrm{th}}$ item, i.e.${\left(\frac{170}{2}\right)}^{\mathrm{th}}$ item, which is 85th item. This corresponds to the class interval of (30 − 40) as median is 35. $\mathrm{Median}={l}_{1}+\frac{\frac{N}{2}-c.f.}{f}×i\phantom{\rule{0ex}{0ex}}\mathrm{so},35=30+\frac{\frac{170}{2}-\left(30+{f}_{1}\right)}{40}×10\phantom{\rule{0ex}{0ex}}\mathrm{or},35=30+\frac{85-30-{f}_{1}}{40}×10\phantom{\rule{0ex}{0ex}}\mathrm{or},20=55-{f}_{1}\phantom{\rule{0ex}{0ex}}\mathrm{or},{f}_{1}=35\phantom{\rule{0ex}{0ex}}⇒{f}_{1}=35\phantom{\rule{0ex}{0ex}}$ 110 + f1 + f2 = 170 or, f2 = 170 − 110 − 35 $⇒$ f2 = 25 Therefore, f1 is 35 and f2 is 25.

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