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Question

# The median value for the following frequency distribution is 35 and the sum of the all frequencies is 170. Using the formula for median, find the missing frequencies. Class 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

## Let, ${f}_{1}\mathrm{and}{f}_{2}$ be the frequencies of the class intervals 20-30 and 40-50, respectively. $\mathrm{Then}10+20+{f}_{1}+40+{f}_{2}+25+15=170\phantom{\rule{0ex}{0ex}}⇒{f}_{1}+{f}_{2}=60$ The median is 35 which lies in the class of 30-40. So, the median class is 30-40. $\mathrm{Now},l=30,h=10,f=40,N=170\mathrm{and}cf=10+20+{f}_{1}={f}_{1}+30\phantom{\rule{0ex}{0ex}}\therefore \mathrm{Median},M=l+\left\{h×\frac{\left(\frac{N}{2}-cf\right)}{f}\right\}\phantom{\rule{0ex}{0ex}}⇒30+\left[10×\frac{85-\left({f}_{1}+30\right)}{40}\right]=35\phantom{\rule{0ex}{0ex}}⇒30+\frac{55-{f}_{1}}{4}=35\phantom{\rule{0ex}{0ex}}⇒55-{f}_{1}=20\phantom{\rule{0ex}{0ex}}⇒{f}_{1}=35\phantom{\rule{0ex}{0ex}}\mathrm{Now},{f}_{2}=\left(60-35\right)=25\phantom{\rule{0ex}{0ex}}\mathrm{Hence},{f}_{1}=35and{f}_{2}=25$

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