Question

# Given below is the distribution of total household expenditure of 200 manual workers in a city: Expenditure (in Rs) No. of manual workers 1000-1500 24 1500-2000 40 2000-2500 31 2500-3000 28 3000-3500 32 3500-4000 23 4000-4500 17 4500-5000 5 Find the expenditure done by maximum number of manual workers.

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Solution

## As the class 1500-2000 has the maximum frequency, it is the modal class. $\mathrm{Now},{x}_{k}=1500,h=500,{f}_{k}=40,{f}_{k-1}=24\mathrm{and}{f}_{k+1}=31\phantom{\rule{0ex}{0ex}}\therefore \mathrm{Mode},{M}_{0}={x}_{k}+\left\{h×\frac{\left({f}_{k}-{f}_{k-1}\right)}{\left(2{f}_{k}-{f}_{k-1}-{f}_{k+1}\right)}\right\}\phantom{\rule{0ex}{0ex}}=1500+\left\{500×\frac{\left(40-24\right)}{\left(2×40-24-31\right)}\right\}\phantom{\rule{0ex}{0ex}}=1500+\left\{500×\frac{16}{25}\right\}\phantom{\rule{0ex}{0ex}}=\left(1500+320\right)\phantom{\rule{0ex}{0ex}}=1820\phantom{\rule{0ex}{0ex}}$ Hence, mode = Rs 1820

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