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Question

# The monthly income of 100 families are given as below : Income in ( in ₹) Number of families 0-5000 8 5000-10000 26 10000-15000 41 15000-20000 16 20000-25000 3 25000-30000 3 30000-35000 2 35000-40000 1 Calculate the modal income.

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Solution

## The maximum class frequency is 41. The class corresponding to this frequency is 10000–15000. So, the modal class is 10000–15000. l (the lower limit of modal class) = 10000 f1 (frequency of the modal class) = 41 f0 (frequency of the class preceding the modal class) = 26 f2 (frequency of the class succeeding the modal class) = 16 h (class size) = 5000 $\mathrm{Mode}=l+\left(\frac{{f}_{1}-{f}_{0}}{2{f}_{1}-{f}_{0}-{f}_{2}}\right)×h\phantom{\rule{0ex}{0ex}}=10000+\left(\frac{41-26}{2×41-26-16}\right)×5000\phantom{\rule{0ex}{0ex}}=10000+\frac{15}{40}×5000\phantom{\rule{0ex}{0ex}}=10000+1875\phantom{\rule{0ex}{0ex}}=11875$ Thus, the modal income is ₹11875.

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