Question 17
The monthly income of 100 families are given as below ?
$\begin{matrix} I n c o m e (i n R s) & N u m b e r o f f a m i l i e s 0 - 5000 & 8 5000 - 10000 & 26 10000 - 15000 & 41 15000 - 20000 & 16 20000 - 25000 & 3 25000 - 30000 & 3 30000 - 35000 & 2 35000 - 40000 & 1 \end{matrix}$
Calculate the modal income.

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Solution

In a given data, the highest frequency $f_{m}$ is 41, which lies in the interval 10000-15000.
$H e r e, l = 10000, f_{m} = 41, f_{1} (p r e c e d i n g) = 26, f_{2} (s u c c e d i n g) = 16 a n d h = 5000 M o d e = l + (\frac{f_{m} - f_{1}}{2 f_{m} - f_{1} - f_{2}}) \times h = 10000 + (\frac{41 - 26}{(2 \times 41) - 26 - 16}) \times 5000 = 10000 + (\frac{41 - 26}{82 - 40}) \times 5000 = 1000 + (\frac{15}{40}) \times 5000 = 10000 + (15 \times 125) = 10000 + 1875 = R s 11875$
Hence, the modal income is Rs 11875.

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