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The monthly income of 100 families is given as below. Rs.[[1]] is the modal income.

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Detailed Solution

The monthly income of 100 families is given as below. Rs.11875 is the modal income.
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From the table we have maximum class frequency = 41
And the modal class is 10000-1500 whose lower limit is l=10000 and class size is h=5000. The frequency of the modal class is

f 1 = 41

, frequency of class preceding the modal class is

f 0 = 26

and frequency of class succeeding the modal class is

f 2 = 16

.
Substituting the following value in mode formula,

Mode = l + f 1 − f 0 2 f 1 − f 0 − f 2 h

Mode = 10000 + 41 − 26 241 − 26 − 16 5000 ⇒ 10000 + 15 82 − 42 5000 ⇒ 10000 + 15125 ⇒ R s .11875

So, required income is Rs. 11875.

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