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Question
The monthly income of 100 families are given as below:
| Income (in Rs) | 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.
Solution
In a given data, the highest frequency is 41, which lies in the interval 10000 – 15000.
Here, l = 10000, fm = 41, f1 = 26, f2 = 16 and h = 5000
∴ Mode = `l + ((f_m + f_1)/(2f_m - f_1 - f_2)) xx h`
= `10000 + ((41 - 26)/(2 xx 41 - 26 - 16)) xx 5000`
= `10000 + (15/(82 - 42)) xx 5000`
= `10000 + (15/40) xx 5000`
= 10000 + 15 × 125
= 10000 + 1875
= ₹ 11875
Hence, the modal income is ₹ 11875.
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