The following table shows frequency distribution of body weight (in gms) of fish in a pond. Find modal body weight of a fish in a pond.
| Body weight (in gms) |
15-15.9 | 16-16.9 | 17-17.9 | 18-18.9 | 19-19.9 | 20-20.9 |
|---|---|---|---|---|---|---|
| No. of fish | 2 | 4 | 8 | 6 | 6 | 4 |
Solution:
Body weight
(in gms)Continuous class No. of fish 15 - 15.9 14.95 - 15.95 2 16 - 16.9 15.95 - 16.95 4 $f_1$ 17 - 17.9 16.95 - 17.95 8 $f_m$ 18 - 18.9 17.95 - 18.95 6 $f_2$ 19 - 19.9 18.95 - 19.95 6 20 - 20.9 19.95 - 20.95 4 Here the maximum frequency $f_m = 8$
The corresponding class $16.95 - 17.95$ is the modal class.
$L = 16.95, f_m = 8, f_1 = 4, f_2 = 6, h = 1$$$ \begin{aligned} \text{Mode} &= L + \left( \frac{f_m - f_1}{2f_m - f_1 - f_2} \right) \times h \\ &= 16.95 + \left( \frac{8 - 4}{2(8) - 4 - 6} \right) \times 1 \\ &= 16.95 + \left( \frac{4}{6} \right) \\ &= 16.95 + 0.67 \\ &= 17.62 \end{aligned} $$
Mode of body weight is $17.62 \text{ gm}$.