Forty persons were examined for their Hemoglobin % in blood (in mg per 100 ml) and the results were grouped as below:
| Hemoglobin % (mg/100 ml) |
13.1 - 14 | 14.1 - 15 | 15.1 - 16 | 16.1 - 17 | 17.1 - 18 |
|---|---|---|---|---|---|
| No. of persons | 8 | 12 | 10 | 6 | 4 |
Determine modal value of Hemoglobin % in blood of a person.
Solution:
Hemoglobin %
(mg / 100ml)Continuous class No. of persons 13.1 - 14 13.05 - 14.05 8 ($f_1$) 14.1 - 15 14.05 - 15.05 12 ($f_m$) 15.1 - 16 15.05 - 16.05 10 ($f_2$) 16.1 - 17 16.05 - 17.05 6 17.1 - 18 17.05 - 18.05 4 Here the maximum frequency $f_m = 12$
The corresponding class 14.05 - 15.05 is the modal class.
$L = 14.05$, $f_m = 12$, $f_1 = 8$, $f_2 = 10$, $h = 1$$$ \text{Mode} = L + \left( \frac{f_m - f_1}{2f_m - f_1 - f_2} \right) \times h $$
$$ = 14.05 + \left( \frac{12 - 8}{2(12) - 8 - 10} \right) \times 1 $$
$$ = 14.05 + \left( \frac{4}{24 - 18} \right) $$
$$ = 14.05 + \left( \frac{4}{6} \right) $$
$$ = 14.05 + \frac{2}{3} $$
$$ = 14.05 + 0.67 $$
$$ = 14.72 $$
Mode of hemoglobin is $14.72 \text{ mg}/100 \text{ ml}$.