The maximum bowling speed (kms/hour) of 33 players at a cricket coaching centre is given below:
| Bowling speed (kms / hr) | 85 - 100 | 100 - 115 | 115 - 130 | 130 - 145 |
|---|---|---|---|---|
| No. of players | 9 | 11 | 8 | 5 |
Find the modal bowling speed of a player.
Solution:
Bowling speed (kms / hr.) No. of players 85 - 100 9 $f_1$ 100 - 115 11 $f_m$ 115 - 130 8 $f_2$ 130 - 145 5 Here the maximum frequency $f_m = 11$.
The corresponding class 100 - 115 is the modal class.
$L = 100$, $f_m = 11$, $f_1 = 9$, $f_2 = 8$, $h = 15$.$$ \text{Mode} = L + \left( \frac{f_m - f_1}{2f_m - f_1 - f_2} \right) \times h $$ $$ = 100 + \left( \frac{11 - 9}{2(11) - 9 - 8} \right) \times 15 $$ $$ = 100 + \left( \frac{2}{22 - 17} \right) \times 15 $$ $$ = 100 + \left( \frac{30}{5} \right) $$ $$ = 100 + 6 $$ $$ = 106 $$Mode of bowling speed is 106 km/hr.