Find mode of the following distribution:
Class 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50
Frequency 4 7 13 9 3

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Solution

Here from table it is clear that maximum frequency is 13 and its corresponding class is 20 - 40
So, modal class = 20 - 30
Thus, I = 20, $f_{1} = 13, f_{0} = 7, f_{2} = 9$ and $h = 10$
$∵$ Mode $= l + (\frac{f_{1} - f_{2}}{2 f_{1} - f_{0} - f_{2}}) \times h$
$= 20 + (\frac{13 - 7}{2 \times 14 - 7 - 9}) \times 10$
$= 20 + (\frac{6 \times 10}{26 - 16})$
$= 20 + \frac{60}{10} = 20 + 6 = 26$
Thus, required mode = 26

Suggest Corrections

Class	0-10	10-20	20-30	30-40	40-50
$f$	6	10	13	7	4

Class	0-10	10-20	20-30	30-40	40-50
Frequency	$7$	$15$	$13$	$17$	$10$

Class	0-10	10-20	20-30	30-40	40-50
Frequency	6	4	3	K	2

Class	0-10	10-20	20-30	30-40	40-50	50-60
Frequence	6	7	15	16	4	2

Class Interval	0 - 10	10 - 20	20 - 30	30 - 40	40 - 50	50 - 60	60 - 70	70 - 80
Frequency	7	14	13	12	20	11	15	8