Calculate mode from the following data:

Class Interval 0-10 10-20 20-30 30-40 40-50 50-70

Frequency 7 10 8 20 32 28

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Solution

X

f

0 – 10

7

10 – 20 10

20 – 30 8

30 – 40

20

40 – 50

32

$\underset{}{\to}$ Modal class

50 – 70

28

By inspection, we can spot that (40 – 50) has the highest frequency, i.e. 32. So, this is the modal class.
$Mode = l_{1} + \frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}} \times i = 40 + \frac{32 - 20}{2 \times 32 - 20 - 14} \times 10 = 40 + \frac{12}{30} \times 10 = 44$
Thus, the mode is 44.
Note, f₂ will be 14 as the adjusted frequency for the class 50 - 70 is 14.

Suggest Corrections

Variable	0−10	10−20	20−30	30−40	40−50	50−60	60−70
Frequency	10	20	35	40	25	25	15

Marks	10−20	20−30	30−40	40−50	50−60	60−70
No. of Students	8	11	9	25	12	16

Marks	0−10	10−20	20−30	30−40	40−50	50−60	60−70	70−80
Number of Students	2	18	30	45	35	20	6	3

Class Interval	0−5	5−10	10−15	15−20	20−25	25−30
Frequency	20	24	32	28	20	26

Class Interval	0-10	10-20	20-30	30-40	40-50	50-70
Frequency	7	10	8	20	32	28

Class	0-10	10-20	20-30	30-40	40-50	50-60	60-70
Frequency	5	10	18	30	20	12	5