Calculate mode from the following data:

Marks (more than) 0-9 10-19 20-29 30-39 40-49 50-59

No of students 2 5 15 25 10 3

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Solution

X

f

0 – 9.5

2

9.5 – 19.5 5

19.5 – 29.5

15

29.5 – 39.5

25

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

39.5 – 49.5

10

49.5 – 59.5

3

By inspection, we can spot that (29.5–39.5) has the highest frequency, i.e. 25. So, this is the modal class.
$Mode = l_{1} + \frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}} \times i = 29.5 + \frac{25 - 15}{2 \times 25 - 15 - 10} \times 10 = 29.5 + \frac{10}{25} \times 10 = 33.5$
Thus, the mode is 33.5.

Suggest Corrections

Marks	0−9	10−19	20−29	30−39	40−49	50−59
No. of Students	3	7	15	25	10	4

Marks	10−19	20−29	30−39	40−49	50−59	60−69	70−79	80−89	90−99
Number of Students	29	87	181	247	263	133	40	9	2

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

Marks	0−5	5−10	10−15	15−20	20−25	25−30	30−35	35−40
Number of Students	7	10	20	13	12	19	14	9

Class-intervals	10−29	30−39	40−49	50−59	59−60	60−69
Frequencies	12	19	20	21	15	13

Marks (more than)	0-9	10-19	20-29	30-39	40-49	50-59
No of students	2	5	15	25	10	3