Variable 0−10 10−20 20−40 40−50 50−70

No. of Students 5 12 40 32 28

Open in App

Solution

In the given question, class intervals are not equal. For the calculation of mode, first the class intervals are made equal and frequencies are adjusted assuming that frequencies are equally distributed. In this manner, we get the following distribution.

Class Interval Frequency
(f)

0 − 10
10 − 20
20 − 30
30 − 40 5
12
20
20 f₀

40 − 50 32 f₁

50 − 60
60 − 70 14 f₂
14

By inspection, we can say that the modal class is (40 – 50) as it has the highest frequency of 32.
$Mode (Z) = l_{1} + \frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}} \times i or, Z = 40 + \frac{32 - 20}{2 (32) - 20 - 14} \times 10 or, Z = 40 + \frac{12}{64 - 34} \times 10 or, Z = 40 + \frac{120}{30} or, Z = 40 + 4 = 44 Hence, mode is 44 .$

Suggest Corrections

Marks	10−20	20−30	30−40	40−50	50−60
No. of students	12	18	14	63	19

Marks	0−10	10−20	20−30	30−40	40−50	50−60
Frequency	12	18	27	?	17	6

Variable	0−10	10−20	20−40	40−50	50−70
No. of Students	5	12	40	32	28