Find the mode of the following data:
Class 0−20 20−40 40−60 60−80
Frequency 15 6 18 10

Open in App

Solution

We have to find the mode of the following distribution,
Class 0-20 20-40 40-60 60-80
Frequency 15 6 18 10
The class (40-60) has the maximum frequency; therefore this is the modal class.
Lower limit of the modal class
Width of the class interval h = 20
Frequency of the modal class f_k = 18
Frequency of the class preceding the modal class f_k₋₁ = 6
Frequency of the class succeeding the modal class f_k₊₁ = 10
Now, we have the following formula to find the value of mode.
Mode = $x_{k} + h (\frac{f_{k} - f_{k - 1}}{2 f_{k} - f_{k - 1} - f_{k + 1}}) = 40 + 20 \times \frac{18 - 6}{2 \times 18 - 6 - 10}$
$= 40 + 12$
$= 52$
Hence, the value of mode is 52.

Suggest Corrections

Similar questions

Compute the mode of the following data: [CBSE 2013]

Class	0−20	20−40	40−60	60−80	80−100
Frequency	25	16	28	20	5

Class interval	0−20	20−40	40−60	60−80
Frequency	15	6	18	10

Class	0−10	10−20	20−30	30−40	40−50	50−60	60−70
Frequency	6	8	10	15	5	4	2

Class-interval	20−40	40−60	60−80	80−100	100−120	120−140	140−160
Frequency	3	7	11	15	13	6	2

Marks	0−10	10−20	20−30	30−40	40−50	50−60	60−70	70−80
No. of Students	2	18	30	45	35	20	6	3

Join BYJU'S Learning Program