Question

Find the mode of the given data:

Class Interval	0 – 20	20 – 40	40 – 60	60 – 80
Frequency	15	6	18	10

 

Answer 1

Here the maximum class frequency is 18, and the class corresponding to this frequency is 40-60.
So, the modal class is 40-60.
Now,
Modal class = 40-60, lower limit (/) of modal class – 40, class size (h)=20,
Frequency `(f_1)` of the modal class =18,
Frequency (𝑓₀) of class preceding the modal class =6,
Frequency (𝑓₂) of class succeeding the modal class = 10.
Now, let us substitute these values in the formula:
𝑀𝑜𝑑𝑒=𝑙+`((f_1−f_0)/(2f_1−f_0−f_2)) ×ℎ`
`= 40+((18−6)/(36−6−10)) ×20`
`= 40+(12/20) ×20`
= 40+12
= 52
Hence, the mode is 52.