Question

Compute the mode of the following data:

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

 

Answer 1

Here, the maximum class frequency is 28, and the class corresponding to this frequency is 40 – 60. So, the modal class is 40 – 60.

Modal class = 40 – 60, lower limit (l) of modal class = 40, class size (h) = 20,
frequency `(f_1)` of the modal class = 28,
frequency `(f_0`) of class preceding the modal class = 16,
frequency `(f_2)` of class succeeding the modal class = 20
Now, let us substitute these values in the formula:

Mode = `l + ((f_1− f_0)/(2f_1− f_0− f_2)) × h`
       `= 40 + ((28−16)/(56−16−20)) × 20`
        `= 40 + ((12)/(20)) × 20`
        = 40 + 12
       = 52
Hence, the mode is 52.