Question

Find the mode of the following distribution:

Marks	10 – 20	20 – 30	30 – 40	40 – 50	50 – 60
Frequency	12	35	45	25	13

Answer 1

Here, the maximum class frequency is 45, and the class corresponding to this frequency is 30 – 40. So, the modal class is 30- 40.
Now,
Modal class = 30 – 40, lower limit (l) of modal class = 30, class size (h) = 10,
frequency `(f_1)` of the modal class = 45,
frequency `(f_0)` of class preceding the modal class = 35,
frequency `(f_2)` of class succeeding the modal class = 25
Now, let us substitute these values in the formula:
Mode = `l + ((f_1− f_0)/(2f_1− f_0− f_2)) × h`
           `= 30 + ((45−35)/(90−35−25)) × 10`
           `= 30 + ((10)/(30)) × 10`
            = 30 + 3.33
            = 33.33
Hence, the mode is 33.33.