Find the mode of the following frequency distribution:


Marks



10 - 20



20 - 30



30 - 40



40 - 50



50 - 60



Number of students



12



35



45



25



13


Here, the maximum class frequency is 45.

The class corresponding to this frequency is the modal class. ⇒ modal class = 30 - 40


∴ lower limit of the modal class (l) = 30


Modal class size (h) = 10


Frequency of the modal class (f1) = 45


Frequency of class preceding the modal class (f0) = 35


Frequency of class succeeding the modal (f2) = 25


Mode is given by,



⇒


⇒


⇒ Mode = 30 + 3.33 = 33.33


Hence, the mode is 33.33


1