The following information gives the marks scored by the students of a class in an examination. Find the mode of the data. `{:("Marks",1-20,21-40,41-60,61-80,81-100),("Number of Students",3,18,23,37,19):}`

Explanation

Here, the given classes are not continuous. Hence, we first rewrite it as shown below:
`{:("Marks","Adjusted Marks","Number of Students"),(1-20," "0.5-20.5," "3),(21-40," "20.5-40.5," "18),(41-60," "40.5-60.5," "23(f_(i))),(61-80," "60.5-80.5," "37(f)),(81-100," "80.5-100.5," "19(f_(2))):}`
From the above table it can be observed that the maximum frequency occurs in the class interval 61-80.
`therefore f = 37, f_(1) = 23, f_(2) = 19, L_(1) = 60.5, C = 20`.
`" "therefore "Mode" = L_(1) + ((f-f_(1))C)/((f-f_(1)) + (f-f_(2)))`
`" " = 60.5 + ((37-23)20)/(14+18) = 60.5 + 8.75 = 69.25`.