Find the mode of the following distribution of marks obtained by the students in an examination:

Given the mean of the above distribution is 53, using empirical relationship estimate the value of its median.

To find mode, we have

Modal class = Interval with highest frequency = 60-80

Where, lower limit of modal class (l) = 60

Class interval (h) = 20 – 0 = 20

Frequency of the modal class (f₁) = 29

Frequency of the class before modal class (f₀) = 21

Frequency of the class after modal class (f₂) = 17

We have all the values needed, so now we’ll calculate mode of the given distribution.

Mode =

⇒ Mode =

⇒ Mode =

⇒ Mode =

⇒ Mode = 60 + 8 = 68

Hence, mode is 68.

Given: Mean of the distribution = 53

Using Empirical relationship, we shall find median. It is given by,

3 Median = Mode + 2 Mean

⇒ 3 Median = 68 + 2×53

⇒ 3 Median = 68 + 106 = 174

⇒ Median = 174/3

⇒ Median = 58

Hence, median of the given distribution is 58.