For the following data obtain the mode.

This is a grouped frequency distribution and an inclusive type of data.

To find mode of this type of data, we must convert this inclusive type of data into exclusive type. For exclusive type data, we need to subtract 0.5 from lower limits of each class interval and add 0.5 to upper limits of each class intervals.

Also, we can interpret the column ‘No. of students’ as frequency.

Note that, highest frequency = 20

Corresponding class interval = 40.5 – 45.5

⇒ Modal class = 40.5 – 45.5

Mode is given by,

Where, l = lower limit of the modal class = 40.5

f = frequency of the modal class = 20

f₁ = frequency of the class preceding the modal class = 18

f₂ = frequency of the class succeeding the modal class = 14

c = width of the class interval = 5

Putting all these values in the modal formula,

⇒

⇒

⇒ Mode = 40.5 + 1.25

⇒ Mode = 41.75

Thus, the mode is 41.75.