Answer :

This is a grouped frequency distribution table which is inclusive type.

We need to convert this inclusive type of data into exclusive type of data to find mode of these data values.


To convert to exclusive type of data, subtract 0.5 from the lower class of the interval and add 0.5 to the upper class of the interval.



Notice the greatest frequency is 32.


Modal class = 74.5 – 84.5


Mode is given by



Where,


L = Lower class limit of the modal class = 74.5


h = class interval of the modal class = 10


f1 = frequency of the modal class = 32


f0 = frequency of the class preceding the modal class = 19


f2 = frequency of the class succeeding the modal class = 12


Substituting values in the formula of mode,





Mode = 74.5 + 3.94


Mode = 78.44


Thus, mode is 78.44.


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