(Q7). The marks distribution of 30 students in a mathematics examination are given in the adjacent table. Find the mode of this data. Also compare and interpret the mode and the mean.

Class Interval	Number of Students(fi)	Class Marks(xi)	fixi
10-25	2	17.5
25-40	3	32.5
40-55	7	47.5
55-70	6	62.5
70-85	6	77.5
85-100	6	92.5
Total	∑fi = 30	-	∑fixi =

Solution : Since the maximum number of students (i.e., 7) have got marks in the interval, 40-65 the modal class is 40 - 55.

Now,

  The lower boundary(l) of modal class = 40, class size (h) = 15

  Frequency of the modal class (f₁) = 7,

  Frequency of class preceding the modal class (f₀) = 3,

  Frequency of class succeeding the modal class (f₂) = 6.

Now, let us substitute these values in the formula-

Mode = l + [

f₁ - f₀

2f₁ - f₀ - f₂

] × h
Mode = + [

-

2 × - -

] × =

Therefore, the mode of the data above is