The mode of the data

Marks	1 - 5	6 - 10	11 - 15	16 - 20	21 – 25
No. of students	7	10	16	32	24

 

Marks	26 - 30	31 - 35	36 - 40	41 – 45
No. of students	18	10	5	1

is

Concept:

Mode:

Mode is that value of the variable which occurs most frequently in a set of observations. In other words, mode of a frequency distribution is the value of the variable (x) corresponding to maximum frequency.

Mode of a grouped frequency distribution is given by the following formula:

\(mode =l + \frac{f_m - f_{m-1}}{2f_m - f_{m-1} - f_{m+1}}i\)
where l = lower limit of the modal class, fm = frequency of the modal class, fm-1 = frequency of the class preceding the modal class, fm+1 = frequency of the class succeeding the modal class, i = class interval.

Calculation:

Given:

We have the maximum number of students in the range 16-20 i.e. 32.

l = 16, f_m = 32, f_m-1 = 16, f_m+1 = 24, i = 4

\(mode = 16+\frac{32-16}{64-16-24} \times 4\)

mode = 18.66

Hence the mode will be 18.66.