# CLASS-10INTRODUCTION & DEFINATION OF MODE

MODE

The value around which there is the greatest concentration is called mode.

Example) Given below is the number of pairs of shoes of different sizes sold by a shop

Ans.) Since, the sale of size 8 is maximum, the modal shoe size is 8

Mode for Individual Data

In the case of individual data, the mode is the variate which occurs most frequently.

Empirical Formulae

We may calculate the mode by using the formulae –

Mode = 3 (median) – 2 (mean)

Example.1) The marks obtained by 14 students in a class are given below –

35, 25, 14, 23, 24, 30, 28, 25, 33, 25, 33, 27, 22

Find the modal marks.

Ans.) Arranging the data in ascending order we get,

14, 22, 23, 24, 25, 25, 25, 26, 27, 28, 30, 33, 33, 35

Clearly, 25 occurs the maximum number of times

Hence, Mode = 25            (Ans.)

Example.2)  Find the mode and median of the following frequency distribution -

Ans.)  We have –

So, n = 29, which is odd

29 + 1

Median =  value of (---------)th observation

2

=  value of 15th observation = 13

Since the frequency corresponding to 14 is maximum, so the mode is 14    (Ans.)