CLASS-10
INTRODUCTION & 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

CLASS-10-Statistics-Median-Quartiles-Mode-2.png

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 -

CLASS-10-Statistics-Median-Quartiles-Mode-3.png

Ans.)  We have –

CLASS-10-Statistics-Median-Quartiles-Mode-4.png

          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.)

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