Mode – Definition – Examples

In this tutorial, we shall learn about mode and how to find mode of a given observation.

Definition: 

The mode of a data set is the value, occurring most frequently in set of observations. In other words, a data set having highest frequency of observations is its mode.

How to find the mode 

There are 3 steps to find the mode.  

Step 1: Put the numbers in numerical order from lowest to highest.

Step 2: Count how many times each number occurs.

 Step 3: The number that occurs the most often is the mode.

Example: Find the mode of the following set of data.

2, 3, 5, 9, 5, 4, 5, 6, 5, 7, 5.

Step 1: Put the numbers in numerical order(lowest to highest).

2, 3, 4, 5, 5, 5, 5, 5, 6, 7, 9.

Step 2: Count how many times each number 
occurs. Here 5 comes five times. 

Step 3: The mode is the number in data set, that occurs most often.  The mode is 5, because 5 occurred more than times than the other numbers.

A distribution with a single or one mode is called “Unimodal”.

Example: Find the mode of the following set of data.

11, 13, 25, 19, 25, 14, 25, 36, 25, 37.

Put the numbers in numerical order(lowest to highest).

11, 13, 14, 19, 25, 25, 25, 25, 36, 37

The mode is 25, because 25 occurred more than times than the other numbers. 

Bimodal – Trimodal – Multimodal modes   

There is a possibility that a data set have more than one observations of same frequency i.e. a data set could have more than one mode. 

In that case a data set having two modes is called “bimodal”.

A set of numbers with three modes is called “Trimodal”.

A set of numbers with four or more than four modes is called “Multimodal”.

Example: Data are 2, 5, 9, 10, 3, 2, 4, 2, 9, 6, 8, 7, 9.

First we put the numbers in order.

2, 2, 2, 3, 4, 5, 6, 7, 8, 9, 9, 9, 10.

Observe the numbers, 2 and 9 both numbers occurs three times and no other number occurs more often.

So there are two modes 2 and 9.

No mode:

If in a set, no numbers occurs more than once, then that set has no mode.

2, 4, 6, 7, 9, 11, 26, 35, 42, 28

In above set of numbers no numbers occurs more than once, then the set has no mode. If the observations are given in the form of a frequency table, the mode is the value that has the highest frequency.

Example: Find the mode of the following set of marks.

Solution: Mode is 6, because 6 has the highest frequency 60.

The frequency table below shows the weights of 5  bags of apples. Find the mode? 

Mode is 33kg(highest frequency of bags of apples)

Note: A set of observation, may have no mode, one mode or more than one mode.