Mode Formula: How to Calculate, Examples with Solution

Mode Formula: Mode is a fundamental concept in statistics. It refers to the value or values that occur most frequently in a dataset. In other words, it's the number or numbers that appear with the highest frequency. Unlike the mean (average) and median (middle value), a mode is not concerned with the numerical values. Instead, it focuses on frequencies of occurrence of a numerical value. If you are wondering why mode is important, mode is advantageous when dealing with categorical or discrete data, such as survey responses or census, where there may not be a clear numerical value. Understanding the mode helps us identify the central tendency or the most typical value within a set of data.

Also check: Median Formula: How to Calculate, Examples with Solution

Mode Meaning: What is Mode?

Mode is a way to determine which number or thing appears the most in a group of numbers or things. 

In other words, mode helps us see what's most popular in a group.

Mode Definition

The Mode is a statistical measure that represents the value that appears the maximum number of time in a given set of data observations. The mode is the number or item that appears most frequently in a set of data. In simpler terms, it's what exists or appears most often when you look at a set of things.

Mode Formula

Calculating the Mode depends on the data given. Based on whether the given dataset is grouped or ungrouped, the mode formula differs. 

Mode Formula For Ungrouped Data

Mode formula for ungrouped data: The most frequently occurred value in the data set

Explanation: If you have an ungrouped data set in hand, you should arrange the data set in ascending order or descending order. Otherwise, you should create a frequency distribution table. This will help you dind the repeated value with the highest frequency. 

Example: Find the mode of the following:

22, 34, 43,27, 37, 46, 46, 45, 39, 39, 29, 34, 39, 35, 35, 34, 39, 40, 41, 37, 46, 30, 30, 43, 30

Solution:

Data in ascending order = 22, 27, 29, 30, 30, 30, 34, 34, 34, 35, 35, 37, 37, 39, 39, 39, 39, 40, 41, 43, 43, 45, 46, 46, 46

Most frequent value = Mode = 39.

Mode Formula For Grouped Data

Since you cannot figure out the value with the maximum appearance in the given grouped data, follow the steps below to find out the mode formula for grouped data:

Step 1: Find the modal class. Modal class is the class interval with the maximum frequency.

Step 2: Using the ‘upper limit - lower limit’ of the modal class, determine the size of the modal class.

Step 3: Substitute the values in this formula to calculate the mode for grouped data”.

L + [(f1 -f0)/2f1-f0-f2)] x h. 

Here, 

L = Lower limit of the modal class

h = Size of the modal class 

f1 = Frequency of the modal class

f0 = Frequency of the class before the modal class

f2 = Frequency of the class after the modal class

Example:

Find the mode of the following dataset:

Step 1: Modal class = 10-15

Step 2: Modal class size =‘upper limit - lower limit’ 15-10 = 5

Step 3: Mode formula = L + [(f1 -f0)/(f1-f2)-f2)] x h.

L = Lower limit of the modal class = 10

h = Size of the modal class = 5

f1 = Frequency of the modal class = 7

f0 = Frequency of the class before the modal class = 3

f2 = Frequency of the class after the modal class = 2

Mode = 10+[(7-3)/(14-3-2)]x 5 

= 110/9

= 12.22 

Relationship between Mean, Median and Mode

Mean, median and mode are related as follows:

Mode = 3 Median - 2 Mean

Practice Questions on Mode Formula for Class 10

Que 1: What is the mode of 10, 9, 8, 7, 10, 9, 8, 10, 9, 7, 8, 7, 8?

Que 2: Calculate the mode from the dataset below:

Que 3: Calculate the mode from the dataset below:

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