Mode

The mode, also known as modal value, indicates the most frequent value in a dataset. This number provides an approximate estimate of which elements in a data collection appear most frequently. Mean, median, and mode are three related but different measures of central tendency. 

Mode = L +  ((f_m- f₁)/(2f_m- f₁- f₂)) × h

Here: 

L = Lower limit of the modal class

h = Class interval size

fₘ = Frequency of the modal class

f₁ = Frequency of the class before the modal class

f₂ = Frequency of the class after the modal class

The modal class represents the data interval with the highest frequency.

• In statistics, the mode is the most frequently observed value in a collection of data
  
   
• In the normal distribution, the mean, median, and mode are the same.
  
   
• In many circumstances, the modal value will not match the data's average value.
   

There are different types of modes depending on the number of modal solutions. We will now see the different types of modes:

Unimodal:

If the dataset has only one mode, it is called unimodal.

For example: In set A= {2, 3, 3, 5, 6, 6, 6, 7}, the mode is 6.

Bimodal:

If there are two modes present in the given data, it is called bimodal.

For example: In set B = {3, 3, 3, 5, 7, 7, 7, 4}, the modes are 3 and 7 because both numbers are repeated three times.

Trimodal:

If there are exactly three modes in a dataset, it is called trimodal.

For example: In set C =  {3, 3, 3, 5, 5, 5, 6, 7, 7, 7, 4}, the modes are 3, 5, and 7 as each of these numbers are repeated three times.

Multimodal:

A dataset can contain multiple modes and if it has more than three modes, it is known as multimodal.

For example: if set A= {1, 2, 2, 2, 3 4, 4, 4, 5, 6, 6, 6, 8, 8, 8,}, the data set has four modes: 2, 4, 6, 8 as these numbers are repeated the same number of times.

The Merits and Demerits of Mode are discussed below:

To calculate the mode of ungrouped data,

• List the values in the dataset in either increasing or decreasing order.
  
   
• Count how many times each value occurs in the dataset.
  
   
• Identify the number that appears the most times, which is the mode.
  
   
• Based on frequency, the mode can be categorized as unimodal, bimodal, trimodal, or multimodal.
   

Understanding the differences between mean, median, and mode enables solving the problems related to them easily. The key differences are listed below:

The mode is the most frequently used in real-life applications such as businesses, social media, etc. Let’s understand the top uses of mode in day-to-day life. 

Businesses:

Businesses use mode quite often to understand which product is in demand. The mode techniques help in understanding the on-demand product, any increase in production rate, etc.

Fashion Retail Industry:

In fashion stores, the retailers will stock up on the most sold sizes, colors, or styles of fashion clothing by using the mode to maximize their sales.

Social Media:

Social media influencers use mode to decide what type of content they should post on social media by analyzing their likes, shares, and comments over their mode value. 

Transportation:

In many countries, the mode is used to analyze which time is the most frequently traveled, to understand the most crowded time of buses, trains, or any public transports.