What is Mode and How to Calculate It?

Welcome to the third in the series of the articles on Basic Statistics. Mode is the third measure of central tendency. In our previous articles, we have discussed the following two:

  1. Mean (Average): Mean is essentially the sum of all values in a data set divided by number of values in that data set. To know about mean, please read our article on What is Mean?
  2. Median: Median is the exact center value in the data set when the data is arranged in a chronological order. To know more about median, please read our article on What is Median?

In this post, we are going to explain what mode is.

What is Mode?

Conceptually, mode is probably the simplest to understand. Mode simply is the most frequently occurring number in a data set. Let’s explain this with the help of an example. Let’s say you have the following data:

Attribute # of Errors
Active Listening 1
Language and Grammar 2
SOP Followed 2
Empathy and Courtesy 4

 

Can you find out the most frequently occurring value in the table above? Of course, it is ‘2’. And hence, the mode of that data set is 2.

Let’s give you another example and we encourage that you find out the mode for the following data set before reading this article further:

Basket Weight in KGs
Basket 1 5
Basket 2 6
Basket 3 6
Basket 4 6
Basket 5 5
Basket 6 4
Basket 7 3
Basket 8 5
Basket 9 1
Basket 10 7

 

Did you find out the mode for the table above? Stumped? There are two values that occur most frequently in that data set. Those values are 5 and 6. So, will there be 2 modes for this data set? Yes! There will be two modes in this data set – 5 and 7. Such data distributions are called bi-modal distributions.

Now! Let’s give you another example:

Game # of Goals
Game 1 2
Game 2 2
Game 3 3
Game 4 3
Game 5 4
Game 6 4
Game 7 5
Game 8 6
Game 9 1
Game 10 7

 

There are 3 modes for the attached data set – 2, 3 and 4. Such data distributions are called multi-modal distributions.

We will give you one last example to build a complete understanding of what mode is:

Player # of Runs Scored
Player 1 22
Player 2 34
Player 3 12
Player 4 0
Player 5 9

 

Can you calculate the mode for the data above? We encourage that you do. Which number occurs most frequently in that data set? Well! Each number appears a single time in that data set. So, is there no mode in that data?

Yes! This is no mode in this data set. This is the biggest disadvantage while using mode as your measure of central tendency.

So, there are 3 kinds of data distributions based on mode: Single-mode data distribution, bi-modal distribution and multi-modal distribution. Each of these distributions has its unique qualities which are out of scope for this article.

Hope you enjoyed learning!

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