The Mode in Statistics – Calculations with Examples

Time to read: 5 Minutes
Mode-Definition

There are several measures of central tendency in statistics, and one of these is the mode.

This post delves into this type of measure and how it is calculated. In addition, you will find examples and when it is relevant to use the mode in academic research.

The Mode – In a Nutshell

  • The mode refers to the figure that is most common in a dataset.
  • A dataset could be unimodal, bimodal, trimodal, or multimodal.
  • You can’t use this measure of central tendency in a dataset, where each value appears the same number of times.

Definition: Mode

This is the value that repeatedly appears in a given set. In other words, it is the value with the highest frequency in a particular set of data. This is one of the measures of central tendency.

Another measure you can use is the mean. This is the average of a dataset, and it is calculated by finding the sum of all the numbers in the set. You then need to divide this figure by the sample size (n).

The third measure is the median. This refers to the middle number in the set.

Multiple modes

Learn the different types of modes in the following:

Unimodal

These are datasets that have one value that appears most frequently. If the data is presented in a histogram, there will only be one peak.1

Mode unimodal distribution

Bimodal

Statistical distributions can have two modes, and these are referred to as bimodal datasets.1

Mode bimodal distribution

Trimodal

Trimodal datasets have three modes. With these datasets, there are three figures that will be appearing most frequently in the distribution.2

Mode trimodal distribution

Multimodal

Multimodal datasets have more than three modes. If the dataset is presented in a histogram, there will be more than three peaks.1

Mode multimodal distribution

Finding the mode

Finding this value is quite simple. You should follow these steps:

  1. Start by arranging the numbers in order.
  2. Then you can count how many times each number appears.
  3. You should then note the number which appears most frequently.3

Numerical mode

A numerical dataset uses numbers instead of natural language. These are also referred to as quantitative data. Since the data uses numbers, you can perform arithmetic operations on it.

Example of a numerical dataset:

The number 2 appears three times and is the most frequent figure in the distribution.

Categorical mode

A categorical dataset is a collection of information that is divided into groups. These datasets can either consist of nominal data or ordinal data.

Example of a categorical dataset.

Shirts worn by five children could be grouped based on the colors. These could be red, green, or blue.

The data collected may be presented as follows: {R, R, R, G, B}. In this distribution, the most frequently appearing color is red.4

Mode for grouped data

Grouped data is given in the form of class intervals. The mode can either be a class interval or a specific value.

  • Modal class: With this option, the mode is given as a category.
  • Modal value: The mode here will be given as a specific value instead of a class.

Example of grouped data:

The scores of 10 students can be as follows: 30, 30, 38, 39, 60, 73, 80, 84, 86, and 89. These can be placed in six categories, as you can see below:

  • 30 to 40 – 4
  • 41 to 50 – 0
  • 51 to 60 – 1
  • 61 to 70 – 0
  • 71 to 80 – 2
  • 81 to 90 – 3

The modal class here is 30 to 40. This is because the highest number of figures occur in this category. The modal value is 30 as it appears twice in the dataset.

No mode

A dataset where all value appears an equal number of times will not have a mode. With such datasets, this method can’t be used to locate the center of the distribution.

Example of a dataset that doesn’t have a mode:

Since each number appears once, you can’t find the most frequent value.5

When to use the mode

This measure of central tendency should be used with categorical data. In fact, it is the only measure of central tendency that you can use with categorical data.

The level of measurement will also determine whether this method will be the most suitable measure of central tendency. It should be used with ordinal data and discrete data.

It is also worth noting the cases where you should never use this method.

  • You shouldn’t use this measure if all values appear the same number of times.
  • Also, it shouldn’t be used if there is a very small number of values.6

FAQs

It is used to locate the most common value in a dataset. It helps researchers draw conclusions about different studies.

The different types are:

  • Unimodal
  • Bimodal
  • Trimodal
  • Multimodal

You can also use the median and mean as measures of central tendency.

Yes, it will be missing in a dataset where all values appear the same number of times.

Sources

1 SOS Statistics Online Support. “Histograms.“ Accessed December 8, 2022. https://sites.utexas.edu/sos/guided/descriptive/numericaldd/descriptiven2/histogram/.

2 Collegedunia Team. “Mode: Definition, Bimodal, Trimodal and Multimodal Values.” Collegedunia. November 11, 2022. https://collegedunia.com/exams/mode-mathematics-articleid-1465.

3 Hayes, Adam. “Mode: What It Is in Statistics and How to Calculate It.” Investopedia. May 19, 2022. https://www.investopedia.com/terms/m/mode.asp.

4 Formplus Blog. “Categorical Data: Definition + [Examples, Variables & Analysis].” Formplus. July 27, 2022. https://www.formpl.us/blog/categorical-data.

5 CueMath. “What if there is no mode in a data set of numbers?” Accessed December 8, 2022. https://www.cuemath.com/questions/what-if-there-is-no-mode-in-a-set-of-numbers/.

6 Frost, Jim. “Mean, Median, and Mode: Measures of Central Tendency.” Statistics By Jim. Accessed December 8, 2022. https://statisticsbyjim.com/basics/measures-central-tendency-mean-median-mode/.