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The mode is an important measure of central tendency in statistics because it is the only measure that can be used to accurately describe the most frequent value in a set of data. This makes it useful for describing characteristics of a population, such as the most popular color or the most common age range. It is also useful for determining the validity of data, as it can indicate if there are any outliers.
The mode represents the value that occurs most often in a dataset.
A dataset can have no mode (if no value repeats), one mode, or multiple modes.
For example, the mode in the following dataset is 19:
Dataset: 3, 4, 11, 15, 19, 19, 19, 22, 22, 23, 23, 26
This is the value that occurs most often.
In statistics, the mode is important for the following reasons:
Reason 1: It lets us know which value(s) in a dataset is the most common.
Reason 2: It’s useful for finding the most frequently occurring value in categorical data when the mean and median can’t be calculated.
Reason 3: It gives us an idea of where the “center” of a dataset is located, although the median and mean are more commonly used (as we’ll see later in this article).
The following examples illustrate each of these reasons in practice.
Reason 1: The Mode Tells Us Which Value is Most Common
Suppose we have a dataset with 100,000 rows that contain the selling price of houses throughout the United States:
Suppose we use some statistical software (like , , , etc.) to calculate the mode of this dataset and find that there are three modes:
- $280,000
- $300,000
- $305,000
This immediately gives us an idea of which house prices occur most frequently in the dataset.
Calculating the mode is also much quicker than staring at thousands of rows of data and attempting to identify which house prices occur most often.
Reason 2: The Mode Finds the Most Common Value in Categorical Data
Suppose we have a dataset with 1,000 rows that tells us the color of the car owned by individuals in a certain neighborhood:
The variable “color” is a , which means the values fall into categories (“red”, “yellow”, “black”, etc.) so we can’t calculate a quantitative value like the mean or median.
However, we can calculate the mode because this simply represents the most commonly occurring value in the dataset.
For example, we might use some statistical software to find that the mode of this dataset is “black” – which tells us that the most frequently occurring car color in this dataset is black.
Reason 3: The Mode Gives Us an Idea of Where the Center of a Dataset is Located
The mode is also considered a , which means it can give us an idea of where the “center” of the dataset is located.
For example, suppose we have the following dataset that shows the exam scores of 20 different students in a class:
The mode turns out to be 82 – this is the most common exam score. This also turns out to be a good indication of the where the “center” exam score value is located in this dataset.
However, suppose we instead had the following dataset of exam scores:
In this dataset, 72 is the mode exam score. However, this turns out to be a poor indication of where the “center” exam score is located.
The mean exam score is 82.9 and the median exam score is 82.5, which both give us a better idea of where the “center” value is located compared to the mode.
Summary
Here’s a quick summary of the main points made in this article:
- The mode represents the value(s) that occurs most often in a dataset.
- The mode tells us the most common value in categorical data when the mean and median can’t be used.
- The mode gives us an idea of where the “center” of a dataset is located, but it can be misleading compared to the mean or median.
The following tutorials provide additional information about the mean, median, and mode in statistics: