# Measures of Central Tendency – Mean, Median & Mode A central tendency measure is a mono value that attempts to describe a set of data by identifying the data’s key position. As a result, measures of central tendency are also known as measures of central location. They’re also known as summary statistics. The mean (also known as the average) is probably the most familiar measure of central tendency, but there are others, such as the median and the mode. The mean median and mode are all valid measures of central tendency, but depending on the circumstances, some are more relevant to use than others. The mean mode median, as well as how to determine them and when they are most useful, will be discussed in the following article. So let’s get started.

## What is Median?

The median is the ordered data’s middle value. The most important part of calculating the median is arranging the data in ascending order from smallest to largest.

A data set’s median is the value in the middle of a data set arranged from smallest to largest.

The median in data sets 1, 2, 3, 4, 5, is 3.

When there are an even number of observations in a data set, the median is calculated by dividing the sum of the two middle values by two. So, in the following order: 1, 2, 3, 4, 5, 6, the median is (3+4)/2, which equals 3.5.

The median can be used with ordinal variables as well as interval variables with a skewed distribution.

Steps for calculating the median of a set of data are given below:

• Firstly you need to arrange the data in ascending order, smallest to largest.
• Find the median in the ordered data using (n+1)/2, where n is the sample size.
• The median is the value that represents the location discovered in Step 2.

### Observation on Odd and Even Sample Sizes

If the sample group is odd, the location point will produce a median value, which is an observed value. If the sample size is an even number, then the median must be calculated by taking the mean of two numbers. As shown in the example below, the result may or may not be an observed value.

## Definition of Mean

A mean is the basic mathematical average of two or more numbers. There are several methods for computing the mean for a given set of numbers, including the arithmetic mean method, which uses the sum of the numbers in the series, as well as the geometric mean method, which takes the average of a group of products. However, most of the time, all of the primary methods for computing a simple average produce the same approximate result.

## Definition of Mode

In a set of data values, the mode is the most common value. If X is a discrete random variable, the mode is the x-value at which the probability mass function maximises. In other words, it is the most likely value to be sampled.

## Keep in Mind!

The measures of central tendency are chosen based on the properties of any given data.

• All three measures of central tendency hold true when the distribution of continuous data is symmetrical. The mean, on the other hand, is used by most analysts because it includes all of the values in the distribution or dataset.
• If your distribution is skewed, the median is the best way to find the central tendency.
• The median and mode are the best ways to measure central tendency if you have the original data.
• The mode is the best option for determining the central tendency when dealing with categorical data.

To understand the topic in a fun and exciting way you can visit the Cuemath website.