Mean and median difference / tabular form

Hello non-mathematical friends! Surely you have already heard about the mean and median in school, in the news or in your company. But do you really know their difference? Has anyone ever tried to confuse you by using these two words for the same thing? If you want to know the differences between these two mathematical concepts, pay attention because we explain them here. Mean and median difference / tabular form

What is the difference between the mean and median?

In statistics, the mean is the average of a data set and the median is the mean value of the organized data set. Both values have their own importance and play a different role in collecting and organizing data.

In math, the mean equals the sum of the values divided by the number of values. Instead, the median is the center point in a set of values, so there are as many upper values as there are lower values.

If you are not very familiar with mathematical or financial concepts, these definitions probably have not made the differences clear to you. But do not worry, below we will give you more details and examples so that you can understand it easily.

Comparative table between mean and median

Half	Median
The average arithmetic of a given set of numbers is called the Mean.	The method of separating the highest sample with the lowest value, usually from a probability distribution, is called the median.
The application of the mean is for normal distributions.	The main application of the median is skewed distributions.
There are many external factors that limit the use of Mean.	It is much more robust and reliable at measuring data for uneven data.
The mean can be found by calculating by adding all the values and dividing the total by the number of values.	The median can be found by listing all the available numbers in the set by arranging the order and then finding the number in the center of the distribution.
The mean is considered an arithmetic mean.	The median is considered a positional average.
It is very sensitive to outliers.	It is not very sensitive to outliers.
Defines the core value of the data set.	Defines the center of gravity of the midpoint of the data set.

What is the mean ?

Definition of mean

The mean is the result obtained by adding two or more quantities and dividing the total by the number of quantities

This definition does not help a little more to understand the introduction mentioned above. Likewise, to finish clarifying the concept, we are going to put practical examples. Mean and median difference / tabular form

Use of the mean

The most common type of mean is the arithmetic mean and is commonly used in countries that use numbers for school assessment, but you can use it in any situation where you want to analyze a set of numbers. For example to calculate the average price of the flights of your trips, the average height of your family, etc.

We generally use the average for relatively small sets of values, and only if we know all the values when doing the math

You will see later that this is not always the best way to do it for other types of data

Example Mean and median difference / tabular form

To give an example, let’s take the average price of a flight from Madrid to Paris
Let’s say you find three different airlines:

As we discussed before, start adding all the values
that is: 800 + 900 + 1300, the total is 3000

Now divide the total by the number of values (3)
So 3000/3 is 1000
The average price of this flight is 1,000 €

What is the median ?

Let’s now discover the median, probably a less known and common concept.

Definition of median

The median is a value in an ordered set of values below and above which there is an equal number of values or which is the arithmetic mean of the two mean values if there is no mean number.

As we see in the definition, the median is more of a statistical term than a mathematical one. The goal of a median is to find the center point in a set of values. So when found it should have both upper and lower values

Using the median Mean and median difference / tabular form

Usually we use the median when the values are not uniformly distributed

For example, it is the case of wages, an average salary does not make sense, the average salary is better information. For example, if the unemployed and billionaires are included, what is the true meaning of the average?

So the median is better, since it excludes the extremes, to find the midpoint. In this way, the result is more relevant. Especially for large sets of values. To demonstrate this, here is an example:

Example of application of the median

Here is an example with different values. I’ll show you the result for the mean and the median in this set.

Let’s say we have 5 people, here are their salaries:

Ana: € 1,500
Roberto: € 1,800
Ramón: € 1,000
Juan: € 25,000
Berto: € 350,000

I will not do the accounts, since tools like Microsoft Excel allow you to do them directly. You can also use a scientific calculator.

Ana	1,500
Robert	1,800
Ramon	1,000
Juan	25,000
Berto	350,000
Half	75,860
Median	1,800

With the results above, you can see that the average salary is € 75,860 .
But it does not make sense, since no one, except Berto, no one has this salary level. So this data is a bit far from reality

On the other hand, the average salary tells us the central point at € 1,800. Since the set of values is small, it is not really the best idea of the situation, but this result is still much closer to reality. We have 2 people over 1800, and 2 under 1800, so that’s exactly what we wanted

Conclusion Mean and median difference / tabular form

Now you know the difference between the mean (= arithmetic mean) and the median in math or statistics.

It is important to remember this difference well so as not to get confused when reading a statistic or an article

We have only presented here a quick comparison of these two values.
Be aware that there are other variations, and that there are other statistical functions such as the standard deviation or the variant.

Mohammad Asif Goraya

M A Goraya has qualification of M.phil in Agricultural Sciences. He has almost 15 years of teaching Experience at college and university level. He likes to share his research based knowledge with his students and audience.