Hello non-math friends! Yes, you probably already heard about average and median at school or in the news

Does someone try to confuse you by using two words for the same thing? I’ll tell you the difference today 🙂

**In mathematics, average and median are different. The average is the sum of the values divided by the number of values, while the median is the central point in a set of values (so there are as many upper values than the lower ones).**

As it’s probably not clear enough in two sentences if you have difficulties with this, I will give you more details and also examples in the following parts

## The average

### Definition

The result you get by adding two or more amounts together and dividing the total by the number of amounts

Cambridge Dictionary

This definition doesn’t help more than my introduction

But I suppose that your problem is not really the average definition, so I’ll move quickly to the following

### Usage

**The most common type of average is the arithmetic mean**It’s commonly used in countries using numbers for school evaluation, but you can use it in any situations where you want to analyze a set of number (the average price for a flight to Japan, the average size of your children, 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’ll see later that this is not always the best way to do for other kinds of data

### Example

I’ll use again the example of the price for a flight from New-York to Japan

Let’s say that you find three different airlines companies:

- Cathay Pacific: $700
- Asiana: $800
- ANA: $1,300

What’s the average?

Like I wrote earlier, **start adding all the values**

That’s to say: 800+900+1300, the total is 3000

You now **divide the total by the number of values (3)**

So 3000/3 is 1000**The average price for this flight is $1,000**

## The median

Let’s move now to the median, probably less known

### Definition

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 middle values if there is no one middle number

Merriam-Webster

The median is more a statistic term than mathematic

**The goal of a median is to find the central point in a set of values**

When found, you must have as many upper than lower values

### Usage

We generally use the median when the values aren’t evenly distributed

For example, it’s the case for salaries**An average salary doesn’t make sense, the median salary is a better information**

For example, if you include unemployed and billionaires, what the real sense of the average?

That’s why the median is better. **The median excludes the extremes, to find the central point. **That is more relevant, mainly for big sets of values

I will show you that in the next example

### Example

Here is an example with different values. I will show you the result for average and median on this set

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

- Anitha: $1,500
- Robert: $1,800
- Raymond: $1,000
- Jack: $25,000
- Bill: $350,000

I’ll not do the math, as tools like Microsoft Excel allow you to make it directly. You can also use a scientific calculator

(In this case, there is no real calculation to do, but hey I don’t spoil you ^^)

I’ll go directly to the result, and explain it to you just after:

So, I just type the same values in Excel

With the results above, you can see that **the average salary is $75,860**

But there is no sense, as nobody except Bill get this salary level

So it’s not a good idea of the reality

**But the median salary tells us the central point, at $1,800**As the set of values is small, it’s not really a better idea of the situation, but this result is still much closer to reality

We have 2 people over 1800, and 2 under 1800, so it’s exactly what we wanted

## Related questions

**How to get the median and average in Excel?** For the average you have the information displayed directly while selecting a data set (bottom right). And you can also use the functions: AVERAGE() and MEDIAN() to find it

## Conclusion

You now know the difference between the average (= arithmetic mean) and the median in mathematic or statistic

It’s important to well remember this difference to not be confused while reading a statistic or an article

I only presented here a quick comparison of these two values

Be aware that there are other variations, and that there are other statistics functions such as standard deviation or variance.

Maybe for another post? 🙂