Autor: Codenga 29.09.2023

What is the Difference Between Mean and Median

You surely know the concept of the average value. It's one of those concepts that you can encounter almost everywhere: average grades, average salary, average housing price. Fewer people are familiar with the concept of the mediana It's a shame because it's equally important, and in many situations, it's a much better measure than the simple average.

In this article, we will explain the basic differences between the mean and the median.

Arithmetic Mean

Terms like "average" or "arithmetic mean" roughly mean the same thing. It's simply the average value from a set of data. Let's take this example set of values:

3, 5, 7, 2, 1

How do we calculate the average value? Very simple: we add up all the values and divide by their quantity.

Average = 18/5 = 3.6

So, we have an average of 3.6.

Median

The median is the middle value in a set. The calculation method depends on whether the number of values in the set is even or odd. If the number of values is odd, we calculate it like this:

Sort the values from smallest to largest.
Take the value exactly in the middle – this is our median.

If the number of values in the set is even, we calculate the median like this:

Sort the values from smallest to largest.
Take the two values in the middle.
Calculate the average of these two values.

Let's return to our data set: 3, 5, 7, 2, 1. The number of values is odd, so we calculate the median as follows:

Sorting: 1, 2, 3, 5, 7 Take the middle value: 3 is the median of this data set.

Another example - two values in the middle:

Now let's try to calculate the median for this data set (even number of values):

4, 3, 8, 2, 6, 1

Sorting: 1, 2, 3, 4, 6, 8
Take two values from the middle: 3, 4
Calculate the average of these values: 3 + 4 = 7 / 2 = 3.5
The median of this data set is 3.5.

When to Use Mean and When to Use Median

The average value can be misleading in many situations because it is highly sensitive to extremely large or extremely small values. Take a look at this example:

4, 5, 2, 99, 2, 5

The arithmetic mean for this set is 19.5. However, the median is only 4.5. Why such a big difference? In the set, we have a value of 99, which significantly deviates from the other values and greatly inflates the mean.

That's why we often use the median because it is not as sensitive to extreme values. The median better reflects the real state of the data set. Most values in our set are around 4, and the value 99 is an outlier. The median accurately represents this situation, while the mean is skewed by the exceptionally high value.

Real-World Applications

In everyday language, we often talk about the average salary, for example. After reading the previous paragraphs, you now know that the mean can significantly deviate from the actual situation. This average salary is likely inflated by a small group of high earners. Therefore, in such a situation, it's better to use the concept of the median. The median will typically be much lower than the mean but will better reflect the real income of the average person.

You can find many more examples like this: average housing price and median housing prices, average grades and median grades, and so on.