# Average : Mean versus Median

The average of a set of numbers is a commonly used, but the defintion of average is poorly understood and can raise the risk of being manipulated.

The average of a set of numbers can be determined with the **mean** or the **median**. To better understand the difference between mean and median I will explain the definition of both and illustrate it with examples.

#### The difference between mean and median

Understanding the difference between the mean and median allows you to take advantage of one another and prevent the risk of being **manipulated**. To illustrate the **difference** we’ll take this set of 5 numbers:

**4 2 14 2 3**

##### Mean

The mean is the also known as the **arithmetic** **mean** and is calculated by adding N numbers in a data set together and dividing it by **N**. The mean of the 5 numbers above is **5.0**

4 + 2 + 14 + 2 + 3 / 5 = **5.0**

##### Median

The median of a data set is the **middle** number when the set is sorted in numerical order. With an odd-numbered data set this is the number that is in the middle. When there is an even-numbered data set the mean of the two middle numbers is taken. The median of the 5 numbers above is **3.0**

Odd-numbered : 2 + 2 + **3** + 4 + 14 = **3.0**

Even-numbered: 2 + 2 + **3 + 4** + 5 + 14 = (3 + 4) / 2 = **3.5**

#### When to use what

In most cases the ari**thmetic mean** is used as the **average** of a data set since it will the take all numbers in the data set in the calculation. In other words, each number in the data set has **influence** on the outcome. If this outcome should not be influenced by **spikes** (high or low) the median will give a better result.

##### An example

A small town with 500 residents earn roughly € 50,000.- per year. Both the median and mean are around € 50.000,-. Now a (super wealthy) family moves in to town, their income is around **€ 1 Billion** a year.

The median income stays around € 50.000,- per year (since all 500 others stil earn around € 50.000,- per year) but the aritmethic mean is **€2.025 million!**

Although nothing has **changed** for the 500 citizens, the way the numbers are presented might affect them. For instance when the tax paid is based on the average income (…).

#### Service levels / performance metrics / ROI

Now what happens if we take this knowledge to our **daily** lives? There are numerous of examples where the average of a set of numbers is used. For instance “The average response time was 100 milliseconds, that’s great!” or “The average load on server X was 10% so the request to order a new server is **denied**.”

#### Conclusion

**Juggling** with numbers is easy, the result can be transformed into a better suiting result (for the **presenter**) just by using a different methodology of calculating the average. Knowing the difference in mean and median can help you **prevent** being misled or **manipulated**, it might even help **you** doing so.

Ingmar Verheij