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**Meaning of the Median**

**Median** is the middle number of a set of numbers arranged in ascending or descending order of magnitude. If it is even, add the two middle numbers and divide the sum by two.

The **median** is a central position statistic that splits the distribution in two, that is, it leaves the same number of values on one side as on the other.

To calculate the **median** it is important that the data are ordered from highest to lowest, or vice versa from lowest to highest. That is, they have an order.

For example, to find the **median** of * 10, 17, 5, 18, 2, 17, 19 and 13*, you need to arrange the scores in ascending order of magnitude as follows:

*The median of the scores from this arrangement is therefore:*

**2, 5, 10, 13, 17, 17, 18, 19.****13 + 17 / 2 = 30 / 2 = 15.**

But if it is odd, then the formula for locating the **median** is to pick the most central figure when arranged in ascending order of magnitude.

The **median**, together with the **mean** and the **variance**, is a very illustrative statistic of a distribution. Unlike the **mean**, which can be shifted to one side or the other, depending on the distribution, the **median** is always located in the center of the distribution.

Incidentally, the shape of the distribution is known as **kurtosis**. With **kurtosis** we can see where the distribution is shifting.

**Formula for the Median**

Once the **median** is defined, we are going to calculate it. For this, we will need a formula.

The *formula* will not give us the value of the **median**, what it will give us is the position in which it is within the data set. We must take into account, in this sense, if the total number of data or observations that we have (n) is even or odd. So the median formula is:

*When the number of observations is even:*

**Median** = (n+1) / 2 → Mean of the observations

*When the number of observations is odd:*

**Median** = (n+1) / 2 → Observation value

In other words, if we have ** 50** data ordered preferably from smallest to largest, the

**median**would be in observation number

*. This is the result of applying the formula for an even data set (50 is an even number) and dividing by 2.*

**25.5**The result is * 25.5* since we divided by

*The median will be the mean between observation*

**50+1.****and**

*25***.**

*26***Advantages of the use of Median**

- It is simple to calculate and understand.
- Extreme items do not affect its value.
- It can be used for measuring qualities and factors to which a more rigorous mathematical measurement cannot be applied.
- It can be calculated from incomplete data.
- It can be determined from frequency diagrams.

**Disadvantages of the use of Median**

- If the items are few, it is not likely to be a fair representative.
- The arrangement of data is often too tedious.
- It cannot be used to determine the total value of all the items.
- It is usually not representative of all the values in distribution.

**Examples of the Median**

Suppose we have the following data:

**2,4,12,6,8,14,16,10,18.**

First of all we order them from smallest to largest with which we would have the following:

**2,4,6,8,10,12,14,16,18.**

Well, the value of the **median**, as indicated by the formula, is the one that leaves the same number of values both on one side and on the other. How many observations do we have?

9 observations.

We calculate the position with the corresponding median formula.

**Median** = 9+1 / 2 = 5

What does this 5 mean? It tells us that the value of the **median** is found in the observation whose position is the fifth.

Therefore the **median** of this would be the number **10**, since it is in the fifth position. In addition, we can check how to the left of 5 there are 4 values (2, 4, 6 and 8) and to the right of 10 there are another 4 values (12, 14, 16 and 18).