# How to Find the Median Value

*It's the middle of a sorted list of numbers.*

## Median Value

The Median is the * "middle"* of a sorted list of numbers.

## How to Find the Median Value

To find the Median, place the numbers in **value order** and find the **middle**.

### Example: find the Median of **12, 3 and 5**

Put them in order:

3, 5, 12

The middle is **5**, so the median is **5**.

### Example:

3, 13, 7, 5, 21, 23, 39, 23, 40, 23, 14, 12, 56, 23, 29

When we put those numbers in order we have:

3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 39, 40, 56

There are **fifteen** numbers. Our middle is the **eighth** number:

3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 39, 40, 56

The median value of this set of numbers is **23**.

(It doesn't matter that some numbers are the same in the list.)

## Two Numbers in the Middle

BUT, when there are an **even amount of numbers** things are
slightly different.

In that case we find the **middle
pair** of numbers, and then find the value that is **half
way** between them. This is easily done by adding them together
and dividing by two.

### Example:

3, 13, 7, 5, 21, 23, 23, 40, 23, 14, 12, 56, 23, 29

When we put those numbers in order we have:

3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 40, 56

There are now **fourteen** numbers and so we don't have just one middle number, we have a **pair of middle numbers**:

3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 40, 56

In this example the middle numbers are **21 and 23**.

To find the value halfway between them, add them together and divide by 2:

**21 + 23 = 44**

then **44 ÷ 2 = 22 **

So the **Median** in this example is **22**.

(Note that 22 was not in the list of numbers ... but that is OK because half the numbers in the list are less, and half the numbers are greater.)

## Your Turn

## Where is the Middle?

A quick way to find the middle: **count how many numbers, add 1 then divide by 2**

### Example: There are 45 numbers

45 plus 1 is 46, then divide by 2 and we get **23**

So the median is the **23rd number** in the sorted list.

### Example: There are 66 numbers

66 plus 1 is 67, then divide by 2 and we get **33.5**

**33 and a half?** That means that the **33rd and 34th** numbers in the sorted list are the two middle numbers.

So to find the median: add the **33rd and 34th** numbers together and
divide by 2.