# Quartiles

Quartiles are the values that divide a list of numbers into quarters:

- Put the list of numbers
**in order** - Then cut the list into
**four equal parts** - The Quartiles are at the "cuts"

Like this:

### Example: 5, 7, 4, 4, 6, 2, 8

Put them in order: 2, 4, 4, 5, 6, 7, 8

Cut the list into quarters:

And the result is:

- Quartile 1 (Q1) =
**4** - Quartile 2 (Q2), which is also the Median, =
**5** - Quartile 3 (Q3) =
**7**

Sometimes a "cut" is between two numbers ... the Quartile is the average of the two numbers.

### Example: 1, 3, 3, 4, 5, 6, 6, 7, 8, 8

The numbers are already in order

Cut the list into quarters:

In this case Quartile 2 is half way between 5 and 6:

Q2 = (5+6)/2 = **5.5**

And the result is:

- Quartile 1 (Q1) =
**3** - Quartile 2 (Q2) =
**5.5** - Quartile 3 (Q3) =
**7**

## Interquartile Range

The "Interquartile Range" is from Q1 to Q3:

To calculate it just **subtract Quartile 1 from Quartile 3**, like this:

### Example:

The **Interquartile Range** is:

Q3 − Q1 = 7 − 4 = **3**

## Box and Whisker Plot

We can show all the important values in a "Box and Whisker Plot", like this:

A final example covering everything:

### Example: **Box and Whisker Plot and Interquartile Range** for

4, 17, 7, 14, 18, 12, 3, 16, 10, 4, 4, 11

Put them in order:

3, 4, 4, 4, 7, 10, 11, 12, 14, 16, 17, 18

Cut it into quarters:

3, 4, 4 | 4, 7, 10 | 11, 12, 14 | 16, 17, 18

In this case all the quartiles are between numbers:

- Quartile 1 (Q1) = (4+4)/2 =
**4** - Quartile 2 (Q2) = (10+11)/2 =
**10.5** - Quartile 3 (Q3) = (14+16)/2 =
**15**

Also:

- The Lowest Value is
**3**, - The Highest Value is
**18**

So now we have enough data for the **Box and Whisker Plot**:

And the **Interquartile Range** is:

Q3 − Q1 = 15 − 4 = **11**