When you are dealing with data, there is sometimes a need to exclude certain values.

If you were finding the average height of people in a reception class one day, you wouldn't include the teacher, as that would distort the data.

In maths, these are called **outliers **and there are two places you could meet them.

**Scatter graphs**

It is quite easy to spot outliers in a scatter graph, they're just the ones that don't fit into the pattern:

We can see that for these two scatter graphs, the points that are circled don't fit into the pattern of the rest - these would be outliers.

**Frequency distributions**

This is a bit more mathematical. There are other activities on how to find the interquartile range (IQR) and median of a distribution, so if you're not too sure about these, it would be a good idea to have a look at one of those before tackling these questions.

Outliers are defined as being:

**Greater than the upper quartile (UQ) + 1.5 x IQR**

**Less than the lower quartile ( LQ) - 1.5 x IQR**

**Example:**

A data set has a lower quartile of 20 and an upper quartile of 28.

**Find the limits for the outliers.**

**Step 1: Find the IQR**

IQR = UQ - LQ = 28 - 20 = **8**

**Step 2: Find 1.5 x IQR**

1.5 x IQR = 1.5 x 8 = **12**

**Step 3: Find the limits for the outliers**

UQ + 1.5 x IQR = 28 + 12 = **40**

LQ - 1.5 x IQR = 20 - 12 = **8**

This means that any numbers** below 8 or above 40 **in the distribution are outliers.

Question time!