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Understand Outliers

In this worksheet, students practise finding the outliers in scatter graphs and frequency distributions

'Understand Outliers' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR,

Curriculum topic:   Statistics

Curriculum subtopic:   Statistics Analysing Data

Difficulty level:  

Worksheet Overview

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 they would distort the data.

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

 

1) 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.

 

2) Frequency Distributions

This is a bit more mathematical.We have already looked at how to find the Inter Quartile Range (IQR) and median of a distribution.

Outliers are defined as being

- Greater than   UQ + 1.5 x IQR

-Less than         LQ - 1.5 x IQR

 

Example: A data set has a Lower Quartile of 20 and and 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.

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