Outliers gcse Edexcel

课 Progress

0% Complete

Exam code:1ST0

Outlier Basics

What are outliers?

Outliers are extreme data values that do not fit with the general pattern of the data
Outliers in a data set can be due to
- genuine extreme events
  - these are valid data, even if unusual
- mistakes in the data collection
  - these should be identified and removed if possible
Outliers will affect some statistics that are calculated from the data
- They can have a big effect on the mean,
  - but not on the median
  - and usually not on the mode
- The range will be completely changed by a single outlier
  - but the interquartile range will not be affected
When calculating the mean or the range it is important to decide whether any outlier(s) should be included in the calculations
- An exam question will tell you whether to include outliers or not
  - But you may have to decide which value(s) are outliers
  - Look for values that are much bigger or smaller than the rest of the data set
In general outliers are
- included if they are a valid piece of data
- excluded if it is likely that they are erroneous

Worked Example

The following data was collected about the ages of a number of students at the time that they sat their GCSE Maths exam

3 13 15 15 15 15 16 16 16 16 16 57

(a) Suggest possible outliers in the data set.

Most students sit their GCSEs when they are 15 or 16
Some students sit them a bit younger, so the ’13’ is not very unusual
However the ‘3’ and the ’57’ are definitely extreme data values compared to the rest of the set!

3 and 57 should probably be considered to be outliers

(b) For each outlier identified in part (a), suggest with a reason whether the data value should be kept in or excluded from the data set.

It is essentially impossible that a 3 year old would be sitting a GCSE exam, so that data value is surely a mistake

On the other hand older people do sometimes sit GCSE exams, so the ’57’ shouldn’t be excluded from the data set without further information

The ‘3’ should be excluded. There is no way a 3 year old would be sitting a GCSE exam, so that is almost certainly an error in the data collection.

The ’57’ should be kept. It is unusual for older people to sit GCSEs, but it is not impossible. So that may be a valid data value.

Calculating Outlier Boundaries

How do I calculate outlier boundaries?

It is sometimes possible to find outliers by inspection
- i.e. look for unusually large or small data values
But on your Higher tier paper you will usually be expected to use outlier boundaries
- An upper boundary
  - Any data value greater than this is considered an outlier
- A lower boundary
  - Any data value less than this is considered an outlier
There are two ways of calculating outlier boundaries that you need to know
- The formulas for these are not on the exam formula sheet, so you need to remember them

Using quartiles and interquartile range

This method uses the lower quartile (LQ), upper quartile (UQ) and interquartile range (IQR)
Use this if you already know the quartiles (or can easily calculate them)
- This includes data presented on a box plot
The lower boundary is the LQ subtract one and a half times the IQR
- $bold Small bold space bold outlier space is space less than space LQ space minus space 1.5 cross times IQR$
The upper boundary is the UQ plus one and a half times the IQR
- $bold Large bold space bold outlier space is space greater than space UQ space plus space 1.5 cross times IQR$

Using mean and standard deviation

This method uses the mean ( $mu$ ) and standard deviation ( $sigma$ )
Use this if you already know $mu$ and $sigma$ (or can easily calculate them)
- Or for data presented in a form that doesn’t allow quartiles to be calculated
The lower boundary is three times the standard deviation less than the mean
- <img alt=”bold Small bold space bold outlier space is space less than space mu minus 3 sigma” data-mathml=”<math ><semantics><mrow><mi mathvaria

Statistics Gcse Edexcel Higher