Outliers & Resistant Measures (College Board AP® Statistics)

Outliers

What are outliers?

• Outliers are extreme data values that do not fit with the rest of the data

  • They are either a lot bigger or a lot smaller than the rest of the data

• There are two primary methods for defining outliers in this course

  1. Outliers are values that are more than 1.5 times the interquartile range (IQR) from the nearest quartile

     • is an outlier if or

  2. Outliers are values that lie two or more standard deviations above or below the mean

     • is an outlier if or

• Outliers can have a big effect on some statistical measures

Should I remove outliers?

• The decision to remove outliers will depend on the context

• Outliers should be removed if they are found to be errors

  • The data may have been recorded incorrectly

    • e.g. the age of a teenager, 17, may have been recorded as 71 by mistake

• Outliers should not be removed if they are a valid part of the sample

  • The data may need to be checked to verify that it is not an error

  • e.g. the annual salaries of employees of a business might appear to have an outlier, but this could be the director’s salary

Resistant measures

What is a resistant measure?

• A resistant measure is a statistical measure that is not greatly affected by an outlier

  • It is sometimes not affected by an outlier at all

  • Resistant measures are sometimes known as robust measures

• The median and the interquartile range (IQR) are considered to be resistant measures

• The mean, standard deviation , and range are considered to be nonresistant measures

  • The value of any of these measures could be significantly affected by an outlier