What are outliers?

• Outliers are extreme data values that do not fit with the general pattern of the data
• They can come from one or two extreme events or from mistakes in the data collection
• 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 or usually 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 the outlier(s) should be included in the calculations
    • The question will tell you whether to include the outliers or not
    • You may have to decide which value is the outlier to be removed
    • In general outliers are included if they are a valid piece of data and excluded if it is likely that they are erroneous

How are outliers calculated?

• Most of the time within this syllabus the outliers will be a particular distance either side of the?interquartile range
  • The most common way to calculate an outlier will be using the formulae:
    • A value that is less than (interquartile range)
    • A value that is greater than (interquartile range)
    • k?is a constant that will be given to you in the exam, commonly?k=1.5
• Outliers could also be situated a number of?standard deviations?away from the?mean
  • The most common way to calculate an outlier will be using the formulae
    • A value that is less than
    • A value that is greater than
    • k is a constant that will be given to you in the exam, commonly

How are outliers represented on box plots?

• On a box plot an outlier is represented as a cross either side of the maximum or minimum value
• If the maximum or minimum value is discovered to be an outlier, the?new?maximum or minimum value will need to be found for the box plot
  • If the data value just above the minimum or just below the maximum is known, this will become the new value
  • If the data value is not known, the new minimum or maximum will become the outlier boundary

When should data be cleaned?

• The cause of the outlier should be examined by looking into the context of the data
• For example:
  • a test score of over 100% would most likely be a data collection error
  • a single salary that is much higher than the others would likely be for the CEO of the company
• If an outlier is determined to be from an error in data collection it should be removed from the data.
  • Removing the incorrect data value(s) is called?cleaning the data
  • It is important to consider very carefully whether you should remove the data value or not
    • If the data value is not an error it should not be removed from the data
• If a data value is removed from the data set before calculations are carried out, a justification for the removal of the outlier must be made
• Cleaning data also involves removing missing data and errors

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