Commenting on outliers

Values below the lower boundary or above the upper boundary are outliers. The boundaries have the same units as the original data.

For example, suppose employees’ annual salaries have a lower quartile of £24,000 and an upper quartile of £36,000. One recorded salary is £90,000. The IQR is $36{,}000-24{,}000=12{,}000$ pounds, so the boundaries are $24{,}000-1.5\times12{,}000=6{,}000$ pounds and $36{,}000+1.5\times12{,}000=54{,}000$ pounds. The £90,000 salary exceeds the upper boundary, so it is an unusually high annual salary under this rule.

That conclusion identifies the outlier, but does not yet explain it. A chief executive might genuinely earn much more than other employees. Checking the employee’s role and salary record would help establish whether the value is correct.

Using the original context to judge the value

A useful comment names what was measured and explains whether the unusual value could reasonably occur.

For example, a score above 100% on a test whose maximum possible score is 100% cannot be a valid result. It suggests an error in calculating or recording the percentage. By contrast, the unusually high salary of a chief executive is possible: being far above other salaries does not make it wrong.

Units also help reveal errors. A recorded human height of 1750 cm is not plausible. It might be a transcription error, with an extra zero entered, but you should check the original measurement rather than assume that the intended value was 175 cm.

Sometimes the context supports several explanations without proving any of them. In that case, give a plausible explanation and say what needs checking. For the salary example, a balanced comment would be: ‘The annual salary of £90,000 is above the £54,000 upper boundary. It could be genuine if the employee is the chief executive, so their role and original salary record should be checked before excluding it.’

Deciding what to do with the value

A genuine outlier should usually remain in the data: it represents something that really occurred. Removing it simply because it is extreme can misrepresent the population and its variation.

A confirmed recording error should be corrected if the true value can be verified. If it cannot be recovered, the erroneous value may need to be removed, with a reason given.

The essential distinction is between unusual and incorrect. Use the boundary to establish that the value is unusual, then use the original context and any available checks to judge whether it is genuine.

Judge and act

• Genuine unusual value: usually keep it; removing it can misrepresent the data.
• Confirmed recording error: correct it using a verified original value, or remove it if correction is impossible.
• Uncertain cause: explain what should be checked before deciding.

Justify any exclusion.