Outliers and cleaning data

Rules you may be given

• Beyond 1.5 × IQR (or another multiple) from the quartiles: below Q1 - k(IQR) or above Q3 + k(IQR).
• More than 2 (or 3) standard deviations from the mean: outside x̄ ± 2σ.

Work out both limits and compare each suspect value.

What to do with an outlier

Cleaning data means removing values that are errors (such as an impossible value or a recording mistake). A genuine but extreme value should usually be kept, because it is real information. Say which, using the context: 'a human height of 2.95 m must be an error'.

Effect of removing a value

Outliers affect the mean, standard deviation and range a lot; the median and IQR hardly change. To recalculate after removing a value v from n values: new Σx = Σx - v and new Σx² = Σx² - v², with n - 1 values.

Worked example

12 values have Σx = 480 and Σx² = 23200. The value 96 is removed. Find the new mean and standard deviation.

1. New n = 11, Σx = 384, Σx² = 23200 - 9216 = 13984.
2. Mean = 384/11 = 34.9091
3. σ² = 13984/11 - (384/11)² = 52.6281

Answer: Mean 34.9, σ = 7.25

Check yourself

1. Data have mean 40 and standard deviation 6. Outliers are more than 2 standard deviations above the mean. Find the upper limit.
   Show answer

   52. 40 + 2 × 6 = 52.

2. Data have mean 40 and standard deviation 6. Find the lower limit for outliers using x̄ - 2σ.
   Show answer

   28. 40 - 12 = 28.

3. 12 values have Σx = 480. The outlier 96 is removed. Find the new mean. Give your answer to 3 significant figures.
   Show answer

   34.9. 384/11 = 34.9.

4. 12 values have Σx = 480 and Σx² = 23200. The value 96 is removed. Find the new standard deviation. Give your answer to 3 significant figures.
   Show answer

   7.25. Σx² becomes 13984 and Σx becomes 384, n = 11: σ² = 52.6281, σ = 7.25.

5. Q1 = 30, Q3 = 42. An outlier is any value more than 2 × IQR above Q3. Find the upper outlier limit.
   Show answer

   66. IQR = 12, so the limit is 42 + 24 = 66.

6. An outlier is removed from a data set. Which statistic is likely to change least?
   • The mean
   • The median
   • The range
   • The standard deviation
   Show answer

   The median. The median depends only on the middle value(s), so one extreme value barely moves it.

7. In a data set of adult heights, one value is recorded as 295 cm. What should be done?
   • Keep it, because all data must be used
   • Replace it with the mean
   • Double every other value
   • Remove it, as it is almost certainly a recording error
   Show answer

   Remove it, as it is almost certainly a recording error. No adult is 2.95 m tall, so it is an error and cleaning the data removes it.

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Sources

• Pearson Edexcel International Advanced Level in Mathematics specification (issue 3), Unit S1
• Pearson Edexcel IAL Statistics S1 (WST01) examiners' report, October 2024

Last updated 7 November 2026. Spotted a mistake? Tell us.