Data Cleaning and Outliers (Foundation)
Data cleaning is the process of checking a data set for errors, such as impossible values, typing mistakes or missing entries, and correcting or removing them before analysis. An outlier is a value that is much higher or lower than the rest of the data and does not fit the general pattern. In GCSE Statistics, spotting and dealing with outliers correctly is an important step before calculating averages or drawing graphs.
Before you start
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Method
- Look through the data set for values that are impossible or clearly wrong for the context, such as a negative age or a height of 1000 cm.
- Check for likely typing errors, such as a missing decimal point or an extra zero.
- Identify outliers by comparing each value to the general spread of the rest of the data.
- Decide whether an outlier is a genuine but unusual result or a clear error; only remove values that are errors or that you have good reason to exclude.
- Recalculate any averages or statistics using the cleaned data set once errors have been corrected or removed.
- State clearly which values were removed or corrected and why, since this affects how the results should be interpreted.
Worked example
A nurse records the weights (kg) of 8 patients: 62, 65, 71, 68, 640, 70, 66, 69. (a) Identify the outlier. (b) Suggest a likely explanation. (c) Calculate the mean weight with the outlier removed.
- Compare each value with the rest: 640 kg is far larger than all the other weights (62 to 71 kg), so 640 is the outlier.
- A likely explanation is a data entry error, for example the decimal point was missed and the true value was 64.0 kg.
- Remove the outlier, leaving 7 values: 62, 65, 71, 68, 70, 66, 69.
- Sum the remaining values: 62 + 65 + 71 + 68 + 70 + 66 + 69 = 471.
- Divide by the number of values: 471 divided by 7 = 67.285714...
- Final answer: the outlier is 640 kg, likely a data entry error, and the mean weight of the remaining 7 patients is 67.3 kg (1 dp).
Practice questions
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Q1A data set of ages is: 12, 13, 12, 14, 13, 99. Which value is most likely an outlier?Show answer
Answer: 99 (far higher than the rest, likely a recording error for an age).
Q2A shop records daily sales in pounds: 340, 355, 360, 348, 2, 352. Which value looks like a data entry error?Show answer
Answer: 2 (a digit was likely missed, for example it should read 320).
Q3Give one reason you might choose to keep an outlier in a data set rather than remove it.Show answer
Answer: It could be a genuine, correct value that shows real variation, so removing it would lose important information.
Q4A data set of test scores out of 100 is: 55, 60, 58, 62, 59, -10. Which value must be an error, and why?Show answer
Answer: -10, because a test score cannot be negative.
Q5The heights (cm) of 6 plants are: 15, 18, 16, 14, 17, 150. Find the mean of the remaining values after removing the outlier.Show answer
Answer: 16 cm (15 + 18 + 16 + 14 + 17 = 80, 80 divided by 5 = 16).
Q6Explain why the median might be a more appropriate average to use on a data set with an outlier, instead of removing the outlier first.Show answer
Answer: The median is not affected much by extreme values, so it can be used on the original data set without needing to identify or remove an outlier.
Exam-style questions
Written in the style of a GCSE Statistics exam paper, with a full mark scheme.
The number of pets owned by 7 students is: 1, 2, 1, 0, 2, 1, 15. (a) Identify the outlier in this data set. (b) Explain why it is unlikely to be a genuine value. (c) State one action the researcher could take.
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A data set of temperatures in degrees C recorded over a week is: 18, 19, 17, 20, 18, -180, 19. State the outlier and explain briefly why it must be an error rather than a real UK summer temperature.
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A researcher records the salaries, in thousands of pounds, of 9 employees: 24, 26, 25, 27, 23, 26, 24, 25, 95. (a) Identify the outlier. (b) Calculate the mean of the original 9 values. (c) Calculate the mean with the outlier removed. (d) Comment on which mean better represents a typical employee's salary.
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Free printable worksheet
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This topic is chapter 1 of GCSE Statistics Foundation Workbook 1, the whole course as one free printable PDF.
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