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Mean, median, mode and range
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Descriptive statistics summarise data. Measures of central tendency (averages) show a typical score; the range shows how spread out the scores are.
Three averages
Mean: add up all the scores and divide by how many there are. Strength: uses every score, so it is the most sensitive. Weakness: distorted by extreme scores (outliers).
Median: put the scores in order and find the middle one. With an even number of scores, take the mean of the middle two. Strength: not affected by extreme scores. Weakness: ignores most of the actual values.
Mode: the most common score. Strength: easy; the only average for categories (such as favourite colour). Weakness: there may be no mode or several modes.
Median: put the scores in order and find the middle one. With an even number of scores, take the mean of the middle two. Strength: not affected by extreme scores. Weakness: ignores most of the actual values.
Mode: the most common score. Strength: easy; the only average for categories (such as favourite colour). Weakness: there may be no mode or several modes.
Range
The range is a measure of dispersion (spread).
Range = highest score - lowest score.
A small range means scores are close together; a large range means they are spread out.
Weakness: it only uses two scores, so one extreme score can make the range very large.
Range = highest score - lowest score.
A small range means scores are close together; a large range means they are spread out.
Weakness: it only uses two scores, so one extreme score can make the range very large.
Worked example
Words recalled by five participants: 12, 15, 9, 14, 10.
Mean: 12 + 15 + 9 + 14 + 10 = 60; 60 ÷ 5 = 12.
Median: in order 9, 10, 12, 14, 15: middle score = 12.
Range: 15 - 9 = 6.
If one participant had recalled 40 words instead of 15, the mean would jump to 17, but the median would stay at 12. That is why the median is better when there are outliers.
Mean: 12 + 15 + 9 + 14 + 10 = 60; 60 ÷ 5 = 12.
Median: in order 9, 10, 12, 14, 15: middle score = 12.
Range: 15 - 9 = 6.
If one participant had recalled 40 words instead of 15, the mean would jump to 17, but the median would stay at 12. That is why the median is better when there are outliers.
Scores: 3, 7, 8, 10, 12, 15. Find the median.
- The scores are already in order and there are 6 of them (even).
- The middle two are 8 and 10, so the median is (8 + 10) ÷ 2 = 9.
Answer: 9
The mean adds and divides (uses all scores, affected by outliers). The median is the middle score in order (not affected by outliers). The mode is the most common score. The range is highest minus lowest and shows spread.
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