Measures of Dispersion for Ungrouped Data · Form 4
Centre vs spread: why an average is never the whole story
The centre, mean, median or mode, tells you roughly where a set of data sits. The spread, range, interquartile range or standard deviation, tells you how scattered it is.
Two sets can share the same centre and still look completely different, so you usually need both to describe data fairly.
Two different questions about the same data
'Centre' answers the question 'what is a typical value?' that is the job of the mean, median and mode from the earlier statistics chapter.
'Spread' answers a different question: 'how close together, or how far apart, are the values?' The range, interquartile range and standard deviation in this chapter are measures of spread.
They are not competing with the average; they describe a feature the average simply cannot show.
Same average, very different data
Imagine two classes that both average 60 marks. In one, everyone scored between 58 and 62; in the other, marks ran from 20 to 95.
The mean alone hides this completely, you only see the difference once you also report the spread. That is why an answer giving a spread alongside an average describes the data honestly, while an average on its own can quietly mislead.
Spotting which one a question wants
Words like mean, median and mode point to the centre; words like range, interquartile range, variance and standard deviation point to the spread. A common slip is to treat a large spread as though it means a large average, it does not.
A data set can have a high mean with a tiny spread, or a low mean with a huge spread; the two ideas move independently.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
If two data sets have the same mean, why might they still look very different?
The mean only marks the centre of a data set, it says nothing about how spread out the values are. One set could have all its values clustered near the mean while another has values scattered widely apart, giving the same mean but very different shapes.
That's why spread must be reported too.
In an SPM comparison question, what must I write besides the mean or median?
Exam questions on dispersion almost always ask you to compare two sets using both a measure of central tendency and a measure of dispersion, then state what each comparison means in the context given. Giving only "Set A has a larger mean" without commenting on spread loses marks, since the question tests both ideas together.
What's the common mistake when comparing two data sets using centre and spread?
A common error is comparing only the centres and forgetting the spread, or reporting numbers without interpreting them in context, for example, saying standard deviation is smaller without explaining that means the data is more consistent. Always link each value back to what it means for the situation in the question.