Measures of Dispersion for Ungrouped Data · 8.1.1
Meaning of dispersion
Dispersion describes how spread out a set of data values is, rather than where its centre lies. Data with low dispersion cluster closely around the mean, while data with high dispersion are widely scattered.
This standard asks students to explain this idea and distinguish it clearly from measures of central tendency.
The official learning standard (8.1.1)
“Explain the meaning of dispersion.”
What it means
Dispersion describes how spread out a set of data values is, rather than where its centre lies. Data with low dispersion cluster closely around the mean, while data with high dispersion are widely scattered.
This standard asks students to explain this idea and distinguish it clearly from measures of central tendency.
How it is examined
Dispersion is usually introduced conceptually in Paper 2 as the opening part of a statistics question, asking students to explain or identify which of two data sets is more spread out before any calculation is done. It may also appear as a short conceptual item in Paper 1.
Worked example
Two classes, A and B, both have a mean score of 65 in a test. Class A: 60, 63, 65, 67, 70.
Class B: 40, 55, 65, 75, 90. Explain which class shows greater dispersion.
- Both classes have the same mean (65), so the mean alone cannot distinguish them.
- Class A's scores lie between 60 and 70, close to the mean.
- Class B's scores lie between 40 and 90, much further from the mean.
- Since Class B's values are more scattered around the same mean, Class B has greater dispersion.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
Can two data sets have the same mean but different dispersion?
Yes. The mean only shows the average value, not how the data is spread.
Two sets can share the same mean while one set has values clustered tightly around it and the other has values scattered far apart, this difference is exactly what dispersion measures.
What does 'zero dispersion' mean?
Zero dispersion means every value in the data set is identical, so there is no spread at all. For example, the data set 5, 5, 5, 5 has zero dispersion since all values equal the mean.
Is a data set with a bigger range always more dispersed?
Usually a bigger range suggests more spread, but range only looks at the two extreme values, so it can be misleading. Other measures like interquartile range, variance and standard deviation give a fuller picture of dispersion across the whole data set, not just the extremes.