Measures of Dispersion for Ungrouped Data · Form 4
Measures of Dispersion for Ungrouped Data: Key Terms
The key Measures of Dispersion for Ungrouped Data terms you need for SPM Mathematics, defined plainly in English, Malay and Chinese.
- Range The difference between the largest and smallest values in a data set.
- Variance A measure of how spread out data is around the mean; the square of the standard deviation.
- Standard deviation A measure of spread in the same units as the data; the square root of the variance.
- Interquartile range The spread of the middle half of the data, from the first to the third quartile.
- Mean The sum of all values divided by how many there are; the usual average.
- Median The middle value when the data is put in order.
- Mode The value that appears most often in a data set.
- Range The difference between the largest and smallest values in a data set.
- Frequency The number of times a value or category occurs in a data set.
Term pairs students mix up
- Variance vs standard deviation, the difference is one square root: variance is the average squared deviation (squared units), and the standard deviation is its square root, in the data's own units. For 12.25 sit-ups², the standard deviation is 3.5 sit-ups.
- Range vs interquartile range, the difference is what they measure across: range spans every value (highest − lowest) and jumps with one outlier, while the IQR spans only the middle half (Q3 − Q1) and stays steady.
- Mean vs median, the difference is how the centre is found: the mean adds all values and divides by N and anchors the variance, while the median is the middle value in order and anchors the quartiles and IQR.
- Measure of central tendency vs measure of dispersion, the difference is centre versus spread: mean, median and mode say where the data sits, while range, IQR, variance and standard deviation say how scattered it is.
- Σx² vs (Σx)², the difference is the order of operations: Σx² squares each value then adds (56 for 2, 4, 6), while (Σx)² adds first then squares (144). They are not equal, and only Σx² belongs in the variance formula.
How these terms are phrased in real SPM questions
Paper questions rarely spell out a formula; they hide the target inside a command word. 'Calculate the standard deviation' or 'the variance' asks directly for the table-and-formula routine, and the plural 'sit-ups²' or 'kg²' in a variance answer is your unit cue.
'Find a suitable measure of dispersion' invites you to name and justify one, usually the standard deviation for its use of every value, or the IQR when outliers are mentioned. 'The range of the data' means highest minus lowest, and 'the interquartile range' expects you to order the data and find Q3 − Q1.
When a question says 'compare the spread of the two groups', it wants two standard deviations and one sentence saying which group is more consistent, the smaller standard deviation is the more consistent set. Watch for 'consistent', 'uniform' or 'reliable', which all point to a smaller measure of dispersion.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
Is 'dispersion' the same word as 'spread'?
Yes, they mean the same thing in this chapter: how far apart the data values are. A question may use either word, or 'variability', for the same idea.
Range, interquartile range, variance and standard deviation are all measures of dispersion. They contrast with central tendency, which describes where the data centres rather than how it scatters.
What is the symbol σ, and how is it different from s?
In the SPM syllabus σ (sigma) is the population standard deviation, found by dividing by N, and σ² is the population variance. The symbol s usually denotes a sample version dividing by N − 1, which is beyond this chapter.
Unless a question says otherwise, use σ and divide by N, matching the formula on the sheet.
The question asks for 'the most appropriate measure' how do I justify my choice in words?
Name the measure, then give one reason tied to the data. If there is an extreme value, choose the interquartile range because it ignores the outlier and reflects the middle half.
If every value matters and there is no rogue reading, choose the standard deviation because it uses all the data. One clear sentence of justification is what earns the reasoning mark.