Measures of Dispersion for Ungrouped Data · Form 4
Range or standard deviation: which measure of spread?
The range is the quickest measure of spread, largest value minus smallest, but it depends on just two values and is thrown right off by a single unusual one. Standard deviation uses every value, so it gives a steadier, fuller picture of how the data is scattered.
How much of the data each one uses
The range is simply largest − smallest, so it notices only the two extreme values and ignores everything in between. The standard deviation, by contrast, measures how far every value lies from the mean and combines them all.
That difference is the heart of choosing between them: one is a two-value snapshot, the other summarises the whole set.
Where the range lets you down
Because it depends on the extremes, a single outlier can blow the range up while the rest of the data stays tightly packed. Marks of 50, 51, 52, 53 and 98 have a range of 48, yet four of the five values sit within 3 marks of each other.
The standard deviation feels an outlier too, but far less violently, because the bulk of ordinary values pull it back, that steadiness is why it is usually the more trustworthy measure.
Choosing between them
If you only want a quick sense of spread, or you have very few values, the range is reasonable and fast. If you need to compare two sets fairly, or the data may contain an odd value, the standard deviation is the fairer choice, and a question will usually make clear which measure it wants.
The misconception to avoid is thinking one is simply 'better': the range is not wrong, only cruder, and each is the right tool in a different situation.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
Why can the range give a misleading idea of spread?
The range only uses the largest and smallest values, so one unusually high or low value can make the range look large even if most of the data is closely bunched together. Standard deviation avoids this problem because it takes every value into account, giving a fairer picture of how scattered the data really is.
Is finding the range enough to answer an SPM dispersion question?
Range is useful as a quick check, but most SPM questions on dispersion expect standard deviation because it's a more complete measure. If a question specifically asks for range, give largest value minus smallest value only; if it asks to compare consistency or describe spread fully, standard deviation is usually the expected measure.
What's a common error when finding the range?
A common slip is subtracting in the wrong order or picking the wrong extreme values from an unsorted list, always identify the true maximum and minimum first, especially in grouped or ungrouped frequency tables. Also remember the range carries the same units as the data, so don't drop or change them in the final answer.