Measures of Dispersion for Grouped Data · 7.2.3
Comparing dispersion of grouped data
Students take a measure of central tendency and a measure of dispersion, such as the mean and standard deviation, or the median and interquartile range, for two or more grouped data sets, compare the pairs of values, judge which set is more consistent or more spread out, and state a clear conclusion.
The official learning standard (7.2.3)
“Compare and interpret two or more sets of grouped data based on measures of dispersion, and make a conclusion.”
What it means
Students take a measure of central tendency and a measure of dispersion, such as the mean and standard deviation, or the median and interquartile range, for two or more grouped data sets, compare the pairs of values, judge which set is more consistent or more spread out, and state a clear conclusion.
How it is examined
Almost always in Paper 2, as the final part of a statistics question: after the mean/median and standard deviation/interquartile range are computed or given for two data sets, students compare each pair of values and write a one- or two-sentence conclusion. Paper 1 rarely tests this since it needs two computed data sets to compare.
Worked example
The masses of durians (kg) from two orchards were recorded from 50 durians each. Orchard A: mean = 2.4 kg, standard deviation = 0.3 kg.
Orchard B: mean = 2.4 kg, standard deviation = 0.7 kg. Compare the two orchards and make a conclusion about the consistency of the durian masses.
- Compare the means first: both orchards have the same mean mass, 2.4 kg, so on average the durians are the same size.
- Compare the standard deviations: Orchard A's standard deviation (0.3 kg) is smaller than Orchard B's (0.7 kg).
- A smaller standard deviation means the values are more tightly clustered around the mean, i.e. more consistent.
- Conclusion: although the average mass is the same, Orchard A's durians are more consistent in mass (less variable), while Orchard B's durians vary more widely from the mean.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
If both sets have the same mean, does that mean they are identical?
No. Two sets can share the exact same mean or median yet be very differently spread out, one tightly clustered around it, the other widely scattered.
You must always check a dispersion measure like the standard deviation or interquartile range before concluding the two sets behave similarly.
Which is better to compare, the standard deviation or the interquartile range?
Use whichever measure the question has already computed or explicitly asks for. Standard deviation uses every value and suits data without unusual classes, while the interquartile range ignores the extremes and is better when a data set has an unusually high or low class.
What should my final conclusion sentence include?
State which set has the higher central value (if relevant) and which set is more consistent or more spread out, both supported by the numbers you compared, for example, 'Orchard A is more consistent because its standard deviation is smaller,' not just 'Orchard A is better.'