Measures of Dispersion for Ungrouped Data · 8.1.2
Comparing dispersion with plots
Students look at stem-and-leaf plots or dot plots of two or more data sets and judge how spread out each one is just by observing the shape and spacing of the values. They then state a conclusion, such as which set has greater or smaller dispersion, based purely on the visual pattern shown.
The official learning standard (8.1.2)
“Compare and interpret the dispersion of two or more sets of data based on stem-and-leaf plots and dot plots, and hence make a conclusion.”
What it means
Students look at stem-and-leaf plots or dot plots of two or more data sets and judge how spread out each one is just by observing the shape and spacing of the values. They then state a conclusion, such as which set has greater or smaller dispersion, based purely on the visual pattern shown.
How it is examined
This is examined in SPM Paper 2, typically as an early part of a statistics question that gives two dot plots or stem-and-leaf plots side by side and asks students to compare and describe their dispersion in words before deeper calculations are required.
Worked example
Dot plots show the number of storybooks read last month by 9 pupils in Group P: 2, 3, 3, 4, 4, 4, 5, 5, 6, and 8 pupils in Group Q: 1, 2, 4, 4, 4, 6, 7, 9. Compare the dispersion of the two groups.
- Group P's values run from 2 to 6, a range of 4, and cluster closely around 4.
- Group Q's values run from 1 to 9, a range of 8, and are spread more widely around 4.
- The dots for Group Q are more scattered from the centre than those for Group P.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
Do I need to calculate anything to compare dispersion from a dot plot?
Not always. Many SPM questions only ask you to compare visually, look at how spread out or clustered the dots are, and describe which set is more spread out in words.
Numeric measures like range or standard deviation are usually calculated in a later part.
How is a stem-and-leaf plot useful for comparing dispersion?
A stem-and-leaf plot keeps all the original data values while showing their shape, so you can see at a glance how far the leaves stretch from the main stem and whether values are bunched together or spread across many stems.
What should my conclusion sentence include?
State clearly which data set has the greater (or smaller) dispersion, and give a reason based on what you observed, for example, a wider spread of values, a longer range, or values lying further from the centre of the plot.