Measures of Dispersion for Grouped Data · 7.1.2
Comparing dispersion from graphs
Students visually compare two or more histograms or frequency polygons drawn on the same axes, judging which dataset is more spread out by examining the width, peak position and overall shape of each distribution, including whether it appears symmetric or skewed to one side, then state a conclusion about which set of data is more consistent or more dispersed.
The official learning standard (7.1.2)
“Compare and interpret the dispersions of two or more sets of grouped data based on histogram and frequency polygon, hence make conclusion.”
What it means
Students visually compare two or more histograms or frequency polygons drawn on the same axes, judging which dataset is more spread out by examining the width, peak position and overall shape of each distribution, including whether it appears symmetric or skewed to one side, then state a conclusion about which set of data is more consistent or more dispersed.
How it is examined
This is examined mainly in Paper 2, where two frequency polygons or histograms are drawn on the same axes and students must compare their spread and shape, then write a conclusion in words. Paper 1 is unlikely to test this directly since it needs a graphical comparison.
Worked example
Two frequency polygons showing the test scores of Class A and Class B, drawn on the same axes, are given. Class A's polygon is narrow and peaks sharply near the centre, while Class B's polygon is wider and flatter, spread across a larger range of marks.
Compare the dispersion of the two classes and make a conclusion.
- Class A's frequency polygon is narrow and tall, with most marks concentrated close to the centre of the distribution.
- Class B's frequency polygon is wide and flat, with marks spread across a much larger range.
- A wider spread on the horizontal axis indicates a greater dispersion (more variation) in the data.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
Do I need to calculate the standard deviation to answer this type of question?
No, this standard is specifically about reading and interpreting the graphs visually, not calculating numerical measures. You are expected to compare shape and spread by eye and describe your observation in words, though a later, related standard does ask you to calculate actual dispersion measures.
What exactly should I look for when comparing two frequency polygons?
Compare three things: the width of the spread along the horizontal axis, the height and sharpness of the peak, and where the peak is positioned. A narrow, tall, sharply peaked polygon shows low dispersion, while a wide, flat, spread-out polygon shows high dispersion.
How do I write a good conclusion for this type of question?
State clearly which set has greater dispersion and which is more consistent, and support your statement by referring to the shape of the graphs, for example, mentioning that one polygon is wider or flatter than the other. Avoid vague statements without linking back to the graph's features.