Measures of Dispersion for Grouped Data · 7.1.1
Histogram and frequency polygon
Students build a histogram from a grouped frequency table by drawing bars over class boundaries with heights equal to the frequencies, then add a frequency polygon by plotting the midpoint of each class against its frequency (including two zero-frequency points at each end) and joining the points with straight lines.
The official learning standard (7.1.1)
“Construct histogram and frequency polygon for a set of grouped data.”
What it means
Students build a histogram from a grouped frequency table by drawing bars over class boundaries with heights equal to the frequencies, then add a frequency polygon by plotting the midpoint of each class against its frequency (including two zero-frequency points at each end) and joining the points with straight lines.
How it is examined
In Paper 2, students are usually given a grouped frequency table and asked to construct the histogram and/or frequency polygon on graph paper as part of a larger statistics question. Paper 1 rarely tests construction directly but may ask about class boundaries or midpoints needed for the construction.
Worked example
The table shows the marks obtained by 20 pupils in a quiz. Construct a histogram and a frequency polygon for this data.
Marks: 1–5, 6–10, 11–15, 16–20; Frequency: 3, 7, 6, 4.
- Find the class boundaries: 0.5–5.5, 5.5–10.5, 10.5–15.5, 15.5–20.5.
- Draw bars over each class boundary interval with heights equal to the frequencies (3, 7, 6, 4), this is the histogram.
- Find the midpoints of each class: 3, 8, 13, 18.
- Plot each midpoint against its frequency, plus two extra points with frequency 0 at midpoints -2 and 23 (one class-width before the first and after the last class), then join all the points with straight lines to form the frequency polygon.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
Why do I need class boundaries instead of class limits for a histogram?
Class boundaries remove the gaps between classes (for example 5.5 instead of 5 and 6), so the bars of the histogram sit exactly next to each other with no space in between, correctly showing that the data is continuous rather than in separate blocks.
Why do I add two extra points with frequency 0 when drawing the frequency polygon?
These points anchor the polygon to the horizontal axis at both ends, at the midpoints of one imaginary class before the first and one after the last. Without them, the polygon would not form a closed shape, and the total area under it would not properly represent all the data.
Can I draw the frequency polygon without first drawing the histogram?
Yes, a frequency polygon only needs the midpoints and frequencies of each class, so it can be plotted directly without bars. However, drawing the histogram first often makes it easier to see and mark the midpoints accurately, especially when class widths are unequal.