Grouped data, histograms and frequency polygons
Sort heights into equal classes, build a frequency table with relative frequencies, draw a histogram whose bars touch and join the class midpoints into a frequency polygon.
- UK: Year 8
- France: grade 7
- Germany: grade 9
- Iran: grade 8
- Afghanistan: grade 8
- Syria: grade 8
- Palestine: grade 9
- Russia: grade 7
Guide
This studio follows KS3 Statistics ("grouped data … charts for grouped numerical data"); the histograms here have equal class widths, so the height of each bar is the frequency.
When there are many different values, we group them into classes of equal width. Each class is closed on the left: 145 ≤ x < 150 contains 145 but not 150, so a value on a boundary belongs to exactly one class.
The frequency of a class is how many values are in it. The relative frequency is the frequency divided by the total; the relative frequencies always add up to 1.
In a histogram the bars touch, because the classes run on into each other with no gaps on the number line. A frequency polygon joins the midpoints of the tops of the bars: the midpoint stands for every value in its class.
Ask: "Which class gets exactly 145? Why can't it go in both?"