Step by step
The question
Question: draw the histogram for 0-10: 3, 10-15: 6, 15-20: 9, 20-40: 10.
The classes are not the same width.
So the bars cannot just be as high as the frequency.
1 Class widths
A table: each class and its frequency.
The width of a class is its end minus its start: 10, 5, 5, 20.
2 Frequency density
Frequency density is the frequency divided by the width: 3 ÷ 10 = 0.3, 6 ÷ 5 = 1.2, 9 ÷ 5 = 1.8, 10 ÷ 20 = 0.5.
The rule for the height of each bar.
Careful!
With different widths, a wide bar as high as its frequency would look too big.
Its area must be the frequency.
3 Draw the bars
Across: the classes.
Up: the frequency density.
Each bar goes across its whole class and up to its density: 0.3 for the first.
Now the area of each bar shows its frequency.
4 Check
Let's check: width times height gives back each frequency: 3, 6, 9, 10.
So the bars are right!
Let's look back.
First: class widths.
Then: frequency density.
Then: draw the bars.
Last: check.