Frequency density: 0-2: 3, 2-5: 9, 5-10: 10, 10-20: 4, 20-30: 2

Step by step

The question

Question: draw the histogram for 0-2: 3, 2-5: 9, 5-10: 10, 10-20: 4, 20-30: 2.

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: 2, 3, 5, 10, 10.

2 Frequency density

Frequency density is the frequency divided by the width: 3 ÷ 2 = 1.5, 9 ÷ 3 = 3, 10 ÷ 5 = 2, 4 ÷ 10 = 0.4, 2 ÷ 10 = 0.2.

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: 1.5 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, 9, 10, 4, 2.

So the bars are right!

Let's look back.

First: class widths.

Then: frequency density.

Then: draw the bars.

Last: check.