Frequency density: 0-4: 6, 4-6: 8, 6-10: 10, 10-20: 5

Step by step

The question

Question: draw the histogram for 0-4: 6, 4-6: 8, 6-10: 10, 10-20: 5.

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: 4, 2, 4, 10.

2 Frequency density

Frequency density is the frequency divided by the width: 6 ÷ 4 = 1.5, 8 ÷ 2 = 4, 10 ÷ 4 = 2.5, 5 ÷ 10 = 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: 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: 6, 8, 10, 5.

So the bars are right!

Let's look back.

First: class widths.

Then: frequency density.

Then: draw the bars.

Last: check.