Frequency density: 0-50: 20, 50-75: 25, 75-100: 15, 100-200: 10

Step by step

The question

Question: draw the histogram for 0-50: 20, 50-75: 25, 75-100: 15, 100-200: 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: 50, 25, 25, 100.

2 Frequency density

Frequency density is the frequency divided by the width: 20 ÷ 50 = 0.4, 25 ÷ 25 = 1, 15 ÷ 25 = 0.6, 10 ÷ 100 = 0.1.

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: 0.4 for the first.

Now the area of each bar shows its frequency.

4 Check

Let's check: width times height gives back each frequency: 20, 25, 15, 10.

So the bars are right!

Let's look back.

First: class widths.

Then: frequency density.

Then: draw the bars.

Last: check.