Histograms and frequency density

In a nutshell

Histograms are like bar charts but with varying bar widths. Rather than height, it is the area of each bar that shows frequency.

Drawing a histogram

Definition

Class width

The difference between the start and end value of the class.

In order to draw a histogram from a frequency table, another quantity needs to be worked out: frequency density - the height of each bar shows this frequency density.

$\text{frequency density} = \text{frequency} \div \text{class width }$

procedure

1.

Add a frequency density column to table.

2.

Draw and label your axes:

the y-axis should have the frequency density.
the x-axis should have the thing being measured.

3.

Draw your bars - remember the width of the bars should correspond to the class widths.

Example 1

Below is a frequency table showing the ages of students in a school production. Draw the histogram.

Age ( $a$ )	Frequency
$6<a\le10$	$4$
$10<a\le12$	$5$
$12<a\le13$	$2$
$13<a\le18$	$1$

Add the frequency density column.

Frequency density ( $\text{frequency density} = \text{frequency} \div \text{class width }$ )

$4\div4=1$

5\div2=2.5

2\div1=2

1\div5=0.2

Now following the steps and drawing the histogram gives:

Maths; Statistics; KS4 Year 10; Histograms and frequency density - Higher