Cumulative frequency

In a nutshell

Cumulative frequency graphs show frequency added up as you go along the classes. This means that the frequency for the last class represents the total frequency.

Drawing a cumulative frequency graph

procedure

1.	Add a cumulative frequency column to the frequency table.
2.	Calculate cumulative frequency by adding frequencies up to and including current row.
3.	Plot the points at the end of each class.
4.	Connect the points using a smooth curve or a straight line.

Example 1

This frequency table shows the height of Mike's classmates. Draw a cumulative frequency graph.

Add a cumulative frequency column and calculate each value.

Height (cm)	Frequency	Cumulative frequency
$140< h \le 145$	$2$	$2$
$145< h \le 150$	$3$	$2+3=5$
$150< h \le155$	$13$	$5+13=18$
$155< h \le 160$	$21$	$18+21=39$
$160 < h \le 165$	$5$	$39+5=44$

Plot points at the end of each class (at $145cm, 150cm, 155cm, 160cm$ and $165cm$ ) and connect using a smooth line.

Maths; Statistics; KS4 Year 10; Cumulative frequency - Higher

Interpreting cumulative frequency graphs

From cumulative frequency graphs you can read off the lower quartile, median and the upper quartile. Simply work out the position of each and read across to meet the line and down to find out the value.

Example 2

In the example above the LQ, median and UQ are at positions $11,22$ and $33$ respectively.

Reading across to the line and down gives that the lower quartile is $\underline{152.5cm}$ , the median $\underline{155.5cm}$ and the upper quartile $\underline{158cm}$ .