We can also display grouped data in a frequency distribution. However, instead of recording each individual score and its corresponding frequency, we record the upper and lower bound for each group and the frequency for all scores in that group. The upper bound is the highest score in a group and the lower bound is the lowest score in a group.

Remember!

Here are some helpful terms to remember for grouped data:

Class centre: the average of the upper and lower limits of the class interval.

Upper bound: The highest score in each subset (ie. once data has been grouped, the highest score in each group will be the upper bound. It can be found by calculating the average of a class centre and the subsequent class centre.

Lower bound: The lowest score in each subset (ie. once data has been grouped, the lowest score in each group will be the lower bound. It can be found by calculating the average of a class centre and the previous class centre.

Cumulative frequency histograms can also be used to display grouped data. The centre of each class is written along the bottom axis. The height of a column in a cumulative frequency histogram is the total number of scores that are less than or equal to the largest value in the column class.

Just like individual scores, we can describe features of the data, such as the modal and median class.

Let's look through some examples that work with frequency distributions with grouped data.

Worked Examples

QUESTION 1

This cumulative frequency histogram shows the centre of each class along the bottom axis.

What is the upper bound for the class with centre $27$27?
How many scores were $29.5$29.5 or less?

QUESTION 2

Complete the frequency distribution table below:

Class	Class Centre	Frequency	Cumulative Frequency
$1-9$1−9	$\editable{}$	$3$3	$\editable{}$
$10-18$10−18	$\editable{}$	$4$4	$\editable{}$
$19-27$19−27	$\editable{}$	$3$3	$\editable{}$
$28-36$28−36	$\editable{}$	$3$3	$\editable{}$
$37-45$37−45	$\editable{}$	$8$8	$\editable{}$
Totals		$\editable{}$

Construct a cumulative frequency histogram to represent the data.
What is the modal class?

$\editable{}$ $-$− $\editable{}$
What is the median class?

$\editable{}$ $-$− $\editable{}$

QUESTION 3

Use the ogive given to estimate the median score.

Outcomes

12D.D.1.5

Interpret statistical summaries to describe the characteristics of a one-variable data set and to compare two related one-variable data sets; describe how statistical summaries can be used to misrepresent one-variable data; and make inferences, and make and justify conclusions, from statistical summaries of one-variable data orally and in writing, using convincing arguments

Frequency distribution for grouped data