Frequency density is proportional to the frequency per unit for the data in each class. Often, the multiplier is 1 meaning that frequency density = frequency ÷ class width.

Histograms with unequal bar width

Maths

In the prior unit, pupils compared two different sets of data. In this unit, pupils consider cumulative frequency graphs and histograms and compare these with other known graphical representations.

Graphical representations of data: cumulative frequency and histograms

is proportional to the frequency per unit for the data in each class.

is the number of people living per unit of area.

is measured as the substance's mass per unit of volume.

Match the type of density with the definition.

Plotting against frequency makes no difference.

It illustrates the major features of the distribution of the data.

Which of the following explains why we plot continuous data with unequal bar widths against frequency density?

Match the frequency density with the correct class interval.

Here is a histogram showing the masses of different parcels. Which class interval shows for every 1 kg, there are 2 parcels?

The bar with the largest area shows the modal class.

The frequency is the frequency density $$\div$$ class width.

The lowest bar shows the class with the lowest frequency.

Select which of the following is true given a histogram with unequal bar widths plotted against frequency density.

50 people were asked how many books they read a week.

50 people were asked how many minutes it takes them to get to work/school.

50 people were asked what their favourite fruit is.

The scale does not need to be consistent.

Equal bar width with the $$y$$ axis labelled frequency.

The $$x$$ and $$y$$ axis must have the same scale.

When constructing a histogram with equal bar widths, select which of the following are important points to remember.

Here is a table showing the time people spent doing physical activity during a day. How many people spent more than 2 hours doing physical activity?

Here is a histogram showing times taken to complete an IQ test. What percentage of people took more than 10 minutes to complete the IQ test?

Here is a histogram showing how long people played a game for before they lost their first life. What percentage of people played for 20 seconds or more?

Here is a histogram showing how long people played a game for before they lost their first life. What percentage of people played for 40 seconds or more?

Starter Quiz