Histograms with unequal bar width | Maths | Quizalize & Oak National Academy

Starter quiz

Select the examples of discrete data.

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. ✓

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

The scale does not need to be consistent.

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

Histograms only display discrete data.

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

'40' ✓
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?

'42%' ✓
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?

'60%' ✓
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?

'5%' ✓

Exit quiz

Match the type of density with the definition.

Frequency density

⇔

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

Population density

⇔

is the number of people living per unit of area. ✓

Substance density

⇔

is measured as the substance's mass per unit of volume. ✓
Which of the following explains why we plot continuous data with unequal bar widths against frequency density?

It is easier.

Plotting against frequency makes no difference.

It illustrates the major features of the distribution of the data. ✓
Match the frequency density with the correct class interval.

$0 < w \leq 5$

⇔

Frequency density = 4 ✓

$5 < w \leq 15$

⇔

Frequency density = 2 ✓

$15 < w \leq 30$

⇔

Frequency density = $\frac{4}{3}$ ✓
Match the frequency density with the correct class interval.

$0 < l \leq 15$

⇔

Frequency density = 1.6 ✓

$15 < l \leq 20$

⇔

Frequency density = 4 ✓

$20 < l \leq 30$

⇔

Frequency density = 1.4 ✓

$30 < l \leq 35$

⇔

Frequency density = 3.2 ✓
Here is a histogram showing the masses of different parcels. Which class interval shows for every 1 kg, there are 2 parcels?

$0 < w \leq 5$

$5 < w \leq 15$ ✓

$15 < w \leq 30$

None
Select which of the following is true given a histogram with unequal bar widths plotted against frequency density.

The highest bar shows the modal class.

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.

Worksheet

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Presentation

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Video

Lesson Details

Key learning points

Sometimes data is presented using unequal class widths
In order to compare, frequency density is used
Frequency density is proportional to the frequency per unit for the data in each class
Frequency is proportional to the area of the bar

Common misconception

Histograms with unequal bar widths are plotted against the frequency and/or pupils read the frequency density as the frequency of the class width.

Show what a histogram with unequal bar widths looks like when plotted against frequency. This visual aid will show pupils the distribution of data is difficult to see.

Keywords

Frequency density - 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.