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Year 11

Higher

Histograms with unequal bar width

I can construct a histogram from a table.

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New

Year 11

Higher

Histograms with unequal bar width

I can construct a histogram from a table.

Download all resources

Share activities with pupils

These resources will be removed by end of Summer Term 2025.

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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

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.

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.

To help you plan your year 11 maths lesson on: Histograms with unequal bar width, download all teaching resources for free and adapt to suit your pupils' needs...

Statistics can be fun. Collecting data and representing it according to the objective of the lesson. A fun task is to collect the time it takes pupils to keep their eyes open. Collect all the times using peer groups and represent in a histogram with equal class widths. Analyse the distribution.

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This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Starter quiz

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6 Questions

Q1.

Select the examples of discrete data.

Correct answer: 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.

Correct answer: 50 people were asked what their favourite fruit is.

50 pieces of fruit were weighed.

Q2.

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.

Correct answer: Equal bar width with the

y

axis labelled frequency.

Histograms only display discrete data.

The

x

and

y

axis must have the same scale.

Q3.

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?

Correct Answer: 40

Q4.

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?

Correct Answer: 42%, 42

Q5.

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?

Correct Answer: 60%, 60

Q6.

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?

Correct Answer: 5%, 5

Exit quiz

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6 Questions

Q1.

Match the type of density with the definition.

Correct Answer:Frequency density,is proportional to the frequency per unit for the data in each class.

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

Correct Answer:Population density,is the number of people living per unit of area.

is the number of people living per unit of area.

Correct Answer:Substance density,is measured as the substance's mass per unit of volume.

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

Q2.

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.

Correct answer: It illustrates the major features of the distribution of the data.

Q3.

Match the frequency density with the correct class interval.

Correct Answer:

0 < w \leq 5

,Frequency density = 4

Frequency density = 4

Correct Answer:

5 < w \leq 15

,Frequency density = 2

Frequency density = 2

Correct Answer:

15 < w \leq 30

,Frequency density =

\frac{4}{3}

Frequency density = $\frac{4}{3}$

Q4.

Match the frequency density with the correct class interval.

Correct Answer:

0 < l \leq 15

,Frequency density = 1.6

Frequency density = 1.6

Correct Answer:

15 < l \leq 20

,Frequency density = 4

Frequency density = 4

Correct Answer:

20 < l \leq 30

,Frequency density = 1.4

Frequency density = 1.4

Correct Answer:

30 < l \leq 35

,Frequency density = 3.2

Frequency density = 3.2

Q5.

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

Correct answer:

5 < w \leq 15

15 < w \leq 30

None

Q6.

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.

Correct answer: 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.

Histograms with unequal bar width

Histograms with unequal bar width

These resources will be removed by end of Summer Term 2025.

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Lesson details

Key learning points

Keywords

Common misconception

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Starter quiz

6 Questions

Exit quiz

6 Questions