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Year 11

Higher

Moving between tables and histograms

I can construct a table from a histogram.

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New

Year 11

Higher

Moving between tables and histograms

I can construct a table from a histogram.

Download all resources

Share activities with pupils

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Lesson details

Key learning points

A frequency table can be used to construct a histogram
A histogram can be used to construct a frequency table
Data is sometimes collected using uneven class widths

Keywords

Continuous data - Continuous data can take any value within a range. (Height, mass, temperature)
Histogram - A histogram is a diagram consisting of rectangles whose area is proportional to the frequency in each class and whose width is equal to the class interval.
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.

Start with a completed histogram and frequency table. Remove values from the table and ask how these can be found using the histogram. Remove bars from the histogram and ask how they can be found using the table. Proceed with giving questions with missing information from both histogram and table.

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Licence

This content is © Oak National Academy Limited (2024), 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.

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

Frequency density = frequency $$\times$$ class width

Correct answer: Frequency density = frequency $$\div$$ class width

Frequency density = class width $$\div$$ frequency

Q2.

Select which statements are true.

Correct answer: Histograms can show discrete and continuous data.

Correct answer: Histograms show the distribution of data using grouped intervals.

Correct answer: Histograms with unequal bar widths must be plotted against frequency density.

Histograms with unequal bar widths must be plotted against frequency.

Histograms with equal bar widths must not be plotted against frequency density.

Q3.

Here is some data on the masses of parcels. Which class interval shows a frequency density of 2?

$$0 < w \leq 5$$

Correct answer: $$5 < w \leq 15$$

$$15 < w \leq 30$$

Q4.

Here is some data on the lengths of some string. Which class interval shows a frequency density of 1.4?

$$0 < l \leq 15$$

$$15 < l \leq 20$$

Correct answer: $$20 < l \leq 30$$

$$30 < l \leq 35$$

Q5.

The histogram shows the masses of different parcels. How many parcels have a mass between 5 and 15 kg?

Correct Answer: 20

Q6.

Select which of the following statements are 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 width with the lowest frequency.

Correct answer: The smallest bar area shows the smallest frequency.

Exit quiz

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6 Questions

Q1.

Which of the following shows the frequency in a histogram with unequal bar widths?

Correct answer: The area of the bar

The height of the bar

The length of the bar

The frequency density

Q2.

Here are the times taken to type the alphabet. Match the class intervals with the correct frequency density.

Correct Answer:$$0 < t \leq 10$$,Frequency density = 0.4

Frequency density = 0.4

Correct Answer:$$10 < t \leq 15$$,Frequency density = 1.6

Frequency density = 1.6

Correct Answer:$$15 < t \leq 20$$,Frequency density = 4

Frequency density = 4

Correct Answer:$$30 < t\leq 50$$,Frequency density = 0.25

Frequency density = 0.25

Q3.

Here is some data on the lengths of some parcels. Match the frequency with the class interval.

Correct Answer:$$0 < l \leq 5$$,12

Correct Answer:$$5 < l \leq 10$$,15

Correct Answer:$$10 < l \leq 14$$,20

Correct Answer:$$15< l \leq 16$$,4

Q4.

Here is a histogram showing lengths of different fruit. Which numbers represent $$x$$, $$y$$ and $$z$$ on the $$y$$ axis?

$$x=1$$, $$y=2$$ and $$z=5$$

Correct answer: $$x=2$$, $$y=4$$ and $$z=6$$

$$x=3$$, $$y=4$$ and $$z=5$$

$$x=4$$ $$y=8$$ and $$z=7$$

Q5.

Here are the times taken to type the alphabet. Match the class interval to the correct frequency.

Correct Answer:$$0 < t \leq 10$$,Frequency = 4

Frequency = 4

Correct Answer:$$10 < t \leq 15$$,Frequency = 8

Frequency = 8

Correct Answer:$$15 < t \leq 20$$,Frequency = 20

Frequency = 20

Correct Answer:$$20 < t \leq 30$$,Frequency = 16

Frequency = 16

Correct Answer:$$30 < t\leq 50$$,Frequency = 5

Frequency = 5

Q6.

Here is a histogram showing the time it takes to solve a puzzle.

Correct Answer:$$0 < t\leq 2$$,Frequency = 10

Frequency = 10

Correct Answer:$$2 < t \leq 4$$,Frequency density = 6

Frequency density = 6

Correct Answer:$$4 < t \leq 5$$,Frequency = 15

Frequency = 15

Correct Answer:$$5 < t\leq 10$$,Frequency density = 2.8

Frequency density = 2.8

Correct Answer:$$10 < t \leq 12$$,Frequency density = 2.5

Frequency density = 2.5