AQA · GCSE · Mathematics
Course version: 8300 · Version from Sept 2015
Statistics: interpret and construct tables, charts and diagrams, including frequency tables, bar charts, pie charts and pictograms for categorical data, vertical line charts for ungrouped discrete numerical data, and know their appropriate use
You need to read and draw statistical tables and diagrams, and choose the right one for the data.
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
You need to read and draw statistical tables and diagrams, and choose the right one for the data. Categorical data are labels or groups, such as eye colour or favourite subject. For categorical data you can use a frequency table to record counts, a bar chart with gaps between bars, a pie chart where each sector angle is proportional to the frequency, or a pictogram where each symbol stands for a number of items. Ungrouped discrete numerical data are separate values that can be counted, such as the number of pets per student. For these you use a vertical line chart, where each value has a vertical line whose height shows its frequency. You should label axes, use a consistent scale and key, and choose the diagram that suits the data type.
What earns the marks
- Interpret a frequency table by reading the frequencies for each category or value.
- Construct a bar chart for categorical data with correctly labelled axes and equal bar widths, leaving gaps between bars.
- Construct or interpret a pie chart by calculating each sector angle as frequency divided by total frequency multiplied by 360°.
- Use a pictogram with a clear key showing what each symbol represents, including part symbols where needed.
- Construct a vertical line chart for ungrouped discrete numerical data, with line heights showing frequencies.
- Select an appropriate diagram for the data type, for example a bar chart for categorical data and a vertical line chart for ungrouped discrete numerical data.
Common mistakes and how to put them right
Drawing a bar chart with no gaps between bars for categorical data.
Put it right: Leave gaps between bars to show the categories are separate.
Using a pie chart without making sector angles proportional to frequency.
Put it right: Calculate each angle as frequency divided by total frequency multiplied by 360°.
Using a vertical line chart for categorical data.
Put it right: Use a bar chart, pie chart or pictogram for categories, and a vertical line chart for ungrouped discrete numerical data.
Drawing a pictogram without a key or with inconsistent symbol sizes.
Put it right: Include a key and keep every symbol the same size.
Exam tips
- Check the data type first: categorical data need a bar chart, pie chart or pictogram, while ungrouped discrete numerical data need a vertical line chart.
- Label both axes and include units, and give a key for a pictogram.
- For a pie chart, show your angle calculation so the examiner can see the frequency-to-angle method.
Try the lesson
The start of the Statistics: interpret and construct tables, charts and diagrams, including frequency tables, bar charts, pie charts and pictograms for categorical data, vertical line charts for ungrouped discrete numerical data, and know their appropriate use lesson, made from checked teaching notes for this specification point.
Have a go first
A pictogram shows the number of books read by pupils in four classes. The key states that one book symbol represents 4 books. Class A has 3 symbols. How many books did Class A read?
Listen
You need to read and draw statistical tables and diagrams, and choose the right one for the data. Categorical data are labels or groups, such as eye colour or favourite subject. For categorical data you can use a frequency table to record counts, a bar chart with gaps between bars, a pie chart where each sector angle is proportional to the frequency, or a pictogram where each symbol stands for a number of items. Ungrouped discrete numerical data are separate values that can be counted, such as the number of pets per student. For these you use a vertical line chart, where each value has a vertical line whose height shows its frequency. You should label axes, use a consistent scale and key, and choose the diagram that suits the data type. A strong answer earns marks for these points. Interpret a frequency table by reading the frequencies for each category or value. Construct a bar chart for categorical data with correctly labelled axes and equal bar widths, leaving gaps between bars. Construct or interpret a pie chart by calculating each sector angle as frequency divided by total frequency multiplied by 360°. Use a pictogram with a clear key showing what each symbol represents, including part symbols where needed. A common slip: Drawing a bar chart with no gaps between bars for categorical data. Instead, leave gaps between bars to show the categories are separate. Exam tip: Check the data type first: categorical data need a bar chart, pie chart or pictogram, while ungrouped discrete numerical data need a vertical line chart.
Key words
Say what each word means before you turn the card.
Categorical data
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Ungrouped discrete numerical data
Try answering aloud or in your head before turning the card.
Frequency tables
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Choosing appropriate diagrams
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See every definition
- Categorical data
- Labels or groups, such as eye colour or favourite subject, for which you can use a frequency table, a bar chart with gaps between bars, a pie chart or a pictogram.
- Ungrouped discrete numerical data
- Separate values that can be counted, such as the number of pets per student, for which you use a vertical line chart where each value has a vertical line whose height shows its frequency.
- Frequency tables
- A table used to record counts for categorical data, read by reading the frequencies for each category or value.
- Choosing appropriate diagrams
- Selecting the diagram that suits the data type, for example a bar chart for categorical data and a vertical line chart for ungrouped discrete numerical data.
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