Charts for Categorical Data

Frequency Tables

Every time you group your music playlist by genre, you are sorting categorical data. Categorical data (or qualitative data) is non-numerical and describes characteristics or groups. Categories must be non-overlapping, meaning every data point must belong to exactly one category.

A standard frequency table consists of three columns: Category, Tally, and Frequency. A tally is a running count using vertical marks grouped in fives. The sum of all values in the frequency column gives the Total Frequency ( $n$ ), which represents the total size of the dataset.

You can find averages for categorical data, but with some limitations. The Modal Category is the specific category name that appears most frequently. The median is the middle category, and its position is calculated using the formula $\frac{n+1}{2}$ . The mean cannot be calculated for qualitative categorical data because there are no numerical values to sum.

Constructing Bar Charts

Visualising data makes it instantly easier to spot trends. A Bar Chart represents discrete or categorical data where the height of rectangular bars is proportional to the frequency.

To construct a bar chart, follow these step-by-step rules:

Place the categories on the horizontal ( $x$ ) axis and Frequency on the vertical ( $y$ ) axis.
Draw a linear scale on the vertical axis that must start at zero and increase by equal, uniform increments (e.g., 2, 4, 6).
Draw bars so they all have the exact same width.
Leave equal gaps between every bar to represent the data as distinct and categorical.

Other variations include the Comparative Bar Chart, which uses side-by-side bars to compare different groups across the same categories, and the Compound (Stacked) Bar Chart, where sub-categories are stacked vertically.

Calculating Angles for Pie Charts

A pie chart represents the whole dataset as a full $360^\circ$ circle. Each Sector has an angle directly proportional to the frequency of that category. You cannot compare actual frequencies between two different pie charts by sector size alone unless the total frequencies are confirmed to be identical.

To construct a pie chart accurately (within a $\pm 2^\circ$ tolerance), you must convert frequencies into angles using a Multiplier. Ensure all sectors are labelled with the category name or a key, as labelling with only angles is insufficient for full marks.

\text{Angle of Sector} = \frac{\text{Frequency of Category}}{\text{Total Frequency}} \times 360^\circ

Worked Example: Pie Chart Angles

Calculate the pie chart angles for a survey of 25 people regarding their favourite fruit: Apple (10), Banana (8), and Pear (7).

Step 1: Calculate the Total Frequency.

$\text{Total Frequency} = 10 + 8 + 7 = 25$ people

Step 2: State the angle formula.

$\text{Angle of Sector} = \frac{\text{Frequency}}{\text{Total Frequency}} \times 360^\circ$

Step 3: Calculate the multiplier.

$\text{Multiplier} = 360^\circ \div 25 = 14.4^\circ \text{ per person}$

Step 4: Substitute and calculate the angle for each category.

$\text{Apple} = 10 \times 14.4^\circ = 144^\circ$
$\text{Banana} = 8 \times 14.4^\circ = 115.2^\circ$
$\text{Pear} = 7 \times 14.4^\circ = 100.8^\circ$

Interpreting Pictograms

Using pictures to represent numbers can be quick, but you must always check what one picture is worth. A Pictogram uses repeated icons or symbols to represent frequency.

Every pictogram must have a Key defining the numerical value of one full symbol. Partial symbols are used for frequencies that are not multiples of the key value. For example, if a full circle represents 8 units, a half-circle represents 4 units. Symbols must be of equal size and clearly aligned in rows or columns for accurate comparison.

Worked Example: Pictogram Frequencies

A pictogram shows 3.5 circles for a specific category. The key states that 1 circle represents 8 units. Calculate the total frequency for this category.

Step 1: State the formula for calculating frequency from symbols.

$\text{Total Frequency} = (\text{Full Symbols} \times \text{Value per Symbol}) + \text{Value of Partial Symbols}$

Step 2: Substitute the known values from the key.

$\text{Value of Full Symbols} = 3 \times 8 = 24$ units
$\text{Value of Partial Symbol} = 0.5 \times 8 = 4$ units

Step 3: Calculate the final answer.

$\text{Total Frequency} = 24 + 4 = 28$ units

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Exam Tips

Common Mistake
Students often mistakenly provide the frequency number (e.g., '12') as the mode instead of the actual category name (e.g., 'Blue').
2
In pie chart questions, always explicitly show your 'Multiplier' calculation (360 ÷ Total Frequency) as a standalone step to secure method marks.
3
If a pie chart is labelled 'Not to scale', you must use calculation methods rather than measuring the printed diagram with a protractor.
4
For bar chart questions, Edexcel often awards a Follow-Through (ft) mark: if your frequency table in Part A is incorrect, you can still gain full marks for drawing a bar chart in Part B that accurately reflects your incorrect values.

Key Terms(13)

Categorical data: Data that can be sorted into distinct, non-numerical, non-overlapping groups.
Tally: A running count using marks (vertical lines), usually grouped in fives with a diagonal strike-through.
Frequency: The number of times a specific category or value occurs within a dataset.
Total Frequency: The sum of all values in the frequency column, representing the total size of the dataset.
Modal Category: The specific category name that appears most frequently in a categorical dataset.
Bar Chart: A visual representation where the height (or length) of rectangular bars is proportional to the frequency.
Linear scale: A scale on an axis that starts at zero and increases by equal, uniform numerical increments.
Comparative Bar Chart: Uses side-by-side bars to compare different groups across the same categories.
Compound (Stacked) Bar Chart: A bar chart where bars for sub-categories are stacked vertically to show a cumulative total.
Sector: A 'slice' of a pie chart representing a specific category, with an angle proportional to its frequency.
Multiplier: The number of degrees assigned to a single unit of frequency in a pie chart, calculated by dividing 360 by the total frequency.
Pictogram: A diagram using repeated icons or symbols to represent frequency.
Key: A mandatory legend on a pictogram explaining the numerical value of a single symbol.

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Key Terms(13)

Categorical data: Data that can be sorted into distinct, non-numerical, non-overlapping groups.
Tally: A running count using marks (vertical lines), usually grouped in fives with a diagonal strike-through.
Frequency: The number of times a specific category or value occurs within a dataset.
Total Frequency: The sum of all values in the frequency column, representing the total size of the dataset.
Modal Category: The specific category name that appears most frequently in a categorical dataset.
Bar Chart: A visual representation where the height (or length) of rectangular bars is proportional to the frequency.
Linear scale: A scale on an axis that starts at zero and increases by equal, uniform numerical increments.
Comparative Bar Chart: Uses side-by-side bars to compare different groups across the same categories.
Compound (Stacked) Bar Chart: A bar chart where bars for sub-categories are stacked vertically to show a cumulative total.
Sector: A 'slice' of a pie chart representing a specific category, with an angle proportional to its frequency.
Multiplier: The number of degrees assigned to a single unit of frequency in a pie chart, calculated by dividing 360 by the total frequency.
Pictogram: A diagram using repeated icons or symbols to represent frequency.
Key: A mandatory legend on a pictogram explaining the numerical value of a single symbol.

Charts for Categorical Data

Frequency Tables

Constructing Bar Charts

Visualising data makes it instantly easier to spot trends. A Bar Chart represents discrete or categorical data where the height of rectangular bars is proportional to the frequency.

To construct a bar chart, follow these step-by-step rules:

Place the categories on the horizontal ( $x$ ) axis and Frequency on the vertical ( $y$ ) axis.
Draw a linear scale on the vertical axis that must start at zero and increase by equal, uniform increments (e.g., 2, 4, 6).
Draw bars so they all have the exact same width.
Leave equal gaps between every bar to represent the data as distinct and categorical.

Calculating Angles for Pie Charts

\text{Angle of Sector} = \frac{\text{Frequency of Category}}{\text{Total Frequency}} \times 360^\circ

Worked Example: Pie Chart Angles

Calculate the pie chart angles for a survey of 25 people regarding their favourite fruit: Apple (10), Banana (8), and Pear (7).

Step 1: Calculate the Total Frequency.

$\text{Total Frequency} = 10 + 8 + 7 = 25$ people

Step 2: State the angle formula.

$\text{Angle of Sector} = \frac{\text{Frequency}}{\text{Total Frequency}} \times 360^\circ$

Step 3: Calculate the multiplier.

$\text{Multiplier} = 360^\circ \div 25 = 14.4^\circ \text{ per person}$

Step 4: Substitute and calculate the angle for each category.

$\text{Apple} = 10 \times 14.4^\circ = 144^\circ$
$\text{Banana} = 8 \times 14.4^\circ = 115.2^\circ$
$\text{Pear} = 7 \times 14.4^\circ = 100.8^\circ$

Interpreting Pictograms

Using pictures to represent numbers can be quick, but you must always check what one picture is worth. A Pictogram uses repeated icons or symbols to represent frequency.

Worked Example: Pictogram Frequencies

A pictogram shows 3.5 circles for a specific category. The key states that 1 circle represents 8 units. Calculate the total frequency for this category.

Step 1: State the formula for calculating frequency from symbols.

$\text{Total Frequency} = (\text{Full Symbols} \times \text{Value per Symbol}) + \text{Value of Partial Symbols}$

Step 2: Substitute the known values from the key.

$\text{Value of Full Symbols} = 3 \times 8 = 24$ units
$\text{Value of Partial Symbol} = 0.5 \times 8 = 4$ units

Step 3: Calculate the final answer.

$\text{Total Frequency} = 24 + 4 = 28$ units

Sign up to continue reading

Get full access to revision notes, key terms, and exam tips for every subtopic.

Exam Tips

Common Mistake
Students often mistakenly provide the frequency number (e.g., '12') as the mode instead of the actual category name (e.g., 'Blue').
2
In pie chart questions, always explicitly show your 'Multiplier' calculation (360 ÷ Total Frequency) as a standalone step to secure method marks.
3
If a pie chart is labelled 'Not to scale', you must use calculation methods rather than measuring the printed diagram with a protractor.
4
For bar chart questions, Edexcel often awards a Follow-Through (ft) mark: if your frequency table in Part A is incorrect, you can still gain full marks for drawing a bar chart in Part B that accurately reflects your incorrect values.

Key Terms(13)

Categorical data: Data that can be sorted into distinct, non-numerical, non-overlapping groups.
Tally: A running count using marks (vertical lines), usually grouped in fives with a diagonal strike-through.
Frequency: The number of times a specific category or value occurs within a dataset.
Total Frequency: The sum of all values in the frequency column, representing the total size of the dataset.
Modal Category: The specific category name that appears most frequently in a categorical dataset.
Bar Chart: A visual representation where the height (or length) of rectangular bars is proportional to the frequency.
Linear scale: A scale on an axis that starts at zero and increases by equal, uniform numerical increments.
Comparative Bar Chart: Uses side-by-side bars to compare different groups across the same categories.
Compound (Stacked) Bar Chart: A bar chart where bars for sub-categories are stacked vertically to show a cumulative total.
Sector: A 'slice' of a pie chart representing a specific category, with an angle proportional to its frequency.
Multiplier: The number of degrees assigned to a single unit of frequency in a pie chart, calculated by dividing 360 by the total frequency.
Pictogram: A diagram using repeated icons or symbols to represent frequency.
Key: A mandatory legend on a pictogram explaining the numerical value of a single symbol.

Previous Subtopic: Populations and SamplesPopulations and Samples Next NoteCharts for Discrete and Time Series Data

Back to Charts and Diagrams

Put your knowledge into practice — try past paper questions for Mathematics

Key Terms(13)

Categorical data: Data that can be sorted into distinct, non-numerical, non-overlapping groups.
Tally: A running count using marks (vertical lines), usually grouped in fives with a diagonal strike-through.
Frequency: The number of times a specific category or value occurs within a dataset.
Total Frequency: The sum of all values in the frequency column, representing the total size of the dataset.
Modal Category: The specific category name that appears most frequently in a categorical dataset.
Bar Chart: A visual representation where the height (or length) of rectangular bars is proportional to the frequency.
Linear scale: A scale on an axis that starts at zero and increases by equal, uniform numerical increments.
Comparative Bar Chart: Uses side-by-side bars to compare different groups across the same categories.
Compound (Stacked) Bar Chart: A bar chart where bars for sub-categories are stacked vertically to show a cumulative total.
Sector: A 'slice' of a pie chart representing a specific category, with an angle proportional to its frequency.
Multiplier: The number of degrees assigned to a single unit of frequency in a pie chart, calculated by dividing 360 by the total frequency.
Pictogram: A diagram using repeated icons or symbols to represent frequency.
Key: A mandatory legend on a pictogram explaining the numerical value of a single symbol.