Representing categorical and simple numerical data

Statistics • Statistics

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How is a pie chart sector angle calculated?

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Sector angle equals (category frequency ÷ total frequency) × 360 degrees.

Key concepts

What you'll likely be quizzed about

Categorical vs numerical data

Categorical data describes labels or groups, such as colours, brands or survey answers; the categories do not imply numerical order. Numerical data consists of values with numerical meaning; simple numerical data is discrete when it takes particular integer values. Identification of type dictates the choice of table or chart because categorical charts emphasise group comparisons while numerical charts emphasise value frequencies or trends.

Frequency tables

A frequency table lists each category or numerical value with its count (frequency). Frequency tables make calculation of totals, relative frequencies and percentages direct. For time series data, a table lists time points and corresponding values; the table arranges data so that plotting and trend analysis follow naturally.

Bar charts for categorical data

Bar charts represent each category by a bar whose height equals the category frequency or percentage. Separate bars prevent misreading by keeping categories distinct; bars require consistent width and gaps between them. A zero baseline prevents distortion because bars grow from zero, so use a zero axis to compare magnitudes accurately.

Pictograms for categorical data

Pictograms use repeated symbols to represent fixed units of frequency. Symbols must represent equal amounts and use a key to state the unit value. Scaling by partial symbols requires clear notation; inconsistency in symbol sizing or unit value causes misleading impressions, so pictograms suit small, simple datasets where counts map cleanly to whole symbols.

Pie charts for categorical data

Pie charts show each category as a sector with angle proportional to its share of the total. Calculation converts frequency to angle by multiplying (frequency/total) by 360 degrees. Pie charts emphasise parts of a whole; many small categories reduce clarity, so limit sectors to a few clear categories or combine minor categories into 'other'.

Vertical line charts for ungrouped discrete numerical data

Vertical line charts place discrete numerical values on the horizontal axis and draw a vertical line at each value with height equal to its frequency. Each line marks the frequency at an exact value, so the display highlights the distribution of discrete values without implying continuity between values. Use vertical line charts when data values are separate integers and exact frequencies matter.

Tables and line graphs for time series data

Time series tables order data by time and list the measured variable beside each time point. Line graphs plot time on the horizontal axis and connect successive data points with straight lines to show direction and rate of change. Connecting points reveals trends and short-term fluctuations; avoid connecting points across missing intervals that change time spacing.

Choosing the appropriate representation

Selection follows data type and purpose: use frequency tables, bar charts, pictograms or pie charts for categorical counts; use vertical line charts for discrete numerical distributions; use tables and line graphs for time-ordered data. Proper choice improves clarity and reduces misinterpretation because each representation emphasises different aspects of the data.

Key notes

Important points to keep in mind

Categorical data: use bar charts, pie charts, pictograms or frequency tables for clear group comparisons.

Discrete numerical data: use frequency tables or vertical line charts to show exact counts at each value.

Time series data: list values in time order in a table and use a line graph to show trends.

Always label axes, include units, and provide a key for pictograms or shaded charts.

Use a zero baseline for bar charts to avoid visual distortion.

Convert frequencies to percentages before drawing pie charts and calculate angles using 360° × (frequency ÷ total).

Keep pictogram symbols equal and state the unit value clearly in a key.

Avoid too many categories in a pie chart; combine minor categories into 'other' for clarity.

Preserve true time spacing on time series graphs to represent trends accurately.

Check that frequencies sum to the total before plotting to prevent calculation errors.