Data can be qualitative, described in words such as colours or brands, or quantitative, made of numbers. Quantitative data is either discrete, taking separate countable values such as the number of pets, or continuous, measured on a scale such as height or time. Data you collect yourself is primary; data someone else collected is secondary.
Classifying data
- Qualitative (categorical): words or categories
- Quantitative: numbers
- Discrete: separate, countable values
- Continuous: measured, can take any value in a range
- Primary: collected by you; secondary: collected by someone else
Qualitative and quantitative data
Qualitative data describes a quality in words: eye colour, favourite sport, type of car. Quantitative data is numerical: height, number of goals, temperature. A quick test is whether you could calculate a mean; you can find the mean of heights but not of eye colours.
Discrete and continuous data
Quantitative data splits into two types. Discrete data takes separate values, usually counted: number of children, number of goals, shoe size. Continuous data is measured and can take any value within a range: height, mass, time. Continuous data is always rounded when it is recorded, which is why it is often grouped using inequalities such as 150 ≤ h < 160.
Primary and secondary data
Primary data is collected by you, for your own purpose, through a survey, experiment or measurements. Secondary data was collected by someone else, such as figures from a government website or a newspaper. Primary data fits your question exactly but takes time to collect; secondary data is quick to obtain but may not match your needs or may be out of date.
Grouping data
Large amounts of data, especially continuous data, are often grouped into classes. Classes for continuous data must not overlap or leave gaps, so use inequalities: 0 ≤ t < 10, 10 ≤ t < 20, and so on. Grouping makes data easier to read but loses the exact values.
Choosing how to display data
The type of data decides the chart. Qualitative data suits bar charts and pie charts; discrete data suits vertical line charts or bar charts; continuous data suits histograms, frequency polygons and cumulative frequency graphs.
Worked examples
Example 1. Classify each as qualitative or quantitative: (a) hair colour (b) number of pets (c) height.
- Hair colour is described in words.
- Number of pets and height are numbers.
Answer: (a) qualitative (b) quantitative (c) quantitative.
Example 2. Classify each as discrete or continuous: (a) shoe size (b) the time taken to run 400 m (c) the number of cars in a car park.
- Shoe sizes and numbers of cars take separate values.
- Time is measured and can take any value.
Answer: (a) discrete (b) continuous (c) discrete.
Example 3. A student measures the reaction times of her classmates. Is this primary or secondary data? Give one advantage.
- She collected it herself.
Answer: Primary data. It is collected exactly for her own question.
Example 4. Explain why a student's mass, recorded as 52 kg, is continuous data.
- Mass is measured, not counted.
- The true mass could be any value, such as 52.38 kg, and has been rounded.
Answer: Because mass can take any value within a range.
Example 5. Write suitable classes for grouping heights between 140 cm and 180 cm into four equal classes.
- Each class is 10 cm wide, with no gaps or overlaps.
Answer: 140 ≤ h < 150, 150 ≤ h < 160, 160 ≤ h < 170, 170 ≤ h < 180.
Common mistakes
- Calling shoe size continuous. Shoe sizes take separate values, so they are discrete.
- Calling all numbers quantitative. Numbers used as labels, like a bus route, are really categories.
- Overlapping class boundaries. Use inequalities such as 10 ≤ t < 20.
- Confusing primary and secondary. Primary is collected by you; secondary by someone else.
- Using a pie chart for continuous data. Continuous data needs a histogram or frequency polygon.
How types of data are examined
Types of data are Foundation content in Edexcel GCSE (1MA1) and the 4MA1 International GCSE, usually as short definition and classification questions. Expect to:
- classify data as qualitative or quantitative
- classify quantitative data as discrete or continuous
- decide whether data is primary or secondary, with an advantage or disadvantage
- write suitable class intervals for grouped data
Practise with the frequency tables worksheet, which has answers, and the GCSE data and statistics revision engine.
Next, see charts and diagrams and averages from raw data.
Frequently asked questions
How is discrete data different from continuous data?
Discrete data takes separate countable values; continuous data is measured and can take any value in a range.
Is age discrete or continuous?
Age is continuous, although it is usually recorded in whole years.
What is secondary data?
Data that was collected by someone else, such as published statistics.