Types of Data
Classifying data and understanding grouped data structures
SPEC 2.1 • DATA PRESENTATION
Why Classify Data?
Before we can analyse data, we need to understand what type of data we're working with. Different data types require different statistical techniques.
Key Concept
The type of data determines which averages, diagrams, and statistical methods are appropriate to use.
Data Classification
CategoryTypeDescriptionQualitativeNon-numerical, descriptive datae.g., colours, names, categoriesQuantitativeDiscreteCountable, specific valuesContinuousMeasurable, any value in range
Qualitative vs Quantitative
Qualitative Data
Data that describes qualities or characteristics. Cannot be measured numerically.
Eye colour (blue, brown, green)
Car brand (Ford, BMW, Toyota)
Favourite subject (Maths, English)
Blood type (A, B, AB, O)
Quantitative Data
Data that can be measured or counted. Expressed as numbers.
Height (1.75 m)
Number of siblings (2)
Temperature (23.5°C)
Test score (87%)
Tip
Ask yourself: "Can I perform meaningful calculations with this data?" If yes, it's quantitative. If no, it's qualitative.
Discrete Data
Definition
Discrete data can only take specific, separate values. These are usually whole numbers that result from counting.
Discrete data has "gaps" between possible values - you cannot have values in between.
ExamplePossible ValuesWhy Discrete?
Number of children0, 1, 2, 3, 4, ...Cannot have 2.5 children
Shoe size (UK)3, 3.5, 4, 4.5, 5, ...Only specific sizes exist
Number of cars0, 1, 2, 3, ...Cannot have 1.7 cars
Dice roll1, 2, 3, 4, 5, 6Only 6 possible outcomes
Key Feature
Discrete data is typically obtained by counting.
Continuous Data
Definition
Continuous data can take any value within a given range. There are no restrictions on the values between measurements.
Continuous data can be measured to any degree of accuracy - the precision is limited only by the measuring instrument.
ExampleRangeWhy Continuous?
HeightAny positive valueCould be 172.456... cm
TimeAny positive valueCould be 12.3847... seconds
TemperatureAny value (including negative)Could be 23.1562...°C
MassAny positive valueCould be 65.2891... kg
Key Feature
Continuous data is typically obtained by measuring.
01Worked Example
Classify each of the following as qualitative, discrete, or continuous data:
(a) The number of goals scored in a football match
(b) The weight of apples in a bag
(c) The colour of cars in a car park
(d) The time taken to run 100 metres
(e) The number of pages in a book
Grouped Data
When we have a large amount of continuous data, it's often impractical to list every individual value. Instead, we group the data into class intervals.
Raw Data (Ungrouped)
23, 45, 31, 67, 52, 38, 41, 29, 55, 48, 33, 61, 44, 37, 50...
Hard to see patterns with many values!
Grouped Data
ClassFrequency
20 ≤ x < 303
30 ≤ x < 405
40 ≤ x < 506
50 ≤ x < 604
60 ≤ x < 702
Important
Grouping data makes patterns visible but we lose some detail about individual values.
Class Boundaries (Inequality Notation)
Key Concept
When classes are written using inequality notation like 10 ≤ x < 20, the boundaries are the values written - no adjustment needed.
The upper boundary of one class equals the lower boundary of the next class:
Class IntervalLower BoundaryUpper BoundaryClass WidthMidpoint
10 ≤ x < 2010201015
20 ≤ x < 3020301025
30 ≤ x < 4030401035
40 ≤ x < 5040501045
Note
A value of exactly 20 goes in the "20 ≤ x < 30" class (included in lower, excluded from upper).
Class Boundaries (Gap Notation)
Sometimes data is presented with apparent gaps between classes (e.g., 10-19, 20-29). For continuous data, we need to find the true boundaries.
Class (as written)Lower BoundaryUpper BoundaryClass WidthMidpoint
10 - 199.519.51014.5
20 - 2919.529.51024.5
30 - 3929.539.51034.5
40 - 4939.549.51044.5
Important
For whole number data: Lower boundary = Lower limit − 0.5, Upper boundary = Upper limit + 0.5
Class Width and Midpoints
Formulas
Inequality Notation
For 30 ≤ x < 50:
Width = 50 − 30 = 20
Midpoint = (30 + 50) ÷ 2 = 40
Gap Notation
For 30 - 49:
Boundaries: 29.5 and 49.5
Width = 49.5 − 29.5 = 20
Midpoint = (29.5 + 49.5) ÷ 2 = 39.5
Why Midpoints Matter
Midpoints are used to estimate the mean when calculating averages from grouped data. We assume all values in a class are at the midpoint.
Practice
Classify each as qualitative, discrete, or continuous:
(a) The number of students absent from school each day
(b) The length of a phone call
(c) The type of pet owned by families
(d) The speed of cars passing a point
Practice
For the following frequency table, find the class width and midpoint for each class:
Height (cm)Frequency
150 ≤ h < 1604
160 ≤ h < 1758
175 ≤ h < 1856
Note: Classes can have unequal widths - always calculate individually!
Summary
Data Classification
TypeDescriptionExamples
QualitativeNon-numerical, descriptiveColour, brand, category
DiscreteCountable, specific valuesNumber of people, goals, pages
ContinuousMeasurable, any value in rangeHeight, time, temperature
Grouped Data Quick Reference
Notation TypeExampleBoundaries
Inequality (10 ≤ x < 20)10 ≤ x < 20LB = 10, UB = 20
Gap (10 - 19)10 - 19LB = 9.5, UB = 19.5
Key Exam Skills
Identify data type by asking: counted or measured?
Read the notation carefully to determine boundaries
Class Width = Upper Boundary − Lower Boundary
Midpoint = (Lower + Upper) ÷ 2
Next: Why Classify Data?