Collecting and Organising Data
5. Data Visualisation
Learning outcomes
- I can construct appropriate statistical graphs.
- I can choose suitable graphical representations.
- I can compare different graph types.
- I can interpret graphical displays.
- I can communicate data effectively using graphs.
Introduction
Large tables of numbers can be difficult to understand, but graphs make patterns much easier to see. By displaying data visually, graphs help us identify trends, compare groups, recognise relationships, and communicate information clearly.
Different types of data require different types of graphs. A bar chart is useful for comparing categories, while a line graph shows changes over time. Choosing the correct graph is an important statistical skill because the wrong graph can make data confusing or even misleading.
What Is Data Visualisation?
Data visualisation is the presentation of data using graphs, charts, or diagrams.
It helps people:
- Understand information quickly.
- Identify patterns.
- Compare values.
- Detect trends.
- Communicate results clearly.
Scientists, businesses, governments, and researchers all use data visualisation to present information effectively.
Figure 1. Different graph types are used to display different kinds of data.
Choosing the Right Graph
Different graphs are designed for different purposes.
| Graph Type. | Best Used For |
|---|---|
| Bar chart | Comparing categories |
| Line graph | Showing changes over time |
| Pie chart | Showing parts of a whole |
| Histogram | Continuous numerical data |
| Scatter plot | Relationships between two variables |
Selecting the correct graph makes the data easier to interpret.
Bar Charts
A bar chart compares quantities in different categories.
Features:
- Separate bars.
- Equal bar widths.
- Categories on one axis.
- Frequency or value on the other axis.
Examples:
- Favourite sports.
- Number of students in each grade.
- Types of pets owned.
Bar charts are best for qualitative or discrete data.
Figure 2. Bar charts compare values across different categories.
Line Graphs
A line graph shows how a quantity changes over time or another ordered variable.
Features:
- Data points joined by lines.
- Ordered horizontal axis.
- Useful for identifying trends.
Examples:
- Daily temperature.
- Population growth.
- Monthly rainfall.
- Stock prices.
Line graphs are best for continuous data collected over time.
Pie Charts
A pie chart shows how a whole is divided into different parts.
Each slice represents a proportion of the total.
Examples:
- Household spending.
- Survey responses.
- Market share.
- Favourite school subjects.
All slices together represent 100% of the data.
Pie charts work best when there are only a few categories.
Figure 3. Pie charts show how categories contribute to a whole.
Histograms
A histogram displays the distribution of continuous data.
Unlike a bar chart:
- Bars touch each other.
- Data is grouped into class intervals.
- The horizontal axis represents numerical ranges.
Examples:
- Heights.
- Test scores.
- Masses.
- Ages.
Histograms help reveal the shape of a distribution.
Scatter Plots
A scatter plot shows the relationship between two numerical variables.
Each point represents one observation.
Examples:
- Height versus weight.
- Hours studied versus exam score.
- Temperature versus electricity use.
Scatter plots help identify:
- Positive relationships.
- Negative relationships.
- No relationship.
Figure 4. Scatter plots help identify relationships between two numerical variables.
Comparing Common Graph Types
| Graph | Best For | Data Type |
|---|---|---|
| Bar chart | Comparing categories. | Qualitative or discrete |
| Line graph | Trends over time | Continuous |
| Pie chart | Parts of a whole | Categorical |
| Histogram | Distribution | Continuous |
| Scatter plot. | Relationships | Two numerical variables |
Each graph highlights different features of the data.
Constructing Good Graphs
A well-designed graph should include:
- A clear title.
- Labelled axes.
- Appropriate units.
- Even scales.
- Accurate plotting.
- A legend (if needed).
Graphs should be neat and easy to read.
Interpreting Graphs
When reading a graph, ask questions such as:
- Which category is largest?
- Is there an increasing or decreasing trend?
- Are there any unusual values?
- Is there a relationship between variables?
- What conclusions can be drawn?
Always consider the scale and labels before interpreting the data.
Avoiding Misleading Graphs
Graphs can be misleading if they use:
- Unequal intervals.
- Missing labels.
- Truncated axes.
- Inappropriate graph types.
- Distorted scales.
Accurate graphs communicate information honestly.
Figure 5. Clear scales, labels, and graph choices help prevent misleading interpretations.
Communicating Data Effectively
Graphs help communicate information because they:
- Summarise large datasets.
- Highlight important patterns.
- Make comparisons easier.
- Support conclusions.
- Improve presentations and reports.
Choosing the correct graph allows others to understand the results quickly.
Worked Example
Question
Choose the most appropriate graph for each dataset.
| Dataset | Best Graph |
|---|---|
| Favourite fruit of students | ? |
| Daily temperature for one month | ? |
| Heights of 200 students | ? |
| Hours studied versus exam marks. | ? |
Solution
| Dataset | Best Graph |
|---|---|
| Favourite fruit | Bar chart |
| Daily temperature | Line graph |
| Heights of students | Histogram |
| Hours studied versus exam marks | Scatter plot |
Real-World Connection
Weather services use line graphs to show changes in temperature over time, while governments often use bar charts to compare population sizes between regions. Scientists commonly use scatter plots to investigate relationships between variables, such as the connection between air pollution and respiratory illnesses. Choosing the correct graph helps people understand complex information quickly and make informed decisions.
Did You Know?
Many misleading graphs exaggerate differences by starting the vertical axis well above zero. A small increase can then appear much larger than it really is. Whenever you look at a graph, always check the scale before drawing conclusions.
Key Terms
Bar chart – A graph that compares values across different categories using separate bars.
Data visualisation – The presentation of data using graphs, charts, or diagrams.
Histogram – A graph showing the distribution of continuous data using touching bars.
Legend – A key that explains the symbols, colours, or patterns used in a graph.
Line graph – A graph showing changes in a variable over an ordered scale, usually time.
Pie chart – A circular chart showing how categories make up a whole.
Scatter plot – A graph that displays the relationship between two numerical variables.
Trend – The general direction in which data changes over time or across values.
Key Takeaways
- Data visualisation presents information in graphical form, making patterns and relationships easier to understand.
- Different datasets require different graphs: bar charts compare categories, line graphs show trends, pie charts display proportions, histograms show distributions, and scatter plots reveal relationships.
- Good graphs include clear titles, labelled axes, appropriate scales, units, and legends where necessary.
- Interpreting graphs involves identifying patterns, trends, comparisons, and unusual values.
- Poor graph design or inappropriate scales can produce misleading conclusions.
- Choosing the most appropriate graph helps communicate statistical information accurately and effectively.