Statistical Diagrams
Statistical Diagrams
Statistical diagrams allow data to be displayed visually, making it easier to identify patterns, compare groups and communicate findings. Each diagram type is suited to particular data types and questions.
Diagram Types and When to Use Them
| Diagram | Data type | Best for |
|---|---|---|
| Frequency table | Any | Recording and organising raw data |
| Bar chart | Categorical or discrete | Comparing frequencies of categories |
| Pie chart | Categorical | Showing proportions of a whole |
| Pictogram | Categorical | Simple frequency comparison with symbols |
| Vertical line chart | Discrete quantitative | Frequency distribution for discrete data |
| Line graph | Continuous (time series) | Trends over time |
Constructing and Interpreting Pie Charts
Each sector angle is proportional to the frequency:
\[ \text{Sector angle} = \frac{\text{frequency}}{\text{total}} \times 360° \]To read a pie chart: \( \text{frequency} = \frac{\text{sector angle}}{360°} \times \text{total} \).
Time Series
A time series line graph plots a variable against time. Key features to comment on: overall trend (increasing, decreasing, stable), seasonal patterns, anomalies (unusual values).
Key Takeaways
- Bar charts: heights represent frequencies; gaps between bars for categorical data.
- Pie charts: \( \text{angle}=\text{freq}/\text{total}\times360° \). All sectors must sum to 360°.
- Line graphs connect points in time order and show trends — not used for categorical data.
- Vertical line charts: lines at each discrete value, height = frequency. No gaps filled in.
- Always label axes, give a title, and include a scale.