A diagram is a graphical representation of data that allows the overall picture to be seen at a glance.

Suitable for: Variable Discrete

Characteristics:

• Vertical bars
• With gaps between the bars (because values are discrete)
• Bar height = frequency

Example: number of siblings (n = 30)

Suitable for: Variable Continuous (grouped table)

Characteristics:

• Adjacent rectangles
• No gaps between rectangles (continuity)
• Rectangle width = class width
• Rectangle height = frequency

Example: grouped scores (n = 40)

⚠️ Key difference: Bar chart vs Histogram

Suitable for: Variable qualitative or presenting relative frequency

Characteristics:

• Circle divided into sectors
• Sector size = relative frequency (fraction of the whole)
• Whole pie = 100% = 360°

Example: Transport to school

💡 Computing the sector angle:

\(\text{angle} = \text{relative frequency} \times 360°\)

Example: 40% → 0.40 × 360° = 144°

Suitable for: Variable Continuous

How to build:

1. Mark a point above the midpoint of each class at the height of the frequency
2. Connect the points with straight lines
3. Close to the x-axis at both ends

Displays: Cumulative frequency

How to build:

1. Mark a point above upper boundary of each class
2. Point height = cumulative frequency
3. Connect with a line

💡 Applications:

• Finding the median graphically
• Finding percentiles
• Answering questions of the type "how many up to…"