Pie Charts

• The $360^\circ$ Rule: Since a circle contains $360^\circ$, the sum of all sector angles in a pie chart must equal exactly $360^\circ$.

• Linear Scaling: The relationship between the data value and the angle is linear. If Category A has twice the value of Category B, its sector angle will be exactly twice as large.

• Unit Conversion: To find the angle for a single unit of data, divide $360^\circ$ by the total frequency ($360 / \text{Total}$). This 'multiplier' can then be applied to each category.

Step-by-Step Construction

• Calculate Total Frequency: Sum the values of all categories to determine the 'whole'.
• Determine the Multiplier: Calculate how many degrees represent one unit of data using the formula: $\text{Multiplier} = \frac{360^\circ}{\text{Total Frequency}}$
• Calculate Sector Angles: Multiply each category's frequency by the multiplier. Alternatively, use the fraction method: $\text{Angle} = \frac{\text{Category Value}}{\text{Total Value}} \times 360^\circ$
• Draw and Measure: Use a compass to draw the circle and a protractor to measure each calculated angle, starting from a vertical radius (the '12 o'clock' position).

Finding Missing Information

• If the angle and the value of one sector are known, find the total by calculating the value of $1^\circ$ and multiplying by 360.

• Check the Scale: Examiners often provide diagrams 'not to scale.' Never measure angles with a protractor unless the question explicitly states the diagram is accurate; use calculation instead.

• The Sum Check: Always verify that your calculated angles sum to $360^\circ$ before drawing. If they don't, re-check your total frequency or division.

• Visual Cues: Look for right angles ($90^\circ$) which represent exactly $25\%$ of the data, or straight lines through the center ($180^\circ$) representing $50\%$.

• Rounding Errors: If rounding angles to the nearest degree, ensure the final sum is still $360^\circ$ by adjusting the largest sector if necessary.

• Confusing Angle with Value: Students often mistake the degree measurement for the actual frequency. Always distinguish between the 'size of the slice' and the 'number it represents'.

• 3D Distortion: Using 3D pie charts in reports can be misleading because the perspective makes the 'front' slices appear larger than the 'back' slices, even if they represent the same value.

• Too Many Slices: Including too many small categories makes the chart unreadable. It is standard practice to group very small values into an 'Other' category.