Pie Charts

Purpose of Pie Charts

Pie charts are used to represent parts of a whole in a clear, visual way. Each sector (or "slice") of the pie shows the proportion of each category relative to the total. This makes it easy to compare how large or small each part is compared to others.

The size of each sector can be shown either as a percentage of the total or as an angle in degrees. Since a full circle is $360^\circ$, the angle of each sector corresponds to the fraction of the total it represents.

For example, if a category makes up $25\%$ of the total, its sector will have an angle of $25\% \times 360^\circ = 90^\circ$.

For instance, if you have 10 out of 40 students liking apples, the angle for apples is calculated as $\frac{10}{40} \times 360^\circ = 90^\circ$.

Constructing Pie Charts

To draw a pie chart, follow these steps:

• Calculate the total frequency (sum of all category frequencies).
• Find the fraction of the total for each category by dividing the category frequency by the total.
• Calculate the angle for each category using the formula:

Angle for category = $\frac{\text{category frequency}}{\text{total frequency}} \times 360^\circ$

Use a protractor to measure and draw each sector with the correct angle, starting from a fixed line (usually the vertical or horizontal axis). Label each sector clearly with the category name and percentage or frequency.

For instance, if you have the following data for favourite fruits among 40 students:

• Apples: 10
• Bananas: 15
• Oranges: 5
• Grapes: 10

The total is $10 + 15 + 5 + 10 = 40$. The angle for Bananas is:

$\frac{15}{40} \times 360^\circ = 135^\circ$

You would draw a sector of $135^\circ$ for Bananas.

Interpreting Pie Charts

When reading pie charts, you can:

• Compare the sizes of sectors to see which categories are larger or smaller.
• Estimate percentages by comparing sector angles to the full circle.
• Identify the largest and smallest categories quickly.

For example, if a sector looks like about one quarter of the pie, it represents roughly $25\%$ of the total.

Advantages and Limitations

Advantages of pie charts include:

• They are easy to understand and visually appealing.
• They clearly show proportions and how each part relates to the whole.

However, pie charts have some limitations:

• They are not suitable for data with many categories, as the sectors become too small and hard to distinguish.
• They do not show exact values as clearly as some other diagrams.

Example: Calculating Angles for a Pie Chart

A school surveyed 50 students about their favourite sports. The results were:

• Football: 20
• Basketball: 10
• Tennis: 5
• Swimming: 15

Calculate the angle for each sport to draw a pie chart.

First, total students = $20 + 10 + 5 + 15 = 50$.

Angle for Football:

$\frac{20}{50} \times 360^\circ = 144^\circ$

Angle for Basketball:

$\frac{10}{50} \times 360^\circ = 72^\circ$

Angle for Tennis:

$\frac{5}{50} \times 360^\circ = 36^\circ$

Angle for Swimming:

$\frac{15}{50} \times 360^\circ = 108^\circ$

These angles can now be used to draw the pie chart sectors with a protractor.