Pie Charts

Purpose of Pie Charts

Pie charts are used to show how different parts make up a whole. They display proportions visually, making it easy to compare categories at a glance. Each slice of the pie represents a category, with its size proportional to the percentage it contributes to the total.

For example, a pie chart could show the percentage of different types of land use in a city, such as residential, commercial, parks, and industrial areas.

Pie charts express data as percentages of 100%, helping to understand the relative importance or size of each category within the whole dataset. They are best used for categorical data rather than continuous data.

Constructing Pie Charts

To construct a pie chart, follow these steps:

• Calculate the percentage of each category from the total.
• Convert each percentage into an angle for the pie chart. Since a full circle is $360^\circ$, multiply each percentage by $\frac{360}{100}$ to get the angle.
• Draw the pie chart with sectors (slices) corresponding to these angles using a protractor for accuracy.

For instance, if a category represents $25\%$ of the total, its angle will be:

$$25 \times \frac{360}{100} = 90^\circ$$

This means the sector for this category will be a quarter of the circle.

Learning example:

Imagine a survey of favourite fruits among 100 people with the following results:

• Apples: 40 people
• Bananas: 25 people
• Oranges: 20 people
• Grapes: 15 people

Step 1: Calculate percentages:

• Apples: $\frac{40}{100} \times 100 = 40\%$
• Bananas: $\frac{25}{100} \times 100 = 25\%$
• Oranges: $\frac{20}{100} \times 100 = 20\%$
• Grapes: $\frac{15}{100} \times 100 = 15\%$

Step 2: Convert percentages to angles:

• Apples: $40 \times \frac{360}{100} = 144^\circ$
• Bananas: $25 \times \frac{360}{100} = 90^\circ$
• Oranges: $20 \times \frac{360}{100} = 72^\circ$
• Grapes: $15 \times \frac{360}{100} = 54^\circ$

Step 3: Draw the pie chart with these sector angles using a protractor.

Interpreting Pie Charts

When interpreting pie charts, focus on:

• Identifying the largest and smallest sectors to understand which categories dominate or are least represented.
• Comparing sector sizes to see how categories relate to each other in size.
• Understanding the overall distribution of data to identify patterns or trends within the dataset.

For example, if a pie chart shows that 60% of a city's land is residential and only 5% is industrial, you can conclude that the city is primarily residential.

Limitations of Pie Charts

While pie charts are useful, they have limitations:

• Many categories: Pie charts become cluttered and hard to read if there are too many categories (usually more than 5 or 6).
• Precision: They are less precise than tables or bar charts because estimating exact values from angles or sector sizes can be difficult.
• Trends over time: Pie charts cannot show changes or trends over time; line graphs are better suited for this.