Pie Chart Maker: Visualizing Proportions and Percentages

What is a Pie Chart?

A pie chart is a circular statistical graphic, which is divided into slices to illustrate numerical proportion. In a pie chart, the arc length of each slice (and consequently its central angle and area) is proportional to the quantity it represents.

Components of a Pie Chart

• Title: Describes the overall content of the chart
• Slices: Represent different categories or parts of the whole
• Labels: Identify each slice
• Legend: Explains what each color or pattern represents
• Percentages: Show the proportion of each slice relative to the whole

Mathematical Representation

The formula for calculating the central angle of each slice in a pie chart is:

\[ \text{Central Angle} = \frac{\text{Value of Category}}{\text{Total of All Values}} \times 360° \]

The percentage for each category is calculated as:

\[ \text{Percentage} = \frac{\text{Value of Category}}{\text{Total of All Values}} \times 100\% \]

Calculation Steps

1. Sum up all the values to get the total
2. For each category:
   • Calculate its percentage of the total
   • Calculate its central angle
3. Draw the circle and divide it into slices based on the calculated angles
4. Label each slice and add the percentages

Example and Visual Representation

Let's create a pie chart showing the distribution of expenses:

• Housing: $1000
• Food: $500
• Transportation: $300
• Entertainment: $200

Calculations:

• Total: $1000 + $500 + $300 + $200 = $2000
• Housing: (1000 / 2000) × 100% = 50%, Angle: 0.5 × 360° = 180°
• Food: (500 / 2000) × 100% = 25%, Angle: 0.25 × 360° = 90°
• Transportation: (300 / 2000) × 100% = 15%, Angle: 0.15 × 360° = 54°
• Entertainment: (200 / 2000) × 100% = 10%, Angle: 0.1 × 360° = 36°

This pie chart visually represents the distribution of expenses. Each slice's area is proportional to the percentage of the total expense it represents, making it easy to compare different categories at a glance.