Pie Chart

A pie chart doesn’t just show you percentages, it can also help you work out actual numbers and find hidden data.

🛎️ Formula to Find the Frequency (Count) of a Category:

$$
\text{Count of the Category} = \left( \frac{\text{Central Angle}}{360^\circ} \right) \times \text{Total Count}
$$

🛎️ Pie Chart Example: 

We are given favourite Pizza Toppings of Students:

• Pepper = 90°, corresponding to 20 students.
• Mushroom = 162°
• Ham = 36°
• Pineapple = unknown

1) How many students took the survey?

We’re told that 90° represents 20 students (Pepper).

• Use the formula:

$$
\frac{90^\circ}{360^\circ} \times \text{Total} = 20
$$

• Solving for Total:

$$
\text{Total} = 80 \text{ students}
$$

2) How many students prefer ham topping?

• Ham = 36°, total students = 80

$$
\frac{36^\circ}{360^\circ} \times 80 = \frac{1}{10} \times 80 = 8 \text{ students}
$$

3) What percentage of students like pineapple?

• Pineapple angle is calculated as:

$$
360^\circ – 90^\circ – 162^\circ – 36^\circ = 72^\circ
$$

• The percentage of students who prefer pineapple:

$$
\frac{72^\circ}{360^\circ} \times 100\% = 20\%
$$