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Data Handling and Probability - Introduction to pie charts

Grade 5IGCSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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A pie chart is a circular graph used to show how a whole set of data is divided into parts or categories.

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The entire circle represents the total amount (100% or 360 degrees).

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Each 'slice' of the pie is called a sector, and its size is proportional to the quantity it represents.

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Comparing sectors: The larger the sector, the higher the frequency or value of that category.

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Interpreting fractions: Common divisions include half (180°), quarters (90°), and eighths (45°).

📐Formulae

Angle of a Sector=Value of CategoryTotal Value×360∘\text{Angle of a Sector} = \frac{\text{Value of Category}}{\text{Total Value}} \times 360^\circ

Fraction of a Sector=Value of CategoryTotal Value\text{Fraction of a Sector} = \frac{\text{Value of Category}}{\text{Total Value}}

Value of Category=Angle of Sector360∘×Total Value\text{Value of Category} = \frac{\text{Angle of Sector}}{360^\circ} \times \text{Total Value}

💡Examples

Problem 1:

In a survey of 40 students about their favorite fruit, 10 students chose 'Apple'. What fraction of the pie chart should the 'Apple' sector occupy, and what is the angle of this sector?

Solution:

Fraction = 1/41/4; Angle = 90∘90^\circ.

Explanation:

To find the fraction, divide the category value by the total: 10/40=1/410/40 = 1/4. To find the angle, multiply the fraction by the total degrees in a circle: 1/4×360∘=90∘1/4 \times 360^\circ = 90^\circ.

Problem 2:

A pie chart showing favorite colors has a sector for 'Blue' with an angle of 180∘180^\circ. If 60 people were surveyed in total, how many people chose Blue?

Solution:

30 people.

Explanation:

Since 180∘180^\circ is exactly half of 360∘360^\circ (180/360=1/2180/360 = 1/2), the number of people who chose Blue is half of the total survey count. 1/2×60=301/2 \times 60 = 30.

Problem 3:

A pie chart is divided into three sections: A, B, and C. Section A is 120∘120^\circ and Section B is 150∘150^\circ. What is the angle for Section C?

Solution:

90∘90^\circ.

Explanation:

The total sum of angles in a pie chart must be 360∘360^\circ. Therefore, Angle C = 360∘−(120∘+150∘)=360∘−270∘=90∘360^\circ - (120^\circ + 150^\circ) = 360^\circ - 270^\circ = 90^\circ.