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Statistics and Probability - Introduction to pie charts

Grade 6IGCSE

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

🔑Concepts

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A pie chart is a circular graph divided into 'slices' or sectors to show the relative sizes of different categories of data.

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The entire circle represents the total data (the sum of all frequencies) and is equal to 360∘360^\circ.

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Each sector represents a fraction or percentage of the whole; a larger sector means a higher frequency.

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Pie charts are best used for comparing parts of a whole rather than showing changes over time.

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A protractor is used to measure and draw the angles for each sector accurately.

📐Formulae

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

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

Total Sum of Angles=360∘\text{Total Sum of Angles} = 360^\circ

💡Examples

Problem 1:

In a survey of 60 students, 15 students said their favorite fruit is Apple. Calculate the angle of the sector for 'Apple' in a pie chart.

Solution:

90∘90^\circ

Explanation:

To find the angle, use the formula: (Frequency÷Total)×360∘(\text{Frequency} \div \text{Total}) \times 360^\circ. Here, (15÷60)×360∘=0.25×360∘=90∘(15 \div 60) \times 360^\circ = 0.25 \times 360^\circ = 90^\circ. This represents a quarter of the circle.

Problem 2:

A pie chart represents the types of pets owned by 120 people. The sector for 'Dogs' has an angle of 108∘108^\circ. How many people own dogs?

Solution:

36 people

Explanation:

To find the value from the angle, use the formula: (Angle÷360∘)×Total Value(\text{Angle} \div 360^\circ) \times \text{Total Value}. Here, (108∘÷360∘)×120=0.3×120=36(108^\circ \div 360^\circ) \times 120 = 0.3 \times 120 = 36.

Problem 3:

A pie chart is divided into three sections: Red, Blue, and Green. If Red is 120∘120^\circ and Blue is 150∘150^\circ, what is the angle for the Green section?

Solution:

90∘90^\circ

Explanation:

The sum of all angles in a pie chart must be 360∘360^\circ. Subtract the known angles from the total: 360∘−(120∘+150∘)=360∘−270∘=90∘360^\circ - (120^\circ + 150^\circ) = 360^\circ - 270^\circ = 90^\circ.