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Data Handling and Probability - Introduction to pie charts

Grade 5Cambridge (IGCSE)

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

🔑Concepts

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A pie chart is a circular statistical graphic, which is divided into slices or sectors to illustrate numerical proportions.

A basic pie chart diagram showing a circle with a sector labeled.
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The entire circle represents the total sum of all data values, and it always adds up to 360∘360^\circ.

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The size of each sector is proportional to the quantity it represents. Larger quantities result in larger angles and larger slices.

A semi-circle representing 50 percent of a data set.
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To find the angle for a category, use the proportion of that category relative to the total, then multiply by 360∘360^\circ.

📐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.

Problem 4:

A school club has 20 members: 5 play Football, 10 play Basketball, and 5 play Tennis. Calculate the angles for each sport to draw a pie chart.

Pie chart divided into 180, 90, and 90 degree sectors.

Solution:

Total Members=20\text{Total Members} = 20 Football Angle=520×360∘=90∘\text{Football Angle} = \frac{5}{20} \times 360^\circ = 90^\circ Basketball Angle=1020×360∘=180∘\text{Basketball Angle} = \frac{10}{20} \times 360^\circ = 180^\circ Tennis Angle=520×360∘=90∘\text{Tennis Angle} = \frac{5}{20} \times 360^\circ = 90^\circ

Explanation:

First, find the total number of members (2020). For each sport, divide the number of players by the total and multiply by the total degrees in a circle (360∘360^\circ). Basketball takes up exactly half the circle (180∘180^\circ) because 1010 is half of 2020.

Problem 5:

In a pie chart representing transport methods, the 'Walking' sector has an angle of 72∘72^\circ. If the chart represents a total of 50 students, how many students walk to school?

Pie chart with a 72 degree sector highlighted for walking.

Solution:

Number of Students=72∘360∘×50\text{Number of Students} = \frac{72^\circ}{360^\circ} \times 50 Number of Students=15×50=10\text{Number of Students} = \frac{1}{5} \times 50 = 10

Explanation:

To find the frequency from the angle, divide the sector angle by 360∘360^\circ to find the fraction of the total. Then multiply this fraction by the total number of students (5050).