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Statistics and Probability - Introduction to pie charts

Grade 6Cambridge (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 (sectors) to illustrate numerical proportion. The entire circle represents the total frequency or 100% of the data.

A basic pie chart showing a circle with a sector and the center point labeled.
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The angle of each sector is directly proportional to the frequency it represents. The sum of all sector angles in a pie chart must always equal 360∘360^\circ.

A 90-degree sector of a circle representing one quarter of the data.
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To construct a pie chart, calculate the angle for each category using the formula: Angle=FrequencyTotal×360∘\text{Angle} = \frac{\text{Frequency}}{\text{Total}} \times 360^\circ. Use a protractor to measure these angles accurately from the center.

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Comparing pie charts: Pie charts are best for showing how a whole is divided. However, if two pie charts represent different total sample sizes, the same angle in both charts does not represent the same absolute frequency.

📐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.

Problem 4:

A group of 40 students were asked about their favorite sport. 10 students chose Football, 20 chose Basketball, and 10 chose Tennis. Calculate the sector angles and visualize the data.

Pie chart divided into three parts: a semi-circle for Basketball and two quarter-circles for Football and Tennis.

Solution:

  1. Total frequency = 10+20+10=4010 + 20 + 10 = 40
  2. Angle for Football: 1040×360∘=90∘\frac{10}{40} \times 360^\circ = 90^\circ
  3. Angle for Basketball: 2040×360∘=180∘\frac{20}{40} \times 360^\circ = 180^\circ
  4. Angle for Tennis: 1040×360∘=90∘\frac{10}{40} \times 360^\circ = 90^\circ Check: 90∘+180∘+90∘=360∘90^\circ + 180^\circ + 90^\circ = 360^\circ.

Explanation:

We first find the fraction of the total for each sport, then multiply that fraction by the 360∘360^\circ available in a circle to find the corresponding angle.

Problem 5:

A pie chart shows the distribution of vehicles in a parking lot. The sector for 'Electric Cars' is 54∘54^\circ. If there are 200 vehicles in total, how many electric cars are there?

Pie chart with a 54-degree sector highlighted for Electric Cars.

Solution:

  1. Identify the angle: 54∘54^\circ
  2. Identify the total vehicles: 200200
  3. Use the formula: Number of Electric Cars=54∘360∘×200\text{Number of Electric Cars} = \frac{54^\circ}{360^\circ} \times 200
  4. Calculation: 0.15×200=300.15 \times 200 = 30.

Explanation:

To find the actual quantity from an angle, we divide the given angle by 360∘360^\circ to find the proportion of the circle, then multiply by the total population.