Statistics and Probability - Processing and presenting data (Pie charts, Bar charts)

Grade 7IGCSE

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

🔑Concepts

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Categorical Data: Data that can be sorted into groups or categories (e.g., favorite colors, types of pets).

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Discrete Numerical Data: Data that involves counting whole numbers (e.g., number of siblings).

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Frequency: The number of times a particular data value or category occurs in a data set.

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Bar Charts: A visual representation where the height of each bar represents the frequency. Bars must be of equal width and usually have gaps between them for categorical data.

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Pie Charts: A circular chart divided into sectors. Each sector represents a proportion of the whole (360 degrees).

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Relative Frequency: The fraction or percentage of the total that a specific category represents.

📐Formulae

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

\text{Frequency} = \frac{\text{Sector Angle}}{360^\circ} \times \text{Total Frequency}

\text{Percentage} = \frac{\text{Frequency}}{\text{Total Frequency}} \times 100\%

💡Examples

Problem 1:

A survey of 40 students asked for their favorite fruit. 10 students chose Apple, 15 chose Banana, 5 chose Orange, and 10 chose Grapes. Calculate the angle for the 'Banana' sector in a pie chart.

Solution:

135^\circ

Explanation:

To find the angle, use the formula: (Frequency / Total) * 360. Here, (15 / 40) * 360 = 0.375 * 360 = 135 degrees.

Problem 2:

In a pie chart representing 120 people, the angle for the 'Travel by Bus' sector is 72 degrees. How many people travel by bus?

Solution:

24 people

Explanation:

To find the frequency from the angle, use the formula: (Angle / 360) * Total. Here, (72 / 360) * 120 = 1/5 * 120 = 24.

Problem 3:

A bar chart shows that 8 students have 0 pets, 12 students have 1 pet, and 6 students have 2 pets. What is the total number of students surveyed?

Solution:

26

Explanation:

The total frequency is the sum of the heights of all the bars. Total = 8 + 12 + 6 = 26 students.