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

Grade 7Cambridge (IGCSE)

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 sectors. Each sector represents a category, and the area (or angle) of each sector is proportional to the frequency of that category relative to the total.

Pie chart illustrating a 90-degree sector representing 25% of the total.
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Bar Charts use rectangular bars to show frequencies of different categories. The height of the bar represents the frequency, and all bars must have equal width with equal gaps between them.

A standard bar chart showing three bars of different heights.
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To calculate the sector angle for a category in a pie chart, you divide the category's frequency by the total frequency and multiply by 360∘360^\circ.

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Comparative bar charts place two or more bars side-by-side for each category to allow for easy comparison between different groups (e.g., Boys vs Girls).

📐Formulae

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

Frequency=Sector Angle360∘×Total Frequency\text{Frequency} = \frac{\text{Sector Angle}}{360^\circ} \times \text{Total Frequency}

Percentage=FrequencyTotal Frequency×100%\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.

Problem 4:

A group of 60 students were asked about their favorite sport. 15 students chose Football, 30 chose Basketball, and 15 chose Tennis. Draw a pie chart to represent this data and calculate the angle for 'Basketball'.

Pie chart with sectors of 180, 90, and 90 degrees.

Solution:

Total Frequency=60\text{Total Frequency} = 60 Angle for Basketball=3060×360∘=180∘\text{Angle for Basketball} = \frac{30}{60} \times 360^\circ = 180^\circ Angle for Football=1560×360∘=90∘\text{Angle for Football} = \frac{15}{60} \times 360^\circ = 90^\circ Angle for Tennis=1560×360∘=90∘\text{Angle for Tennis} = \frac{15}{60} \times 360^\circ = 90^\circ

Explanation:

Since Basketball represents half of the total students (30 out of 60), its angle is exactly half of the circle (180∘180^\circ). Football and Tennis share the remaining half equally (90∘90^\circ each).

Problem 5:

The following bar chart shows the number of cars sold over three days: Monday (5), Tuesday (8), and Wednesday (3). Calculate the total number of cars sold.

Bar chart showing car sales for Monday (5), Tuesday (8), and Wednesday (3).

Solution:

Total=5+8+3=16\text{Total} = 5 + 8 + 3 = 16 Total cars sold=16\text{Total cars sold} = 16

Explanation:

To find the total, we read the height of each bar on the vertical axis and sum the values: 5 for Monday, 8 for Tuesday, and 3 for Wednesday.