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Data Handling - Circle Graph or Pie Chart

Grade 8CBSE

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

🔑Concepts

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A circle graph, also known as a pie chart, represents data as sectors of a circle where the size of each sector is proportional to the information it represents.

Illustration of a pie chart showing a circle divided into sectors representing parts of a whole.
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The central angle of each sector is calculated based on the fraction of the total it represents. Since the total angle at the center of a circle is 360∘360^{\circ}, the formula used is: Central Angle=ValueTotal×360∘\text{Central Angle} = \frac{\text{Value}}{\text{Total}} \times 360^{\circ}.

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

A circle divided into three sectors showing 25%, 25%, and 50% distribution.
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To draw a pie chart, first convert the data values into fractions of the total, then multiply by 360∘360^{\circ} to find the central angle for each component, and finally use a protractor to draw the sectors.

📐Formulae

Fraction of a Component=Value of the ComponentTotal Value\text{Fraction of a Component} = \frac{\text{Value of the Component}}{\text{Total Value}}

Central Angle=(Value of the ComponentTotal Value)×360∘\text{Central Angle} = \left( \frac{\text{Value of the Component}}{\text{Total Value}} \right) \times 360^{\circ}

Central Angle=Fraction×360∘\text{Central Angle} = \text{Fraction} \times 360^{\circ}

Percentage of a Component=(Central Angle360∘)×100\text{Percentage of a Component} = \left( \frac{\text{Central Angle}}{360^{\circ}} \right) \times 100

💡Examples

Problem 1:

In a school of 720 students, 180 students like Mathematics, 240 like Science, and 300 like English. Calculate the central angle for each subject to represent this data in a pie chart.

Solution:

Step 1: Identify the total value. Total students = 180+240+300=720180 + 240 + 300 = 720.\nStep 2: Calculate the central angle for Mathematics: 180720×360∘=14×360∘=90∘\frac{180}{720} \times 360^{\circ} = \frac{1}{4} \times 360^{\circ} = 90^{\circ}.\nStep 3: Calculate the central angle for Science: 240720×360∘=13×360∘=120∘\frac{240}{720} \times 360^{\circ} = \frac{1}{3} \times 360^{\circ} = 120^{\circ}.\nStep 4: Calculate the central angle for English: 300720×360∘=512×360∘=150∘\frac{300}{720} \times 360^{\circ} = \frac{5}{12} \times 360^{\circ} = 150^{\circ}.\nVerification: 90∘+120∘+150∘=360∘90^{\circ} + 120^{\circ} + 150^{\circ} = 360^{\circ}.

Explanation:

We find the central angle by taking the value of each subject as a fraction of the total student count and multiplying by 360∘360^{\circ}.

Problem 2:

A pie chart showing the expenditure of a family has a central angle of 108∘108^{\circ} for 'Food'. If the total monthly income is 50,000, calculate the amount spent on food.

Solution:

Step 1: Use the relationship between the central angle and the total value.\nStep 2: Amount spent on Food = Central Angle360∘×Total Value\frac{\text{Central Angle}}{360^{\circ}} \times \text{Total Value}.\nStep 3: Substitute the values: Amount=108∘360∘×50,000\text{Amount} = \frac{108^{\circ}}{360^{\circ}} \times 50,000.\nStep 4: Simplify the fraction: 108360=310\frac{108}{360} = \frac{3}{10}.\nStep 5: Calculate the final amount: 310×50,000=15,000\frac{3}{10} \times 50,000 = 15,000.

Explanation:

To find the actual value from a pie chart, we divide the specific sector's angle by the total angle of the circle (360∘360^{\circ}) and multiply by the total quantity.

Problem 3:

A group of 36 children were asked about their favorite fruit. 18 chose Mango, 9 chose Apple, and 9 chose Banana. Represent this data as a pie chart by calculating the central angles.

Pie chart with Mango taking half the circle and Apple and Banana taking a quarter each.

Solution:

  1. Total children = 3636.
  2. Central angle for Mango: 1836×360∘=180∘\frac{18}{36} \times 360^{\circ} = 180^{\circ}.
  3. Central angle for Apple: 936×360∘=90∘\frac{9}{36} \times 360^{\circ} = 90^{\circ}.
  4. Central angle for Banana: 936×360∘=90∘\frac{9}{36} \times 360^{\circ} = 90^{\circ}.

Explanation:

Mango occupies half the circle (180∘180^{\circ}), while Apple and Banana each occupy a quarter (90∘90^{\circ}).

Problem 4:

The following pie chart shows the time spent by a student in a day (24 hours). If the sector for 'Sleeping' has a central angle of 120∘120^{\circ}, how many hours does the student sleep?

Pie chart showing a 120 degree sector labeled Sleep.

Solution:

  1. Total hours in a day = 2424 hours.
  2. Total angle of a circle = 360∘360^{\circ}.
  3. Hours spent sleeping = Central Angle360∘×Total Hours\frac{\text{Central Angle}}{360^{\circ}} \times \text{Total Hours}.
  4. Hours spent sleeping = 120∘360∘×24=13×24=8\frac{120^{\circ}}{360^{\circ}} \times 24 = \frac{1}{3} \times 24 = 8 hours.

Explanation:

Since the central angle for sleep is 120∘120^{\circ}, it represents one-third of the total daily cycle of 24 hours.

Circle Graph or Pie Chart Class 8 Notes & Examples