In a test in Mathematics, 20% of the students obtained “first class”. If the data are represented by a Pie-Chart, what is the central angle corresponding to “first class”?
72°
Understanding Pie Charts and Central Angles
A pie chart is a type of graph that represents data as a circular graph. The entire circle represents the whole dataset, which is equal to 100% of the total or 360 degrees of a full circle.
Each slice of the pie chart corresponds to a category of data, and the size of the slice (both in terms of area and the central angle it subtends) is proportional to the percentage of the whole that the category represents.
Calculating Central Angle for a Percentage
To find the central angle corresponding to a specific percentage in a pie chart, you use the following formula:
\( \text{Central Angle} = \left( \frac{\text{Percentage}}{100\%} \right) \times 360^\circ \)Finding Central Angle for 20% First Class Students
In this specific problem, we are told that 20% of the students obtained “first class” in the Mathematics test. We need to find the central angle that represents this 20% in a pie chart.
Using the formula mentioned above, we substitute the given percentage:
Percentage = 20%
Total degrees in a circle = \(360^\circ\)
So, the central angle for the “first class” category is:
\( \text{Central Angle} = \left( \frac{20}{100} \right) \times 360^\circ \) \( \text{Central Angle} = 0.20 \times 360^\circ \) \( \text{Central Angle} = 72^\circ \)Resulting Central Angle
The central angle corresponding to the 20% of students who obtained “first class” is \(72^\circ\).
Revision Table: Pie Chart Basics
| Concept | Description | Value |
|---|---|---|
| Total Percentage | Represents the whole data set | 100% |
| Total Central Angle | Represents the whole circle | \(360^\circ\) |
| Relationship | 1% corresponds to \(360^\circ / 100 = 3.6^\circ\) | \(1\% \equiv 3.6^\circ\) |
Additional Information: Representing Data with Pie Charts
Pie charts are useful for showing the proportion of different categories within a whole. They are particularly effective when you have a small number of categories.
- Each slice represents a category.
- The size of the slice is proportional to the frequency or percentage of that category.
- The sum of all percentages in a pie chart must be 100%.
- The sum of all central angles in a pie chart must be \(360^\circ\).
To create a pie chart, you typically need to:
- Calculate the percentage for each category.
- Calculate the central angle for each category using the formula: \( \left( \frac{\text{Percentage}}{100} \right) \times 360^\circ \).
- Draw a circle and divide it into sectors using the calculated central angles.
- Label each sector and often include the percentage or value.
Similar Questions
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Expenditure (in Rs.)
Items
Family A
Family B
Food
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Important Questions from Classification of Data
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The following table gives the monthly expenditure of two families:
Expenditure (in Rs.)
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Rent
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Education
2,000
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Miscellaneous
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The approximated mean of this distribution is:
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