The numbers of Science, Arts and Commerce graduates working in a company are 30, 70 and 50 respectively. If these figures are represented by a pie chart, then what is the angle corresponding to Science graduates?
72°
Understanding Pie Charts and Angles
A pie chart is a circular statistical graphic which is divided into sectors, illustrating numerical proportion. In a pie chart, the entire circle represents the total quantity, and each sector represents a part of that total. The angle of each sector is proportional to the quantity it represents.
The total angle in a circle is \(360^\circ\). To find the angle corresponding to a specific category in a pie chart, we use the following formula:
\[ \text{Angle for a category} = \left( \frac{\text{Number in the category}}{\text{Total number}} \right) \times 360^\circ \]
Calculating Total Graduates
We are given the number of graduates in three streams: Science, Arts, and Commerce. To find the angle for Science graduates in the pie chart representation, we first need to calculate the total number of graduates working in the company.
- Number of Science graduates = 30
- Number of Arts graduates = 70
- Number of Commerce graduates = 50
The total number of graduates is the sum of graduates from all three streams:
\[ \text{Total graduates} = \text{Science} + \text{Arts} + \text{Commerce} \]
\[ \text{Total graduates} = 30 + 70 + 50 = 150 \]
So, there are a total of 150 graduates working in the company.
Finding the Angle for Science Graduates in the Pie Chart
Now we can calculate the angle corresponding to the Science graduates in the pie chart. We use the formula mentioned earlier:
\[ \text{Angle for Science graduates} = \left( \frac{\text{Number of Science graduates}}{\text{Total graduates}} \right) \times 360^\circ \]
Substitute the values:
\[ \text{Angle for Science graduates} = \left( \frac{30}{150} \right) \times 360^\circ \]
Simplify the fraction \(\frac{30}{150}\):
\[ \frac{30}{150} = \frac{3}{15} = \frac{1}{5} \]
Now calculate the angle:
\[ \text{Angle for Science graduates} = \frac{1}{5} \times 360^\circ \]
\[ \text{Angle for Science graduates} = \frac{360^\circ}{5} \]
\[ \text{Angle for Science graduates} = 72^\circ \]
Therefore, the angle corresponding to Science graduates in the pie chart is \(72^\circ\).
| Stream | Number of Graduates | Proportion of Total | Angle in Pie Chart |
|---|---|---|---|
| Science | 30 | \(\frac{30}{150} = \frac{1}{5}\) | \(\frac{1}{5} \times 360^\circ = 72^\circ\) |
| Arts | 70 | \(\frac{70}{150} = \frac{7}{15}\) | \(\frac{7}{15} \times 360^\circ = 7 \times 24^\circ = 168^\circ\) |
| Commerce | 50 | \(\frac{50}{150} = \frac{1}{3}\) | \(\frac{1}{3} \times 360^\circ = 120^\circ\) |
| Total | 150 | \(\frac{150}{150} = 1\) | \(72^\circ + 168^\circ + 120^\circ = 360^\circ\) |
The angle corresponding to Science graduates is \(72^\circ\). This matches one of the given options.
Revision Table: Pie Chart Calculations
| Concept | Description | Formula |
|---|---|---|
| Pie Chart | A circle divided into sectors representing proportions of a whole. | N/A |
| Total Angle | The sum of angles of all sectors in a pie chart. | \(360^\circ\) |
| Angle for a Sector | Angle representing a category's proportion of the total. | \(\left( \frac{\text{Part}}{\text{Total}} \right) \times 360^\circ\) |
Additional Information: Representing Data with Angles
Representing data using angles in a pie chart is a common way to visualize how different parts contribute to a whole. The total value of all categories corresponds to the total angle of the circle (\(360^\circ\)). The process involves finding the proportion of each category relative to the total and then multiplying this proportion by \(360^\circ\) to get the central angle for that category's sector. This method ensures that the sum of all sector angles in the pie chart always equals \(360^\circ\). This visual representation makes it easy to compare the relative sizes of different categories at a glance.
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