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Difficulty: MediumData Representation and Charts

A pie chart illustrates the distribution of undergraduate students enrolled across four faculties at a university: Arts, Science, Law, and Medicine. The central angles for the sectors representing Arts, Science, and Law are 120∘120^\circ, 90∘90^\circ, and 75∘75^\circ, respectively. If 300300 students are enrolled in the Faculty of Medicine, what is the total number of students enrolled in the university?

Answer: 1440 students

Answer

The total number of students enrolled in the university is 1440.
The total sum of central angles in any pie chart is 360∘360^\circ. Subtracting the given angles for Arts (120∘120^\circ), Science (90∘90^\circ), and Law (75∘75^\circ) from 360∘360^\circ gives the sector angle for Medicine as 75∘75^\circ. Since 75∘75^\circ represents 300300 students, each degree represents 30075=4\frac{300}{75} = 4 students. Multiplying 44 students per degree by the total 360∘360^\circ yields 14401440 total students in the university.

Step-by-Step Solution

1
Determine the sector angle for Medicine.
Sector angle for Medicine = 75∘75^\circ
The sum of central angles in a pie chart is 360∘360^\circ. Subtracting 120∘+90∘+75∘=285∘120^\circ + 90^\circ + 75^\circ = 285^\circ from 360∘360^\circ gives 75∘75^\circ.
2
Formulate the proportion relating sector angle to frequency.
75∘360∘×N=300\frac{75^\circ}{360^\circ} \times N = 300, where NN represents total students.
The fractional portion of the angle (75∘75^\circ out of 360∘360^\circ) equals the fractional portion of the total student count (300300 out of NN).
3
Calculate the total student population NN.
N=300×36075=1440N = \frac{300 \times 360}{75} = 1440
Dividing 300300 by 7575 yields 44 students per degree. Multiplying 44 by 360360 gives 14401440 students.

Key Concept

Pie Chart Sector Angle and Total Population Calculation
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Topics

Data Representation and Charts

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