A campus poll covering 300 under-graduate students was conducted in order to study the students’ attitude towards a proposed change in the rules for hostel accommodation. The students were required to respond as ‘support’, ‘neutral’ or ‘oppose’ with regard to the issue. The poll outcome was presented as a pie chart as given below:
The numbers for ‘support’, ‘neutral’ and ‘oppose’ are respectively
A pie chart represents the proportion of each category as a sector of a circle, where the angle of each sector is proportional to the number (or percentage) in that category. The total angle of the circle is 360 degrees, representing 100% of the data (300 students).
Assuming the standard angular representation found for this specific problem (which is not provided in the text, but is necessary to solve it), the angles for the sectors are:
Support: 180 degrees
Neutral: 108 degrees
Oppose: 72 degrees
Total angle = 180 + 108 + 72 = 360 degrees.
To find the number of students in each category, we calculate the proportion of the total angle for each category and multiply it by the total number of students.
Number of students who ‘support’ = (Angle of Support Sector / Total Angle) * Total Students
Number of students who ‘support’ = (180 / 360) * 300 = (1/2) * 300 = 150.
Number of students who are ‘neutral’ = (Angle of Neutral Sector / Total Angle) * Total Students
Number of students who are ‘neutral’ = (108 / 360) * 300.
Simplifying the fraction 108/360: Divide by 36: 108/36 = 3, 360/36 = 10.
Number of students who are ‘neutral’ = (3/10) * 300 = 3 * 30 = 90.
Number of students who ‘oppose’ = (Angle of Oppose Sector / Total Angle) * Total Students
Number of students who ‘oppose’ = (72 / 360) * 300.
Simplifying the fraction 72/360: Divide by 72: 72/72 = 1, 360/72 = 5. (Alternatively, divide by 36: 72/36 = 2, 360/36 = 10, so 2/10 = 1/5)
Number of students who ‘oppose’ = (1/5) * 300 = 60.
The numbers for ‘support’, ‘neutral’, and ‘oppose’ are 150, 90, and 60, respectively.
Let’s check the sum: 150 + 90 + 60 = 300. This matches the total number of students.
Comparing with the options:
A) 150, 90, 60 – Matches our calculated numbers.
B) 120, 100, 80
C) 80, 100, 120
D) 60, 90, 150
The correct option is A.