Question

For an MCQ question in an examination, the number of students who marked each option is recorded in the form of a bar graph. If the same data is recorded as a pie chart, find the angle that each option would subtend at the center of the chart.


Options

• A. A :36°; B: 72°; C: 108°; D: 144°
• B. A: 30°; B: 60°; C: 90°; D: 180°
• C. A: 60°; B: 80°; C: 100°; D: 120°
• D. A: 36°; B: 72°; C: 90°; D: 108°

Answer 1

The correct option is A A :36°; B: 72°; C: 108°; D: 144°

$\text{Total number of students}=25+50+75+100=250$

$\text{Students who opted for A as a fraction of the}\text{total number of students:}$

$=\frac{StudentswhooptedforA}{Totalnumberofstudents}=\frac{25}{250}=\frac{1}{10}$

$\text{Students who opted for B as a fraction of the}\text{total number of students:}$

$=\frac{StudentswhooptedforB}{Totalnumberofstudents}=\frac{50}{250}=\frac{1}{5}$

$\text{Students who opted for C as a fraction of the}\text{total number of students:}$

$=\frac{StudentswhooptedforC}{Totalnumberofstudents}=\frac{75}{250}=\frac{3}{10}$

$\text{Students who opted for A as a fraction of the}\text{total number of students:}$

$=\frac{StudentswhooptedforD}{Totalnumberofstudents}=\frac{100}{250}=\frac{2}{5}$

Now, to calculate the angle made by each option in the pie chart, we multiply the corresponding fraction of each option with 360°.

So,
$AnglemadebyA=\frac{1}{10}\times 360°=36°AnglemadebyB=\frac{1}{5}\times 360°=72°AnglemadebyC=\frac{3}{10}\times 360°=108°AnglemadebyD=\frac{2}{5}\times 360°=144°$

Hence, the angle made by each option is:

$A:36°;B:72°;C:108°;D:144°$