Question
A school surveyed 360 students about their favourite sport. The results are shown in a pie chart where Cricket = 120°, Football = 80°, Badminton = 60°, Kabaddi = 50°, and Others = 50°.
(a) How many students chose Cricket? (b) Which sport is least popular? (c) What fraction of students chose Football?
(NCERT Class 7 — Data Handling)
Solution — Step by Step
A full circle = 360°, representing all 360 students. So each degree = 1 student (convenient numbers here). In general, the formula is:
Cricket’s angle = 120°.
Compare the angles: Kabaddi and Others both have 50° — the smallest angle. So Kabaddi and Others are tied as least popular, with 50 students each.
Football = 80° out of 360°.
As a percentage: .
Why This Works
Pie charts represent data as parts of a whole circle. The central angle of each sector is proportional to the quantity it represents. The key relationship is:
Bar graphs work differently — the height of each bar directly shows the value. Reading a bar graph is straightforward: just read the height from the y-axis. Pie charts need the angle-to-value conversion.
When comparing data across categories, bar graphs are easier to read. When showing how each category relates to the total, pie charts are better.
Alternative Method
Instead of using the formula each time, notice that per student in this problem. So you can read the angle directly as the number of students. This shortcut works only when Total = 360. For other totals, stick with the formula.
In CBSE exams, always show the formula even when the shortcut is obvious. Write: “Number = (Angle/360) x Total” and then substitute. This earns you full method marks.
Common Mistake
Students often confuse the angle with the percentage. An angle of 120° does NOT mean 120%. To convert angle to percentage: . Always divide by 360 (total degrees), not by 100.