Q.5 (i) A survey was conducted in the school. Student using different modes of transport is given below :
| Mode of Transport | Percentage of Students |
|---|---|
| Bicycle | 35 |
| Bus | \(a\) |
| Railway | \(2a\) |
| Rickshaw | 20 |
Find the value of \(a\) and draw the Pie diagram.
Best answer
Answer: \(a = 15\); central angles — Bicycle \(126^\circ\), Bus \(54^\circ\), Railway \(108^\circ\), Rickshaw \(72^\circ\).
The percentages must add up to 100:
\(35 + a + 2a + 20 = 100 \Rightarrow 3a + 55 = 100 \Rightarrow 3a = 45 \Rightarrow a = 15\).
So Bus \(= 15\%\) and Railway \(= 2 \times 15 = 30\%\). Central angle \(= \dfrac{\text{percentage}}{100} \times 360^\circ\).
| Mode of transport | Percentage | Central angle |
|---|---|---|
| Bicycle | 35 | \(\dfrac{35}{100} \times 360 = 126^\circ\) |
| Bus | 15 | \(\dfrac{15}{100} \times 360 = 54^\circ\) |
| Railway | 30 | \(\dfrac{30}{100} \times 360 = 108^\circ\) |
| Rickshaw | 20 | \(\dfrac{20}{100} \times 360 = 72^\circ\) |
| Total | 100 | \(360^\circ\) |
Pie diagram (to be drawn): Draw a circle of convenient radius (say 3 cm) and draw one radius as the starting line. With a protractor mark consecutive sectors of \(126^\circ\) (Bicycle), \(54^\circ\) (Bus), \(108^\circ\) (Railway) and \(72^\circ\) (Rickshaw), which together complete \(360^\circ\). Write the name of the mode of transport (or shade with an index) in each sector and give the title “Modes of transport used by students”.
(Note: a picture of the pie diagram cannot be shown here; in the examination the diagram itself must be drawn as described above.)
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