Averages (Mean, Median, Mode and Range): Question 4

Worked solution

(a) Number of people who chose Tea

A full pie chart represents the whole group and turns through $360^\circ$. The Tea sector is a fraction of the whole equal to its angle out of $360^\circ$:

$\text{Tea} = \frac{120}{360} \times 90 = \frac{1}{3} \times 90 = \boxed{30}\text{ people}$

(b) Angle of the Water sector

Now we go the other way: the angle is the same fraction of $360^\circ$ as the people are of the whole group.

$\text{Water angle} = \frac{15}{90} \times 360^\circ = \frac{1}{6} \times 360^\circ = \boxed{60^\circ}$

Check

$90$ people share $360^\circ$, so one person = $4^\circ$. Then $30$ people $= 120^\circ$ ✓ and $15$ people $= 60^\circ$ ✓.