The pie chart below shows the age distribution of population in thousands of an island Y for the year 2000 The total population of the island is 245,000. Us...

Answer Details

(a) Number of persons in each age group

A pie chart is a full circle of \(360^\circ\), so each age group's share of the total population of 245,000 equals its sector angle divided by \(360^\circ\). The angles read from the chart are \(0\text{-}16 = 220^\circ\), \(17\text{-}45 = 75^\circ\), \(46\text{-}60 = 43^\circ\) and \(61+ = 22^\circ\); these correctly add up to \(220+75+43+22 = 360^\circ\).

Applying \(\text{Group} = \dfrac{\text{sector angle}}{360^\circ}\times 245{,}000:\)

• 0-16 years: \(\dfrac{220}{360}\times 245{,}000 = 149{,}722\) persons
• 17-45 years: \(\dfrac{75}{360}\times 245{,}000 = 51{,}042\) persons
• 46-60 years: \(\dfrac{43}{360}\times 245{,}000 = 29{,}264\) persons
• 61+ years: \(\dfrac{22}{360}\times 245{,}000 = 14{,}972\) persons

Check: \(149{,}722 + 51{,}042 + 29{,}264 + 14{,}972 = 245{,}000\) (to the nearest person).

(b) Dependency ratio

The dependants are the young (0-16 years) plus the aged (61+ years); the working, productive group is 17-60 years.

Dependants \(= 149{,}722 + 14{,}972 = 164{,}694\).
Working population \(= 51{,}042 + 29{,}264 = 80{,}306\).

\[\text{Dependency ratio} = \dfrac{\text{dependants}}{\text{working population}}\times 100 = \dfrac{164{,}694}{80{,}306}\times 100 \approx 205\%\]

Using the angles directly gives the same result: \(\dfrac{220+22}{75+43} = \dfrac{242}{118} \approx 2.05\). So the ratio is about \(2:1\) - roughly two dependants rely on every one person of working age.

(c) Three implications of this population structure

1. Heavy dependency burden. With about 61% of the people aged 0-16, the relatively small working group must feed, clothe, house and educate a very large number of non-workers, keeping living standards low.
2. Low savings and capital formation. Most income is spent at once on consumption for dependants, leaving little for saving and investment, which slows economic growth.
3. Pressure on social services. The huge child population forces heavy government spending on schools, clinics and other amenities, straining public finances - though it does promise a large labour force in the future.