Use TABLE ll below and the attached map A for Nigeria to answer the questions that follow TABLE II: Volume of Rail Passenger Traffic Generated by Five Niger...

(a) Representing the statistics with proportional circles

In a proportional circle map the area of each circle is drawn in proportion to the quantity it represents. Because the area of a circle is proportional to the square of its radius (\(A = \pi r^2\)), the radius of each circle must be made proportional to the square root of the value, i.e. \(r \propto \sqrt{V}\). This prevents the larger circles from being exaggerated.

Step 1: Find the square root of each value.

Step 2: Choose a radius scale. Let the smallest city (Minna, \(\sqrt{V}=1000\)) be drawn with a radius of 1.0 cm. The scale factor is therefore \[k = \frac{1.0\text{ cm}}{1000} = 0.001\ \text{cm per unit }\sqrt{V}.\] Multiplying every \(\sqrt{V}\) by \(k\) gives the radii in the last column above.

Step 3: Draw the circles. On the map of Nigeria, at the location of each city, draw a circle with the radius calculated above using a pair of compasses. Draw the smallest circle first and the largest last. Add a title, a key that shows a specimen circle with its value (e.g. a 1.0 cm circle = 1,000,000 passengers), and label each circle with the city name.

(b) Two advantages of representing data with proportional symbols

1. They show the actual geographical location of each value on the map, so the reader sees both the quantity and where it occurs at the same time.
2. They give an immediate visual comparison of magnitude, since the eye can quickly rank places by the size of the symbol without reading the figures.