Choosing a Classification for a Population-Density Map
A class is preparing a choropleth of population density (persons per km²) by district for Kerala, to be printed on an A4 sheet (210 × 297 mm) with a title, legend and scale bar. The densities supplied are: Idukki 255, Wayanad 384, Pathanamthitta 453, Palakkad 627, Kasaragod 654, Kottayam 896, Thrissur 1026, Kollam 1054, Ernakulam 1072, Malappuram 1072, Kannur 1136, Kozhikode 1318, Alappuzha 1501, Thiruvananthapuram 1508. One student proposes five classes of equal interval, beginning at 255. Another proposes a scale on a 1:1,000,000 base map. The teacher notes that the state measures roughly 580 km north to south and asks the class to defend its choices before the map is drawn, and to state what the finished map will and will not show.
1. Test the equal-interval proposal against the data and decide whether it should be adopted.
Read the worked answer
Equal interval, range 255–1508, five classes of about 250:
| Class | Districts | Number |
|---|---|---|
| 255–505 | Idukki, Wayanad, Pathanamthitta | 3 |
| 505–755 | Palakkad, Kasaragod | 2 |
| 755–1005 | Kottayam | 1 |
| 1005–1255 | Thrissur, Kollam, Ernakulam, Malappuram, Kannur | 5 |
| 1255–1508 | Kozhikode, Alappuzha, Thiruvananthapuram | 3 |
The distribution is not even - it clusters in the 1,000–1,100 band and stretches thin at both ends - but equal interval here still puts only one district in a whole class and leaves no class empty, so it is usable. Its virtue is honesty: the legend states a fixed numerical interval, so the reader can compare any two shades and know the absolute difference, and the highland–coastal contrast (a three-district lowland group against a three-district highland group) reads clearly.
A quantile (equal-count) classification would put roughly three districts in each class and produce a prettier, more evenly shaded map - but its class breaks would fall at arbitrary values, so two adjacent shades might differ by 20 persons per km² in one part of the legend and by 300 in another. Recommendation: keep equal interval for this data, and state the class breaks on the legend. Adopt quantile only if the purpose is to rank districts rather than to show actual density levels.
2. The 1:1,000,000 base map is proposed for an A4 sheet. Test the scale and recommend a workable one, showing the arithmetic.
Read the worked answer
Test the proposed scale: at 1:1,000,000, 1 mm on the map = 1 km on the ground. A north–south extent of 580 km would therefore need 580 mm of map. The A4 sheet is 297 mm tall; after allowing for title, legend and scale bar, usable height is roughly 230–250 mm. The proposal overshoots by more than a factor of two.
Required scale: 580 km must fit in about 230 mm.
- 580 km = 580,000,000 mm
- 580,000,000 ÷ 230 ≈ 2,520,000
So a scale of about 1:2,500,000 is the practical choice (580 ÷ 2.5 = 232 mm), and the sheet should be set portrait, since the state is longer north–south than east–west. At that scale 1 cm on the map = 25 km on the ground.
Consequences to state on the map: at 1:2,500,000 the smallest district is only a few centimetres across, so district names should be numbered and listed in the legend rather than lettered on the map; the scale bar must be drawn in kilometres, not left as a representative fraction only; and the class should note that no projection is stated, so the map is acceptable for a small area but the shapes are not for area measurement. Checking the scale before drawing is the step that saves redrawing the whole map.
3. The map is finished and a reader concludes that 'Malappuram and Ernakulam have the same population problem'. What does the choropleth allow the reader to say, and what does it hide?
Read the worked answer
What it allows: that both districts have the same arithmetic density - 1,072 persons per km², identical to the nearest whole number, falling in the same class and therefore the same shade. It also allows the ranking of all fourteen districts and the broad contrast between the crowded coastal belt (Thiruvananthapuram, Alappuzha, Kozhikode) and the sparsely peopled highlands (Idukki 255, Wayanad 384).
What it hides - three things:
- Internal variation. A district figure is an average over its whole area. Ernakulam's density is concentrated in a narrow coastal and urban strip with large sparsely settled areas inland; Malappuram's is spread more evenly across a densely settled rural plain. The same number describes two different settlement patterns, and the reader's sentence conflates them.
- What is being divided. Density is people per unit of total area, including forest, water and plantation. Idukki's low value is largely a statement about how much of the district is reserved forest and reservoir, not about how crowded its townships are. A map of density per unit of cultivated or settled area would rank districts quite differently.
- Composition and change. The map shows no age structure, urban share, migration or growth rate, so it cannot support any inference about 'population problem' at all - density alone says nothing about dependency, employment or service load.
The correct classroom conclusion is that the choropleth is a valid statement of district-level averages and invalid as a statement about living conditions; the reader should be referred to a second map or table before drawing a conclusion about either district.