One Data Set, Four Maps: Choosing How to Show Boro Paddy Intensity
A student must map the intensity of boro paddy across the eight community development blocks of a district, using a table that gives, for each block, net sown area, area under boro paddy and yield. The boro shares, as percentages of net sown area, are 4, 8, 11, 16, 19, 33, 38 and 71. The student first plans a choropleth with equal intervals of 0 to 20, 20 to 40, 40 to 60 and 60 to 80 per cent, then a dot map showing absolute paddy area, and finally considers isopleths drawn through points of equal share. The teacher says the district average must also be marked on the map. There is no data on the number of holdings or on irrigation source, though the report has to explain why the last block reaches 71%. The student must submit one map and a paragraph of interpretation.
1. Calculate the mean and median share and explain why they differ; say what this does to the planned equal-interval classes.
Read the worked answer
Mean = (4 + 8 + 11 + 16 + 19 + 33 + 38 + 71) / 8 = 200 / 8 = 25%
Median = average of the 4th and 5th values when ordered = (16 + 19) / 2 = 17.5%
Why they differ: the mean exceeds the median, so the distribution is right-skewed. The single block at 71% pulls the mean up by about 5.75 percentage points on its own (71 - 25 = 46, divided by 8). Seven blocks sit below the mean; only one is far above it.
Effect on the planned classes (0-20, 20-40, 40-60, 60-80):
- 0-20: five blocks (4, 8, 11, 16, 19)
- 20-40: two blocks (33, 38)
- 40-60: none
- 60-80: one block (71)
So five of eight blocks merge into one indistinguishable shade, one class is empty, and the one block that most needs explaining is isolated in its own class. The map would show a pattern of classification, not a pattern of reality.
Extra caution: the arithmetic mean of block percentages is not the district share unless all blocks have equal net sown area. A weighted mean is needed, and the available table allows it.
2. Choose one mapping method and justify it against the other two, using the nature of the data.
Read the worked answer
Chosen method: a choropleth of boro share (a relative value) with quantile or natural-break classes - not equal intervals.
Why choropleth fits: the data are already ratios per administrative unit, which is exactly what a choropleth requires, and the blocks are the mapping units. With quantiles, two blocks fall in each of four classes and the outlier stands alone; with natural breaks, the grouping could be 4-19, 33-38 and 71, which matches the real clustering and flags the anomaly.
Why not the dot map: dots show absolute paddy area, not intensity. A large block with a low share would look darker than a small block with a high share, so the map would answer a different question. Dot maps also need positional data - where within each block the crop actually stands - which is not in the table.
Why not isopleths: isolines are drawn through point values to show a continuous surface. Block percentages are averages over areas with no true value at any point, so drawing lines between block centres invents a smoothness the data do not have and shifts the boundary at every step.
Refinement: if the report must also show production, add proportional circles keyed to absolute area on a second small map. Do not mix the two variables in one choropleth.
3. State the two most important cautions the student must carry into the interpretation paragraph, and why each matters here.
Read the worked answer
Caution 1 - the choropleth assumes uniformity inside each block. A block averaging 19% may contain a fully irrigated command at 60% and dry upland at 3%. The map shades the average and hides the variation, so no conclusion about any particular village can be drawn. This matters because the whole point of the exercise is to explain why one block is at 71%, and that explanation lives at a scale finer than the block.
Caution 2 - do not read 71% as the district's main producer. A high share on a small net sown area can be a small absolute area. Without the absolute figures, the block cannot be called the leading producer; and the district mean of 25% is unweighted, so it is not the district's true share either.
A third, if space allows: the missing data on irrigation source and number of holdings are the variables most likely to explain the outlier. The report should say so rather than guess. A map that states what it cannot show is stronger than one that implies more than its data support.