Reading a Choropleth: Class Intervals, Correlation and the Wrong Graphic
A student maps literacy for 12 districts of a state. Values run from 61.2% to 90.1%, and five equal-interval classes are used: 61.2–66.98, 66.98–72.76, 72.76–78.54, 78.54–84.32, 84.32–90.1. Eight districts fall in the first class, three in the second, one in the fifth, and the third and fourth are empty. The single district in the top class has 38,000 people; the bottom-class district with 61.2% has 8.4 lakh. The student reports the state's average literacy as 67.1% - the unweighted mean of the twelve district values. On a second sheet, female literacy (X) is plotted against the female work participation rate (Y) for six districts and yields r = –0.78; the student concludes that 'female education pushes women out of work'.
1. Diagnose what is wrong with the map and with the 67.1% figure, then propose a classification and a summary measure that would serve a reader better.
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Fault 1 - the cartographic one. The range is 90.1 − 61.2 = 28.9 points, so equal intervals of 5.78 produce two empty classes and dump 8 of 12 districts into a single shade. The reader sees a uniformly backward state with one dark speck. That is a picture of the class scheme, not of the state. Equal intervals assume a roughly even spread; here one outlier at 90.1 stretches the range and forces the empty classes.
Better classification: quartile (quantile) classes of three districts each, which show relative ranking honestly, or natural breaks if - and only if - the data show a genuine break around 66.5–67, where the first cluster ends. Fix the number of classes at four or five before choosing the method.
Fault 2 - the statistical one. 67.1% is the mean of twelve district values, so the district of 38,000 with 90.1% counts as heavily as the district of 8.4 lakh with 61.2%. That is not the state's literacy rate; it is the average of district averages.
Better measure: the population-weighted mean, i.e. total literates ÷ total population. Given that the largest district sits near the bottom of the range, the weighted figure will fall well below 67.1%, probably near the low sixties - a materially different headline. Any per-district average must be labelled as such.
2. Assess the conclusion drawn from r = –0.78. Give two alternative explanations and one methodological caution.
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The correlation may be real; the causal claim is not supported.
Sample-size caution first. n = 6. With six points, one district can swing r substantially, and the confidence interval around –0.78 is wide. A correlation of that size on six observations is a hypothesis, not a finding.
Alternative explanation 1 - income effect (the U-shape). Districts with high female literacy are usually the urbanised, higher-income ones. As household income rises, women withdraw from low-paid agricultural labour. The driver is household income and urban structure, not schooling as such; the literacy–WPR relationship is known to be non-linear for this reason.
Alternative explanation 2 - measurement of 'work'. Census work categories count main workers, and unpaid family labour on farms and home-based work are systematically undercounted, especially in rural districts. The Y variable is therefore noisy in exactly the places where X is low.
Alternative explanation 3 - reverse causation. A district may have low female work participation because there are few suitable jobs, not because women are educated; education and job availability travel together.
Methodological caution - ecological fallacy. A district-level association says nothing about individual women. Reading 'education pushes women out of work' from district averages commits exactly that error. A better test would disaggregate work by category and control for urban share.
3. The same data must show the sectoral composition (primary, secondary, tertiary) of workers in each of the 12 districts. Choose a graphic, and justify it against at least one alternative.
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Choice: a grouped or stacked bar chart - one bar per district, each bar split into primary, secondary and tertiary shares on a 0–100% axis.
Why it fits the data: composition is a part-to-whole relationship within each district, and the question also requires comparison across districts. Stacking preserves the whole (each bar totals 100%) while placing twelve districts side by side on a common scale, so both readings are possible from one figure. A 100% stacked bar makes the shares directly comparable regardless of workforce size.
Alternatives and why they are worse here:
- Twelve pie charts. They show composition well but destroy cross-district comparison - the eye cannot reliably compare slice angles across separate circles, especially at 12 panels.
- A line graph. It implies the three sectors lie along a continuum, which they do not; sectors are categories, not an ordered series.
- A choropleth of one sector's share. It answers a different question and loses the composition entirely.
Practical cautions: keep segment order identical in every bar (primary at the base), label the axis as percentage and state it in the title, and if the districts differ greatly in workforce size say whether the bars show shares or absolute numbers - otherwise the reader will mistake a small district's composition for a small workforce.