Census Arithmetic Under a Changing Boundary
A district in Bihar had a population of 24,00,000 in a census year. By the next census it had grown to 30,00,000, but during the decade two blocks with a combined population of 3,00,000 (at the later census) were transferred into it from a neighbouring district. A student computes the decadal growth rate as (30,00,000 − 24,00,000)/24,00,000 = 25% and concludes the district grew faster than the state average of 21%. Separately, the student is asked to find the number of males if the sex ratio is 900 females per 1000 males in the later census. The student writes males = 30,00,000 × 900/1000 = 27,00,000 and is puzzled that males plus females exceeds the total.
1. Is the 25% growth figure a valid measure of the district's demographic growth? Recompute appropriately and explain.
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No - 25% is a crude change that mixes real growth with boundary change.
- The transferred blocks contributed 3,00,000 at the later census. To compare like with like, the earlier population must be adjusted to the same boundary, or the later figure reduced by the transferred population.
- Comparable later population ≈ 30,00,000 − 3,00,000 = 27,00,000.
- Comparable growth = (27,00,000 − 24,00,000)/24,00,000 = 3,00,000/24,00,000 = 12.5%.
So on a constant-boundary basis the district grew about 12.5%, below the state's 21%, not above it. The lesson: before comparing growth rates, confirm that the territorial unit is identical in both periods; otherwise the comparison is meaningless. The student's arithmetic was right but the denominator and numerator described different geographies.
2. Correct the sex-ratio calculation and state the number of males and females.
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The student misread the ratio. "900 females per 1000 males" means females/males = 900/1000, so females are 900 parts for every 1000 male parts - total 1900 parts.
- Males = 30,00,000 × 1000/1900 = 30,00,000/1.9 ≈ 15,78,947.
- Females = 30,00,000 × 900/1900 ≈ 14,21,053.
- Check: 15,78,947 + 14,21,053 = 30,00,000. Ratio ≈ 900 per 1000. ✓
The student's error was multiplying the total by 900/1000, which treats the ratio as a share of the whole. A ratio compares two parts; a proportion compares a part to the whole. Converting a sex ratio to a share requires dividing by (1000 + 900), not by 1000.
3. If the district's literacy rate rose from 52% to 61% over the decade, can we conclude that the number of illiterates fell? Show the arithmetic.
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Not necessarily - it depends on population growth.
Using the comparable later population of 27,00,000:
- Illiterates earlier = 48% of 24,00,000 = 11,52,000.
- Illiterates later = 39% of 27,00,000 = 10,53,000.
Here illiterates did fall, by about 99,000, because the literacy rate rose faster than population. But the conclusion is conditional: had the later population been 30,00,000, illiterates would be 39% × 30,00,000 = 11,70,000 - a rise despite a higher literacy rate.
The general rule: a rising percentage does not guarantee a falling absolute count when the base is growing. Always convert percentages back to counts before drawing a conclusion about numbers of people.