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CAT 2021 Slot 1 · VARC · Reading Comprehension · easy

CAT 2021 Slot 1 VARC: What a Single Number Can and Cannot Say

Economists have no shortage of ways to describe how unevenly income or wealth is distributed within a population, yet the most widely cited of these, the Gini coefficient, is also among the most frequently misunderstood. Defined as a single number between zero and one — zero representing perfect equality, one representing total concentration in a single hand — it condenses an entire distribution into one figure, which is precisely what makes it both useful and misleading. Two countries can report identical Gini coefficients while having starkly different distributions: one might have a very poor bottom decile and a broad, only moderately unequal middle and top, while another has a comfortable bottom half and extreme concentration at the very top. The single number cannot, by construction, distinguish between these very different social realities.

This is not a flaw unique to the Gini coefficient; any summary statistic sacrifices some information for the sake of comparability, and the alternative of reporting an entire distribution for every country and year would overwhelm most audiences. The more serious concern raised by critics is not that the measure summarises but that its particular mathematical construction happens to be comparatively insensitive to changes at the very top of the distribution. Because the coefficient is derived from the cumulative share of income held by successive population deciles, a transfer of wealth among the already-wealthy top one percent moves the statistic far less than an equivalent transfer within the middle of the distribution, even though the former may matter enormously for questions of concentrated economic and political power.

In response, some economists have promoted supplementary measures that are more sensitive to the extremes: the top decile's or top percentile's share of total income or wealth, for instance, tracked over time, which is exactly the kind of number that revealed the sharp rise in top-end concentration across many developed economies since the 1980s, a trend that aggregate Gini figures registered only faintly by comparison. Others advocate ratios comparing specific points in the distribution, such as the income of a household at the ninetieth percentile against one at the tenth, a measure that is easy to explain to a lay audience even if it, too, ignores everything that happens outside those two points.

None of these measures is a strict improvement on the others; each simply makes a different choice about which feature of a distribution to foreground and which to compress. The practical lesson for anyone using inequality statistics to inform policy is therefore not to search for a single superior index but to ask, for any specific question, which part of the distribution the question actually concerns, and to choose — or better, to combine — measures accordingly, rather than treating one number as a complete description of who has what.

Question 1

Single correct option

According to the passage, the Gini coefficient is comparatively insensitive to which of the following?
  1. A. Changes in income among the poorest decile of a population.
  2. B. Changes in income or wealth transfers occurring among the already-wealthy top of the distribution.
  3. C. Any change whatsoever in the middle of the income distribution.
  4. D. Differences between two countries' total population sizes.
Show answer and solution

Answer: (B) Changes in income or wealth transfers occurring among the already-wealthy top of the distribution.

The passage states plainly: 'a transfer of wealth among the already-wealthy top one percent moves the statistic far less than an equivalent transfer within the middle of the distribution' — this is the specific insensitivity described, matching B. A and C reverse the actual relationship (the coefficient is relatively more, not less, responsive to middle-of-distribution changes), and D is not discussed.

Question 2

Single correct option

Which of the following, if true, would most strengthen the passage's claim that top-income-share measures reveal trends that Gini coefficients register 'only faintly'?
  1. A. Top-decile income share in several developed economies rose sharply after 1980 while their Gini coefficients over the same period rose only marginally.
  2. B. The Gini coefficient and the top-decile income share are calculated using entirely unrelated raw data sources.
  3. C. Most economists agree that the Gini coefficient is the single best available measure of inequality.
  4. D. Top-decile income share is more difficult for policymakers to explain to the public than the Gini coefficient is.
Show answer and solution

Answer: (A) Top-decile income share in several developed economies rose sharply after 1980 while their Gini coefficients over the same period rose only marginally.

The claim being tested is that top-share measures moved sharply while Gini moved only faintly over the same historical period. Direct evidence of exactly this divergence — sharp top-decile rise alongside marginal Gini movement — would most directly strengthen it (A). B is irrelevant to the comparison of magnitudes; C actually cuts against the passage's argument that no single measure is superior; D concerns communicability, not the empirical claim being strengthened.

Question 3

Single correct option

The main idea of the passage is best summarised as:
  1. A. The Gini coefficient should be abandoned in favour of the ninetieth-to-tenth percentile ratio, which is a strictly superior measure of inequality.
  2. B. No inequality statistic is inherently superior to the others; each foregrounds a different feature of a distribution, so the right choice depends on the specific question being asked.
  3. C. Economists cannot agree on how to measure inequality, which suggests that inequality itself cannot be meaningfully measured.
  4. D. Summary statistics are useless for policy purposes and full distributional data should always be reported instead.
Show answer and solution

Answer: (B) No inequality statistic is inherently superior to the others; each foregrounds a different feature of a distribution, so the right choice depends on the specific question being asked.

The final paragraph states this explicitly: 'None of these measures is a strict improvement on the others... the practical lesson... is therefore not to search for a single superior index but to ask... which part of the distribution the question actually concerns.' This is a direct match for B. A contradicts this conclusion; C is an unsupported overreach; D contradicts paragraph 2, which defends summary statistics as necessary for comparability.

Question 4

Single correct option

It can be inferred that the ninetieth-to-tenth percentile ratio mentioned in the passage shares which limitation with the Gini coefficient?
  1. A. Both are impossible to calculate without access to an entire country's tax records.
  2. B. Both compress information about parts of the distribution they do not directly capture, foregrounding some features while ignoring others.
  3. C. Both were invented after the 1980s specifically to track top-end income concentration.
  4. D. Both are always reported as percentages rather than as decimals or ratios.
Show answer and solution

Answer: (B) Both compress information about parts of the distribution they do not directly capture, foregrounding some features while ignoring others.

The passage says the percentile ratio 'ignores everything that happens outside those two points' — echoing the earlier critique of the Gini coefficient's single-number compression. Both measures, in the author's framing, foreground some information while compressing or ignoring the rest, matching B. A, C and D are not supported by anything stated in the passage.
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