How Do We Draw a Lorenz Curve from Quintiles?
Inequality and poverty
What you will learn
- Add each quintile's income share to all earlier shares before plotting.
- Apply the model to an original scenario and justify its limits.
Essential definitions
- Quintile
- One of five equally sized groups in a population ranked by income.
- Cumulative share
- The combined percentage belonging to a group and all lower-ranked groups.
Prepare ranked shares
A quintile is one fifth, or 20%, of the population. For a Lorenz curve, the five groups must be ordered from poorest to richest. Their income shares should add to 100%. Unequal-sized occupational or regional groups cannot be treated as quintiles merely because there are five of them.
Suppose the quintile shares are 5%, 10%, 15%, 25% and 45%. The third group's 15% is its own income share. To find the income of the poorest 60%, add the first three groups: 5 + 10 + 15 = 30%. This is why plotting the five original shares directly is incorrect.
Calculate and plot cumulative coordinates
Cumulative population percentages are 0, 20, 40, 60, 80 and 100. Cumulative income percentages are 0, 5, 15, 30, 55 and 100. Put population percentage horizontally and income percentage vertically, then plot each matching pair and connect them in order. Draw the diagonal equality line for comparison.
Start at (0, 0) and end at (100, 100). With non-negative income shares, neither coordinate should move backwards. If the endpoint is wrong, check missing groups, arithmetic or incompatible data. The segments between points summarise groups; they do not show inequality within a quintile.
Interpret a second distribution
Now consider shares of 8%, 12%, 18%, 25% and 37%. Their cumulative values are 8, 20, 38, 63 and 100. Use the same axes and compare the curves at a common population share. The poorest 40% now receive 20% instead of 15% of income.
The second curve is closer to equality at the observed interior points. This shows less measured concentration. It does not prove the poorest households have higher real incomes: their share could rise while total income falls. Finish a construction by explaining both the distributional result and what additional information is needed.
Hypothetical worked application
- Add the poorest two shares: 5 + 10 = 15%.
- At population share 60%, add 5 + 10 + 15 = 30%.
- At 80%, cumulative income is 55%; the richest quintile receives the remaining 45%.
Plot (0,0), (20,5), (40,15), (60,30), (80,55), (100,100).
Lorenz curves and income distribution
Initial grouped Gini ≈ 0.32; selected distribution ≈ 0.19. Cumulative income shares at 0, 20, 40, 60, 80, 100% of people: 0%, 8.94%, 25.3%, 46.48%, 71.55%, 100%. HL construction: add successive quintile shares; do not plot individual shares as cumulative values.
Rank households from poorest to richest. A Lorenz point shows the cumulative income share held by the corresponding cumulative population share. A curve closer to equality generally indicates less inequality when curves do not cross.
How to draw it and model assumptions
- Both axes run 0–100%; population share horizontally, income share vertically.
- Draw the equality line from (0,0) to (100,100).
- Add cumulative quintile shares, beginning (0,0) and ending (100,100).
Hypothetical income shares for equal-sized quintiles. Curve interpretation is shared; constructing from quintile data is HL. The displayed grouped Gini is an approximation from straight segments, not a required guide calculation.
Apply and evaluate
- Grouped data conceal inequality within each quintile and may conceal crossing between observation points.
Common misconceptions
- Plot cumulative shares, not the five individual quintile shares.
Knowledge check
If the poorest quintiles receive 7%, 11% and 17%, what is the third cumulative income coordinate?
Real-world application
Poverty lines depend on a PPP vintage
5 June 2025: The World Bank’s June 2025 update set the international extreme-poverty line at $3.00 per person per day in 2021 PPP international dollars, replacing $2.15 in 2017 PPP dollars.
The change is not an ordinary market-exchange-rate conversion. PPP data and the national poverty lines underlying the benchmark changed. Comparing poverty counts across releases requires a consistent method; a statistical revision is not itself proof that living conditions suddenly worsened.
World Bank, June 2025 update to global poverty lines ↗Historical evidence checked 9 October 2026. The model interpretation is an original teaching application.
What to remember
Add each quintile's income share to all earlier shares before plotting. The coordinates describe cumulative distribution, not the income of each group on its own.
Completion is your own reflection on learning, not a test score. Syllabus references: 3.4.04.
Sources and applications
Lessons in this section
- What Is Economic Inequality?
- How Do Lorenz Curves and Gini Coefficients Work?
- How Do We Draw a Lorenz Curve from Quintiles? · HL
- How Is Poverty Measured?
- Why Does Inequality Persist?
- How Do Taxes Affect Income Distribution?
- How Are Income Tax and Sales Tax Calculated? · HL
- How Can Transfers and Public Services Reduce Poverty?
- How Can Policy Support Incomes and Fair Access to Work?
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