Calculator Inputs
Example Data Table
This sample uses five equal-sized groups. You can load the same example directly into the calculator.
| Group Label | Population | Average Wealth | Group Wealth |
|---|---|---|---|
| Lowest 20% | 2,000 | $1,500 | $3,000,000 |
| Second 20% | 2,000 | $9,000 | $18,000,000 |
| Middle 20% | 2,000 | $28,000 | $56,000,000 |
| Fourth 20% | 2,000 | $85,000 | $170,000,000 |
| Top 20% | 2,000 | $360,000 | $720,000,000 |
Formula Used
\( W_i = n_i \times a_i \)
where \( n_i \) is population in group \( i \), and \( a_i \) is average wealth per person.
\( p_i = \frac{n_i}{\sum n_i} \), \( s_i = \frac{W_i}{\sum W_i} \)
cumulative population share \( X_i = \sum p_i \), cumulative wealth share \( Y_i = \sum s_i \)
\( G = 1 - \sum (Y_i + Y_{i-1})(X_i - X_{i-1}) \)
\( H = \frac{1}{2}\sum |s_i - p_i| \)
\( T = \sum s_i \ln\left(\frac{s_i}{p_i}\right) \)
this version uses \( \varepsilon = 0.5 \) with grouped average wealth values.
\( \text{Palma} = \frac{\text{Top 10% Wealth}}{\text{Bottom 40% Wealth}} \)
Percentile shares and ratios are grouped estimates. Each group is treated as internally uniform because only grouped averages are provided.
How to Use This Calculator
- Select how many groups you want to compare.
- Enter each group label, population size, and average wealth per person.
- Use equal population bands for quintiles or deciles when possible.
- Click Calculate Distribution to generate metrics and the Lorenz curve.
- Review the summary cards, grouped table, and exports for reporting.
FAQs
1. What does this calculator measure?
It measures how unevenly wealth is distributed across groups. It reports concentration, inequality, cumulative shares, and key summary ratios from grouped population and average wealth inputs.
2. What inputs should I enter?
Enter a label, the number of people or households in that group, and the average wealth for one member of that group. The tool multiplies them to estimate group wealth.
3. Why can the calculator reorder my groups?
Lorenz and inequality measures require groups sorted from lowest to highest average wealth. If your entries are not already ordered, the calculator sorts them before computing cumulative shares.
4. Can I use quintiles, deciles, or custom bands?
Yes. You can use any grouped structure between two and ten bands. Equal population bands often make interpretation easier, but custom segments also work well.
5. What does the Gini coefficient tell me?
A Gini near zero suggests a more even distribution. A higher Gini shows stronger concentration of wealth in richer groups relative to the rest of the population.
6. What is the Palma ratio?
The Palma ratio compares wealth held by the top ten percent with wealth held by the bottom forty percent. Larger values indicate stronger concentration at the top.
7. Is this suitable for individual raw records?
This page is designed for grouped summaries, not row-level microdata. You can still approximate a raw dataset by forming many narrow wealth bands first.
8. What are the main limitations?
The tool assumes non-negative average wealth and equal wealth inside each group. That makes outputs practical, but still approximate when internal variation is large.