What Are Deciles?
Deciles are nine values dividing sorted data into ten equal parts, each containing ~10% of observations. D1 marks the 10th percentile, D5 is the median, D9 is the 90th percentile. They reveal distribution shape and spread more effectively than quartiles alone.
Deciles are widely used in education (class rankings), finance (income distribution), and public policy (poverty analysis). The D9/D1 ratio is a standard inequality measure.
Calculation
Linear interpolation between adjacent values produces smooth estimates. For example, D3 is at position 0.3 × (n-1) in the sorted array.
Deciles vs Quartiles vs Percentiles
| Measure | Divides Into | Values |
|---|---|---|
| Quartiles | 4 parts | Q1, Q2, Q3 |
| Deciles | 10 parts | D1-D9 |
| Percentiles | 100 parts | P1-P99 |
Applications
In income analysis, D9/D1 ratio measures inequality. In education, decile ranks compare students across schools. In health, growth chart deciles track child development against population norms.
Frequently Asked Questions
Is D5 the median?
Yes. D5 = 50th percentile = Q2 = median. All three terms describe the same central value.
Minimum sample size for deciles?
Technically 2+, but deciles are most meaningful with n > 20. With very small samples, interpolation becomes a rough approximation.
How are deciles different from percentiles?
Deciles are specific percentiles: D1=P10, D2=P20, etc. They provide a manageable 9-value summary vs 99 percentile values.