What deciles are
Deciles divide an ordered dataset into ten equal-sized groups. There are nine decile cut points, written D1 through D9. D1 is the value below which roughly 10% of the data lie, D2 marks the 20% point, and so on up to D9, which marks the 90% point. Because they slice the data at every tenth of the distribution, deciles are a compact way to describe the shape and spread of a dataset without assuming it follows any particular curve.
Deciles belong to the same family as quartiles and percentiles. A decile is just a percentile at a multiple of ten: D1 is the 10th percentile, D3 is the 30th percentile, and D9 is the 90th percentile. The 5th decile (D5) sits at the 50% point, so it is identical to the median and to the second quartile (Q2).
The formula this calculator uses
Sort the n values in ascending order. For the k-th decile (k = 1 to 9), find the rank position:
L = (k / 10) × (n + 1)
If L is a whole number, the decile is simply the value at rank L. If L falls between two ranks, interpolate linearly between the neighbouring values: take the lower value plus the fractional part of L times the gap to the next value. When L is at or below 1 the decile is clamped to the minimum, and when L is at or beyond n it is clamped to the maximum. This is the standard "n + 1" interpolation method taught in introductory statistics and used for percentiles and quartiles alike.
Worked example: for the dataset 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 (already sorted, n = 10), D3 has position L = 0.3 × 11 = 3.3. That lands between the 3rd value (6) and the 4th value (8): D3 = 6 + 0.3 × (8 − 6) = 6.6. D5 has L = 5.5, giving 10 + 0.5 × (12 − 10) = 11, which is the median of this set.
Where deciles are used
- Income and wealth: economists routinely report figures "by income decile" — the bottom decile, the top decile, and everything between — to describe distribution and inequality.
- Standardised testing: a student "in the 9th decile" scored higher than about 90% of test-takers.
- Growth charts and reference ranges: height, weight, and clinical measurements are often summarised against population deciles.
- Business analytics: customers or products are frequently ranked into deciles to target the top or bottom 10%.
Reading the results
The gap between adjacent deciles tells you where data is dense or sparse. Tightly spaced deciles mean values cluster there; a large jump between, say, D8 and D9 signals a long upper tail. The distance from D1 to D9 (the interdecile range) captures the middle 80% of the data and is more robust to outliers than the full min-to-max range, because it ignores the extreme 10% at each end.