Deciles are the nine values that divide sorted data into ten groups with the same number of observations. The first decile D1 has 10% of the data below it, D5 is the median and D9 has 90% below it. They sit between quartiles (four groups) and percentiles (a hundred groups) in detail, and are a common way to report incomes, wealth and test results: “the top decile of earners”, “pupils in the bottom decile”.
The gap between D9 and D1, the interdecile range, covers the middle 80% of the data and is a useful measure of spread that is less sensitive to extremes than the full range. The ratio D9 ÷ D1 is widely used in economics to describe income inequality.
Because the decile positions are usually fractional, the value is interpolated between neighbouring observations. The default rule places Dₖ at position k(n + 1)/10; Excel’s PERCENTILE.INC uses 1 + k(n − 1)/10. With fewer than nine values, the (n + 1) rule needs positions outside the data, which are clamped to the minimum or maximum.
How to use the Decile Calculator
- Data set
- Decile method
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How it works
Sort the data, compute the position of each decile with the chosen rule and interpolate between the values at the neighbouring ranks.
Worked example
Twenty values: 35, 41, 44, 47, 50, 52, 55, 57, 58, 61, 63, 64, 67, 70, 72, 75, 79, 83, 88, 94. With the (n + 1) rule D1 is at position 2.1: 41 + 0.1 × 3 = 41.3. D5 is at position 10.5: (61 + 63)/2 = 62, the median. D9 is at position 18.9: 83 + 0.9 × 5 = 87.5. The interdecile range is 87.5 − 41.3 = 46.2.
| Decile | Position | Value |
|---|---|---|
| D1 | 2.1 | 41.3 |
| D2 | 4.2 | 47.6 |
| D3 | 6.3 | 52.9 |
| D4 | 8.4 | 57.4 |
| D5 | 10.5 | 62 |
| D6 | 12.6 | 65.8 |
| D7 | 14.7 | 71.4 |
| D8 | 16.8 | 78.2 |
| D9 | 18.9 | 87.5 |
Where deciles are used
- Income and wealth statistics (D9/D1 ratio, “top 10%”).
- School performance bands and exam grading.
- Ranking neighbourhoods by deprivation indices.
- Splitting customers into ten equal groups for marketing analysis.
Formula
Position of Dₖ = k(n + 1)/10 (or 1 + k(n − 1)/10) · Dₖ = x₍⌊r⌋₎ + (r − ⌊r⌋)(x₍⌊r⌋+1₎ − x₍⌊r⌋₎), k = 1 … 9
Worked example
Inputs — Data set: 35, 41, 44, 47, 50, 52, 55, 57, 58, 61, 63, 64, 67, 70, 72, 75, 79, 83, 88, 94; Decile method: (n + 1)·p rank, interpolated (NIST, Excel PERCENTILE.EXC).
Results — First decile (D1, 10th percentile) = 41.3; D2 (20th percentile) = 47.6; D3 (30th percentile) = 52.9; D4 (40th percentile) = 57.4; D5 (50th percentile = median) = 62; D6 (60th percentile) = 65.8.
Key terms
- Decile
- A cut point dividing the data into tenths.
- Interdecile range
- D9 − D1, the spread of the middle 80% of the data.
- D9/D1 ratio
- A common measure of inequality.
Frequently asked questions
What is a decile?
One of nine values that split sorted data into ten equal-sized groups. D1 is the 10th percentile and D9 the 90th.
How do I calculate deciles?
Sort the data, find the position k(n + 1)/10 for the k-th decile and interpolate between the neighbouring values.
How many deciles are there?
Nine cut points (D1 to D9) create ten groups, sometimes also called deciles.
Is the 5th decile the median?
Yes, D5 is the 50th percentile, the median.
What is the first decile of the example data?
Its position is 21/10 = 2.1, so D1 = 41 + 0.1 × (44 − 41) = 41.3.
What is the difference between deciles, quartiles and percentiles?
They divide data into 10, 4 and 100 equal parts. D9 = P90, D5 = Q2 = P50.
What does "top decile" mean?
The 10% of observations above D9.
How many values do I need?
At least 9 for every decile to be inside the data with the (n + 1) rule; 20 or more for stable results.