How this calculator works
Deciles are quantiles at probabilities 0.1, 0.2 and so on through 0.9. Linear interpolation uses position 1 + (n - 1)p; nearest rank uses ceil(np). The exclusive position method uses (n + 1)p and clamps positions beyond the observed ends. Small samples can give repeated cut points, and tied observations prevent exact equal-sized partitions.
Formula
Dk = Q(k/10), k = 1,...,9. Linear Q uses one-based position 1 + (n - 1)k/10.
Worked example
For 10, 20, 30, 40, 50, D3 lies at position 2.2 and equals 22 by linear interpolation. Nearest-rank D8 is the fourth value, 40.
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Frequently asked questions
Is a decile a group or a boundary?
This tool reports boundaries. Ten groups are separated by nine internal cut points.
Why do two deciles have the same value?
There may be too few distinct observations or many ties. A numeric boundary cannot split identical values cleanly.
Can a decile fall between observations?
Yes for interpolation. Nearest rank always returns a value present in the data.