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Decile Calculator

This decile calculator turns your numbers into D1 to D9. Example: for 12 values from 10 to 22, D1 is 11.1, the median D5 is 15.5 and D9 is 19.9.

Source: Wikipedia – Decile. Updated: .

Separate with spaces or semicolons; commas also separate values, so use a decimal point (2.5), not a comma.
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Result

Result
Deciles D1 to D9: 11.1; 12.2; 13.3; 14.4; 15.5; 16.6; 17.7; 18.8; 19.9 (n = 12, inclusive method)
All values
DecilePosition hValue
D12.111.1
D23.212.2
D34.313.3
D45.414.4
D56.515.5
D67.616.6
D78.717.7
D89.818.8
D910.919.9
Calculation steps
  • Sorted values (n = 12): 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 22.
  • D1: h = (n − 1) · 0.1 + 1 = 2.1; value = x(2) + 0.1 · (x(3) − x(2)) = 11.1.
  • D9: h = (n − 1) · 0.9 + 1 = 10.9; value = x(10) + 0.9 · (x(11) − x(10)) = 19.9.
The inclusive method matches QUARTILE.INC and gives the same Q1 and Q3 as the quartile calculator with that method; D5 is always the median. Other programs (and the textbook halves method for quartiles) can give slightly different deciles.

How it is calculated

Deciles split a sorted list of numbers into ten equal parts: D1 cuts off the lowest 10%, D5 is the median and D9 cuts off the top 10%.

Method and working

The values are sorted. With the inclusive method the p-quantile (p = 0.1 for D1 up to 0.9 for D9) sits at position h = (n − 1) · p + 1; with the exclusive method at h = (n + 1) · p. When h falls between two values, linear interpolation applies: x(h) = x(⌊h⌋) + (h − ⌊h⌋) · (x(⌊h⌋+1) − x(⌊h⌋)). The calculator uses the same rule for quartiles (QUARTILE.INC or QUARTILE.EXC), so D2.5 equals Q1 and D7.5 equals Q3.

Worked example

Sorted, the list is 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22 (n = 12). Inclusive, the position for D1 is 11 · 0.1 + 1 = 2.1, giving 11 + 0.1 · (12 − 11) = 11.1. D5 sits at position 6.5 and gives (15 + 16) / 2 = 15.5; D9 sits at position 10.9 and gives 19 + 0.9 · (20 − 19) = 19.9. Exclusive, the positions are 13 · p: D1 at position 1.3 gives 10.3 and D9 at position 11.7 gives 21.4.

Frequently asked questions

How do you calculate deciles?

Sort the values, find the position h = (n − 1) · p + 1 for p = 0.1 to 0.9 and interpolate linearly between neighbouring values. For our 12 values, D1 = 11.1.

What is the difference between a decile and a quartile?

Quartiles split the data into four parts, deciles into ten. D5 is the median like Q2; Q1 corresponds to D2.5 and Q3 to D7.5.

Which method should I choose?

The inclusive method is the default in Excel (PERCENTILE.INC) and R. You only need the exclusive method if your specification names PERCENTILE.EXC.

Sources and legal basis

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