Decile Calculator

What the decile calculator does

Deciles split a sorted data set into ten equal parts. The nine cut points between them are the deciles, marking the values below which 10 percent, 20 percent, and so on of the data falls. This calculator finds all nine from your data, and lays out how many values land in each tenth.

Deciles are how large groups get sorted into bands, from income brackets to exam cohorts, when quarters are too coarse and full percentiles are too fine. Below is how it works and how to read the table it produces.

How to use it

1. Enter your data values, one per box. These are the numbers in your data set, not the deciles themselves, and you need at least nine of them.
2. Add more boxes with the buttons if your data set is larger.
3. Press Calculate for the deciles and their table, or Reset to clear it.

How the deciles are worked out

The calculator sorts your data, then for each decile works out its position in the sorted list. The position of the k-th decile is set by:

Position = k × (number of values + 1) ÷ 10

When that position lands exactly on a value, that value is the decile. When it lands between two, the calculator slides between them in proportion, the same linear interpolation used for percentiles. This particular rule, using the count plus one, is a common textbook method. It is worth noting it differs slightly from the rule in our percentile calculator, so a decile here and the matching percentile there may not be identical, which is the usual story with these positional measures.

Reading the decile table

The result is a table with a row for each of the ten bands. It shows the decile number, the value at that cut point, the span of values the band covers, and two counts: how many of your values fall in that band, and the running total as you move up through the bands.

Read down the table and you can see how your data is distributed across its range, which tenths are crowded and which are sparse. The running total on the right reaches the full size of your data set by the final band.

Deciles, quartiles, and percentiles

Deciles are one of a family of tools that all do the same job at different resolutions. Quartiles cut the data into four parts, deciles into ten, and percentiles into a hundred. They line up at the shared points: the fifth decile, the second quartile, and the 50th percentile are all the median, the very middle of the data.

So the choice between them is really about how finely you want to slice. Deciles are the natural pick when you want ten roughly equal bands, more detail than quarters give but without the fuss of a full hundred.

A worked example

Take the nine numbers 3, 5, 7, 8, 12, 13, 14, 18, 21, already sorted. With nine values, the position of each decile works out to a whole number, so the deciles fall right on the data points: the first decile is 3, the second is 5, the third is 7, and so on up.

The fifth decile lands on 12, which is exactly the median, the middle of the set, just as it should be. With a larger or less tidy data set the positions would fall between values, and the calculator would interpolate to find each decile.

Entering your data, and the rounding

Enter each data value in its own box, adding boxes as your data set grows, up to fifty values. Every box you use needs a number, and you need at least nine values in all for the ten bands to be meaningful. Interpolated deciles are shown to one decimal place.

Questions people ask

What are deciles?

The nine values that split sorted data into ten equal parts. Each decile marks a 10 percent step through the data, from the first decile at 10 percent to the ninth at 90 percent.

What do I enter, my data or the deciles?

Your data values, one per box. The calculator finds the deciles from them. You need at least nine values.

How are deciles different from quartiles?

They slice the data more finely. Quartiles make four parts, deciles make ten. The fifth decile and the second quartile are both the median.

Which decile is the median?

The fifth. It sits at the 50 percent mark, which is the definition of the median, the middle of the data.

References

A quick note on where the methods here come from. Deciles and the other positional measures are set out in the NIST/SEMATECH e-Handbook of Statistical Methods, the US government's public statistics reference. The different position rules these measures can use are surveyed in Hyndman and Fan's paper on quantile methods, the standard reference on the subject.

1. NIST/SEMATECH e-Handbook of Statistical Methods (percentiles and positional measures). https://www.itl.nist.gov/div898/handbook/
2. Hyndman, R. J. and Fan, Y. (1996), Sample Quantiles in Statistical Packages, The American Statistician. https://www.tandfonline.com/doi/abs/10.1080/00031305.1996.10473566