What it means
Deciles work by ranking rather than by value. Sort every observation from lowest to highest, cut the list into ten equal-sized slices, and the boundary values between those slices are the deciles.
Slightly confusingly, people use the word in two ways. Strictly, a decile is a boundary value, so the ninth decile is the number below which 90% of observations fall; loosely, people call each of the ten groups a decile, as in the top decile of customers.
Both usages are common enough that it is worth checking which one a report means. In business they earn their keep as a segmentation tool.
Ranking customers by annual spend into ten groups shows immediately how concentrated revenue really is, and the same split applied to sales representatives, stores or products reveals where performance is genuinely coming from. They also describe distributions that an average would misrepresent.
If a handful of very large accounts drags the mean upwards, comparing the first decile with the ninth tells you far more about the typical customer and the spread between customers than any single average could. The main limitation is that deciles ignore magnitude within each group.
Two businesses can have identical decile boundaries while one has a single enormous account inside its top group, so it is wise to pair deciles with totals or revenue shares whenever the size of the tail matters.
In practice
Real-world examples.
Example
A subscription software company ranks its 3,000 accounts by annual value and finds the top decile of 300 accounts produces 52% of total revenue. The board reallocates two account managers to that group and sets a separate retention target for it.
Example
An HR director benchmarking pay finds that her firm's engineers sit around the third decile of the market for their region. She uses the decile position rather than a single average salary because it shows how far the whole distribution runs, not just where the middle sits.
Example
A grocery chain ranks its 240 stores by profit per square foot and looks at the bottom decile of 24 stores. Rather than closing them, it discovers that 15 share the same layout, and a refit programme moves most of them up two deciles within a year.
Formula
Calculation
Position of the kth decile in a list of n values ranked from lowest to highest:
Position = k x (n + 1) / 10
A retail chain ranks its 59 stores by annual profit, from lowest to highest, and wants to know its ninth decile.
Position of the ninth decile = 9 x (59 + 1) / 10 = 9 x 60 / 10 = 54
So the ninth decile is the profit of the 54th store in the ranking. Suppose that store made $412,000. Roughly 90% of the chain's stores earned less than that figure, and the five stores ranked above it make up the top decile.
For the first decile: Position = 1 x (59 + 1) / 10 = 60 / 10 = 6, so the sixth store in the ranking sets the boundary. If that store made $88,000, then the chain's ninth decile is $412,000 / $88,000 = 4.7 times its first decile. That ratio tells the board something a single average profit per store would have hidden completely: the network is nowhere near uniform.Case study
Seen in the real world.
The following example is illustrative and the company is fictional. Pelham Coffee, a chain of 30 shops, ran a loyalty scheme with 4,000 members and spent its marketing budget evenly across all of them, on the reasonable-sounding basis that every member was worth having. Total loyalty spend came to $3,000,000 a year, so the average member was worth $750.
A new marketing manager ranked the 4,000 members by annual spend and cut them into ten deciles of 400 members each. The top decile alone accounted for $1,200,000, which is 40% of all loyalty revenue, and worked out at $1,200,000 / 400 = $3,000 per member, four times the overall average of $750. The bottom three deciles combined contributed less than the top decile did on its own.
Pelham did not abandon the smaller members, but it did stop treating everyone identically. The top 400 received a named contact, early access to seasonal drinks and a small free-coffee allowance, while the lower deciles were moved to cheaper automated messaging. The change cost nothing extra overall, and retention in the top decile improved noticeably over the following year.
Watch out
Common mistakes.
- Confusing the boundary with the group. The ninth decile is a single number, while the top decile is the set of observations above it, and reports frequently mix the two.
- Calculating deciles on unsorted data. The ranking has to be done first, because the whole concept depends on position in an ordered list rather than on the values themselves.
- Using deciles on very small samples. Splitting 20 observations into ten groups leaves two per group, which makes each boundary far too sensitive to a single unusual value.
Questions
People also ask.
How many deciles are there?
There are nine boundary values dividing the data into ten groups, in the same way that three quartiles divide data into four groups.
How is a decile different from a percentile?
A decile is simply every tenth percentile, so the third decile and the thirtieth percentile are the same number.
When should I use deciles instead of an average?
Whenever the spread matters, particularly where a few very large or very small values would pull the average away from anything typical.
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