Concept Architecture
Concept
Theoretically, Decile is a positional measure that divides an ordered dataset into ten equal parts, each containing approximately 10% of the observations. It is founded on order statistics and descriptive statistics and provides a means of describing the distribution of continuous or ordinal data. Deciles exist to summarise the relative position of observations within a distribution and to compare groups across different sections of that distribution.
Mathematically, deciles are represented as the nine cut-points that partition an ordered sample into ten equally sized intervals. Their values are determined from the ranked observations using recognised quantile estimation methods. When the required position falls between two observations, interpolation is commonly applied according to the selected quantile algorithm.
In practice, deciles are calculated by sorting observations in ascending order and determining the value corresponding to each decile position. They are widely used in health economics to classify patients by healthcare costs, rank providers by performance, group populations by socioeconomic deprivation and stratify risks for economic evaluation and resource allocation.
Purpose
Used to divide an ordered dataset into ten equal groups, enabling assessment of distributional characteristics, ranking of observations and comparison of outcomes across population segments.
Mathematical Formulae
Primary Formula
Position of the k-th decile:
P(D?) = k(n + 1) / 10
where:
- k = 1, 2, ?, 9
- n = sample size
Supporting Formulae
Linear interpolation (when the position is non-integer):
D? = x?P? + (P ? ?P?) ? (x?P? ? x?P?)
where:
- P = calculated decile position
- x?P? = lower ranked observation
- x?P? = upper ranked observation
Related Mathematical Methods
- Quantiles
- Percentiles
- Quartiles
- Quintiles
- Order Statistics
- Rank Statistics
Example
A health economist analyses annual healthcare expenditure for 100 patients.
To determine the seventh decile:
P(D?) = 7(100 + 1) / 10
P(D?) = 70.7
The seventh decile lies between the 70th and 71st ranked observations. If these values are �5,200 and �5,300:
D? = 5200 + 0.7 ? (5300 ? 5200)
D? = �5,270
Approximately 70% of patients have annual healthcare costs below �5,270.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| PERCENTILE.INC | =PERCENTILE.INC(A2:A101,0.7) | Calculates the seventh decile of healthcare costs or outcomes. |
| PERCENTILE.EXC | =PERCENTILE.EXC(A2:A101,0.7) | Calculates the seventh decile using the exclusive percentile definition. |
| SORT | =SORT(A2:A101) | Orders observations before manual decile calculation. |
| RANK.EQ | =RANK.EQ(A2,$A$2:$A$101) | Determines observation ranks within the dataset. |
VBA (Optional)
Automate calculation of all nine deciles for multiple healthcare variables and generate distribution summaries for reporting.
Sources
- Hyndman RJ, Fan Y. Sample Quantiles in Statistical Packages. The American Statistician. 1996.
- Conover WJ. Practical Nonparametric Statistics.
- Agresti A. Foundations of Linear and Generalized Linear Models.
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation.
- NICE. Health Technology Evaluation Manual.
Related Concepts (3)
Library
Publications
1
Bayesian Methods in Health Economics — Gianluca Baio, 1st Edition ed., 2012 (Chapman & Hall / CRC Press)
An overview of Bayesian statistical methods for the analysis of health economic data, covering economic evaluation concepts, statistical cost-effectiveness analysis, Bayesian computation and MCMC, and applied health economic evaluation.
BookView source →
Frequently Asked Questions (6)
What is a decile?
A descriptive statistic dividing a ranked dataset into ten equal-sized groups, the first decile being the bottom ten percent and the tenth the top.
Source: Casella G, Berger RL. Statistical Inference. 2nd ed. Duxbury; 2002.
What does dividing data into deciles show?
A decile divides a ranked dataset into ten equal-sized groups, so the first decile holds the lowest tenth of values and the tenth the highest. Splitting data this way shows how a quantity is distributed across a population, for instance grouping people by income or risk to compare the extremes and the steps between them. It is one member of the family of quantiles, finer than quartiles but coarser than percentiles. Carving a distribution into ten equal parts is what it does. Kirkwood and Sterne (2003) describe this.
Source: Kirkwood & Sterne 2003
How are deciles used?
Deciles are used to describe the distribution of a dataset and to place individuals or observations within it, for example ranking areas or people into tenths by income, risk, or deprivation, so that groups can be compared across the range. They are common in describing inequalities and in summarising skewed data. So deciles are used to divide and summarise data into ten ordered groups, which allows comparison of the top and bottom parts of a distribution and the positioning of cases within it, making them useful for describing spread, inequality, and gradients across a population without assuming a particular distributional shape.
Source: Casella & Berger 2002
How do deciles relate to other quantiles?
Deciles relate to other quantiles as the division of data into ten equal parts, alongside quartiles, which divide into four, percentiles, which divide into a hundred, and quantiles in general, which divide into any specified number of equal groups. Deciles correspond to particular percentiles, the tenth, twentieth, and so on. So deciles are one member of the family of quantiles, splitting ordered data into tenths, and they can be expressed as percentiles, with the choice among quartiles, deciles, and percentiles depending on how finely the distribution is to be divided for the purpose at hand.
Source: Casella & Berger 2002
Why are deciles useful?
Deciles are useful because they summarise how values are spread across a distribution in an interpretable way, dividing data into ten ordered groups that reveal the range and the concentration of values, and they are robust to the distribution's shape, being based on rank. They are particularly helpful for comparing the extremes. So deciles are useful for describing and comparing distributions, especially skewed ones, and for expressing gradients such as inequalities across a population, since dividing data into tenths allows the top and bottom and intermediate groups to be examined, giving a clear picture of the distribution without relying on the mean or assuming normality.
Source: Casella & Berger 2002
What is the difference between a decile and a percentile?
The difference between a decile and a percentile is the fineness of the division: deciles split ordered data into ten equal groups, while percentiles split it into a hundred, so each decile corresponds to a specific percentile, the first decile to the tenth percentile, the second to the twentieth, and so on. So deciles and percentiles are both quantiles dividing data into equal parts, differing in the number of divisions, with deciles giving a coarser, ten-part summary and percentiles a finer, hundred-part one, and the choice between them depends on how detailed a description of the distribution is required.
Source: Casella & Berger 2002
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 15 Dec 2025
Content version: 1.0.0
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- Term code
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