Concept Architecture
Concept
Theoretically, Range is a descriptive statistical measure of dispersion that quantifies the spread of a dataset by calculating the difference between its largest and smallest observed values. It is the simplest measure of variability and provides a direct indication of the total extent of observed values. Although easy to calculate and interpret, the range is highly sensitive to extreme observations and therefore provides only a coarse summary of dispersion.
Mathematically, the range is calculated as the maximum observation minus the minimum observation. Because it depends solely on two observations, it ignores the distribution of all intermediate values. Consequently, the range is often reported alongside more robust measures of variability such as the interquartile range or standard deviation.
In practice, the range is calculated directly from observed data after identifying the minimum and maximum values. In health economics it is commonly reported to summarise the spread of healthcare costs, quality-adjusted life years, waiting times, treatment durations, and resource utilisation, particularly during exploratory data analysis and descriptive reporting.
Purpose
Used to summarise the overall spread of observed data, identify the extent of variability, support exploratory data analysis, and provide a simple descriptive measure of dispersion in health economic studies.
Mathematical Formulae
Primary Formula
Range = x??? ? x???
where:
- x??? = maximum observed value
- x??? = minimum observed value
Supporting Formulae
None.
Related Mathematical Methods
- Dispersion
- Standard Deviation
- Variance
- Interquartile Range
- Percentile
- Quartile
- Descriptive Statistics
Example
Annual healthcare costs are observed for a sample of patients.
Minimum annual cost:
�1,250
Maximum annual cost:
�18,900
The range is:
Range = �18,900 ? �1,250
= �17,650
This indicates that observed annual healthcare costs span �17,650 across the study population.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| MAX | =MAX(B2:B201) | Identify the highest observed healthcare cost or outcome. |
| MIN | =MIN(B2:B201) | Identify the lowest observed healthcare cost or outcome. |
| MAX-MIN | =MAX(B2:B201)-MIN(B2:B201) | Calculate the range of healthcare costs or resource utilisation. |
| LARGE | =LARGE(B2:B201,1) | Retrieve the largest observed value for descriptive summaries. |
| SMALL | =SMALL(B2:B201,1) | Retrieve the smallest observed value for descriptive summaries. |
VBA (Optional)
Automate calculation of descriptive statistics, including the range, across multiple health economic outcome variables and generate summary tables.
Sources
- Altman DG. Practical Statistics for Medical Research.
- 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.
- Drummond MF, et al. Methods for the Economic Evaluation of Health Care Programmes.
- NICE Health Technology Evaluation Manual.
Related Concepts (2)
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 the range?
A dispersion measure calculated as the difference between the maximum and minimum values in a dataset, sensitive to extreme outliers.
Source: Casella G, Berger RL. Statistical Inference. 2nd ed. Duxbury; 2002.
What does the range tell us about a dataset's spread?
The range is the simplest measure of spread, the difference between the largest and smallest values in a dataset. It tells us the full extent the data cover, from lowest to highest, in a single easily grasped figure. Because it depends only on the two most extreme values, it is highly sensitive to outliers and ignores everything in between, so a single unusual point can inflate it and it says nothing about how the bulk of values are distributed. The gap between the extremes is what it captures. Kirkwood and Sterne (2003) describe this measure.
Source: Kirkwood & Sterne 2003
How is the range calculated?
The range is calculated by subtracting the smallest value in the dataset from the largest, giving the difference between the maximum and minimum. So the range is calculated simply as the maximum minus the minimum, which makes it easy to compute and interpret as the total span of the data, but because it uses only the two extreme values and ignores all the others, it provides no information about how the data are distributed between them and is strongly affected by any outlier, which is why it is a crude measure of dispersion.
Source: Casella & Berger 2002
Why is the range sensitive to outliers?
The range is sensitive to outliers because it depends entirely on the maximum and minimum values, so a single extreme value at either end greatly increases the range, even if the rest of the data are tightly clustered. So the range is easily distorted by outliers, since it reflects only the extremes and not the bulk of the data, which means an unusual value can make the range large and unrepresentative of the typical spread, and this sensitivity is why the range is often supplemented or replaced by more robust measures such as the interquartile range, which ignores the extreme quarters of the data.
Source: Casella & Berger 2002
What are the limitations of the range?
The limitations of the range include its extreme sensitivity to outliers, since it depends only on the maximum and minimum; its failure to convey how the data are distributed between the extremes; and its tendency to increase with sample size, since larger samples are more likely to include extreme values. So the range is a limited measure of dispersion, useful for a quick sense of the total spread but unreliable as a summary of variability, which is why it is usually reported alongside or replaced by measures such as the standard deviation or interquartile range that use more of the data and are more robust, giving a fuller and more stable picture of dispersion.
Source: Casella & Berger 2002
How does the range compare with other measures of dispersion?
The range gives the total spread from minimum to maximum and is simple but sensitive to outliers and uninformative about the distribution between the extremes, while the standard deviation uses all the values to summarise average spread around the mean, and the interquartile range gives the spread of the middle half, robust to outliers. So the range is the crudest measure of dispersion, useful for a quick overview but inferior to the standard deviation and interquartile range for describing variability, which is why those measures are generally preferred, with the range reserved for simple description or as a supplement, since it captures only the extremes.
Source: Casella & Berger 2002
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 23 Dec 2025
Content version: 1.0.0
Canonical Identity
- Persistent URI
- https://healtheconomics.wiki/concept/range
- Term code
- HE-ES-SA-173
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