Concept Architecture
Concept
Theoretically, the Mode is a measure of central tendency defined as the value that occurs with the greatest frequency in a dataset or the point at which a probability distribution attains its maximum density. Unlike the mean and median, the mode identifies the most commonly occurring observation rather than an average or midpoint. It exists to describe the most typical or prevalent value within a distribution and is particularly useful for categorical, discrete and multimodal data.
Mathematically, the mode is determined by identifying the value associated with the highest observed frequency or, for continuous distributions, the value that maximises the probability density function. A dataset may have one mode (unimodal), two modes (bimodal), several modes (multimodal) or no unique mode if all observations occur with equal frequency.
In practice, the mode is calculated by counting the frequency of each observed value and selecting the most frequently occurring one. In health economics, the mode is used to identify the most common diagnosis, treatment pathway, healthcare resource use category, waiting time interval or survey response. For continuous variables such as healthcare costs, the mode is generally estimated using grouped data or density estimation because exact repeated values are uncommon.
Purpose
Used to identify the most frequently occurring value in a dataset, summarise categorical and discrete variables and describe the most common outcome or characteristic in health economic analyses.
Mathematical Formulae
Primary Formula
For a discrete random variable:
Mode = arg max? P(X = x)
For grouped data:
Mode � L + [(f? ? f?) / (2f? ? f? ? f?)] ? h
where:
- L = lower boundary of the modal class
- f? = frequency of the modal class
- f? = frequency of the preceding class
- f? = frequency of the succeeding class
- h = class width
Supporting Formulae
There is no universally recognised canonical mathematical formula.
Related Mathematical Methods
- Mean
- Median
- Frequency Distribution
- Kernel Density Estimation
- Histogram Analysis
- Measures of Central Tendency
Example
A health economist records the number of outpatient visits made by ten patients during one year:
1, 2, 2, 3, 3, 3, 4, 5, 5, 7
The frequencies are:
- 1 visit: 1 patient
- 2 visits: 2 patients
- 3 visits: 3 patients
- 4 visits: 1 patient
- 5 visits: 2 patients
- 7 visits: 1 patient
The mode is:
Mode = 3 visits
This indicates that three outpatient visits per year is the most common level of healthcare utilisation within the sample.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| MODE.SNGL | =MODE.SNGL(B2:B501) | Calculate the most frequently occurring value. |
| MODE.MULT | =MODE.MULT(B2:B501) | Identify multiple modes in multimodal datasets. |
| COUNTIF | =COUNTIF(B2:B501,B2) | Count the frequency of each observed value. |
| UNIQUE | =UNIQUE(B2:B501) | Generate distinct values before calculating frequencies. |
| SORT | =SORT(B2:B501) | Order observations when exploring frequency distributions. |
VBA (Optional)
A VBA routine can automatically calculate the mode, identify multimodal distributions and produce frequency tables for multiple health economic variables.
Sources
- Mood AM, Graybill FA, Boes DC. Introduction to the Theory of Statistics. McGraw-Hill.
- Rice JA. Mathematical Statistics and Data Analysis. Cengage Learning.
- Agresti A. Statistical Methods for the Social Sciences. Pearson.
- Conover WJ. Practical Nonparametric Statistics. Wiley.
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation. Oxford University Press.
- Drummond MF, et al. Methods for the Economic Evaluation of Health Care Programmes. Oxford University Press.
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 mode?
A central tendency measure representing the most frequently occurring value within a dataset.
Source: Casella G, Berger RL. Statistical Inference. 2nd ed. Duxbury; 2002.
What does the mode identify in a dataset?
The mode identifies the value that occurs most often in a dataset, the single most common observation. It is the only measure of central tendency that applies to categorical data, where averaging or ranking makes no sense, so it answers which category is most frequent, such as the commonest blood type. For numerical data it can be unstable or undefined when values rarely repeat, or misleading when a distribution has several peaks. The most frequent value is what it captures. Kirkwood and Sterne (2003) describe this measure.
Source: Kirkwood & Sterne 2003
How is the mode determined?
The mode is determined by finding the value or category that occurs most frequently in the dataset, that is the one with the highest count or frequency. For continuous data grouped into intervals, the modal interval is the one with the greatest frequency. So the mode is determined simply by counting the occurrences of each value and identifying the most common, which is straightforward for categorical or discrete data, while for continuous data the concept is applied to the interval or region of greatest frequency, since exact repeated values are less common, and a dataset may have more than one mode if several values share the highest frequency.
Source: Casella & Berger 2002
When is the mode useful?
The mode is useful for categorical, or nominal, data, where the mean and median cannot be calculated, since it identifies the most common category; and for describing the most typical or popular value in any data, such as the most frequent diagnosis or response. So the mode is useful when the most common value or category is of interest, particularly for categorical data where it is the only applicable measure of central tendency, and it can also reveal features such as multiple peaks in a distribution, which the mean and median would not show, making it a complement to the other measures of central tendency.
Source: Casella & Berger 2002
How does the mode differ from the mean and median?
The mode is the most frequently occurring value, the mean is the arithmetic average, and the median is the middle value of ordered data. The mode can be used for categorical data and can be non-unique or absent, while the mean and median require numerical or ordinal data. So the mode differs from the mean and median in identifying the most common value rather than the average or the centre, and in its applicability to categorical data, which is why all three are used to describe central tendency from different angles, with the mode capturing frequency, the mean the average, and the median the positional centre.
Source: Casella & Berger 2002
What are the limitations of the mode?
The limitations of the mode include that it may not be unique, since a dataset can have several modes, or may not exist if all values occur equally often; that for continuous data exact modes are rare, requiring grouping; and that it ignores the magnitudes of the values, using only frequency. So the mode is used with awareness that it can be ambiguous or uninformative for some data, particularly continuous data, and that it does not reflect the overall distribution as the mean and median do, which is why it is most valuable for categorical data and as a complement to the other measures rather than a standalone summary of numerical data.
Source: Casella & Berger 2002
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 18 Dec 2025
Content version: 1.0.0
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- Persistent URI
- https://healtheconomics.wiki/concept/mode
- Term code
- HE-ES-SA-127
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