Measures of Central Tendency: Mean, Median and Mode
Measures of central tendency identify a single value that represents the centre or typical value of a dataset. They help clinicians and public-health workers summarise observations, compare groups and communicate findings clearly.
Learning objectives
- Define mean, median and mode.
- Calculate each measure for raw and frequency data.
- Select the most appropriate measure for different data distributions.
- Interpret results in clinical and epidemiological contexts.
Arithmetic mean
The mean is the sum of all observations divided by their number: x̄ = Σx/n. For 2, 4, 4, 5 and 10, the mean is 25/5 = 5.
Strengths
Uses every observation; supports further statistical analysis; relatively stable between samples.
Limitations
Strongly affected by outliers and skewed distributions; inappropriate for nominal data.
Median
The median is the middle observation after arranging data in ascending order. With an even number of values, average the two middle observations. For 2, 3, 7, 9, 20, the median is 7. For 2, 3, 7, 9, it is (3+7)/2 = 5.
The median is preferred for skewed variables such as hospital stay, household income and waiting time because extreme observations have little influence.
Mode
The mode is the most frequent value. The dataset 1, 2, 2, 3, 4 has mode 2. A dataset may be unimodal, bimodal, multimodal or have no mode. It is the only central measure suitable for nominal categories, such as the commonest blood group.
| Measure | Best used when | Main weakness |
|---|---|---|
| Mean | Numerical, roughly symmetric data | Sensitive to extremes |
| Median | Ordinal or skewed numerical data | Does not use magnitudes of all values |
| Mode | Nominal data or most common value | May be absent or multiple |
Grouped-data mean
For a frequency table, multiply each class midpoint by its frequency, sum the products, then divide by total frequency: x̄ = Σfx/Σf. The result is an estimate because individual observations are represented by class midpoints.
Relationship to distribution shape
- Symmetric unimodal distribution: mean ≈ median ≈ mode.
- Positively skewed distribution: mode < median < mean.
- Negatively skewed distribution: mean < median < mode.
Clinical interpretation
Always report the unit, sample, period and distribution. A mean blood pressure without variability may conceal important spread. Pair the mean with standard deviation, and the median with interquartile range.
Review questions
- Calculate the mean, median and mode of 3, 4, 4, 6, 13.
- Why is the median often preferred for length of hospital stay?
- Which measure can summarise a nominal variable?
Return to the Clinical Medicine Year 2 curriculum
References
- World Health Organization. Basic Epidemiology.
- CDC. Principles of Epidemiology in Public Health Practice.
Educational content only; use approved institutional guidance for clinical decisions.
