Measures of Central Tendency: Mean, Median, and Mode Explained

Imagine a research team has just collected blood pressure readings from 5,000 adults across a district. The raw numbers, sitting in a spreadsheet, mean almost nothing on their own. To make sense of such data, researchers reach for a small but powerful set of statistical tools called measures of central tendency. These measures pull thousands of scattered observations into a single representative value, helping demographers, epidemiologists, and policymakers understand what is “typical” in a population.

What are measures of central tendency? 🔗

A measure of central tendency is a single value that attempts to describe a dataset by identifying its central position. In population and family health studies, this central value helps researchers communicate findings about birth weights, fertility rates, household incomes, age at marriage, contraceptive use, and many other variables that shape public health policy.

The three primary measures are the mean, the median, and the mode. Each captures the “centre” of a dataset in a different way, and as the statistical guide from Scribbr notes, they are best understood as complementary tools rather than interchangeable ones. Choosing the right one depends on the type of data and the shape of its distribution.

The mean: the arithmetic average 🔗

The mean is the most familiar measure. It is calculated by adding all the values in a dataset and dividing the sum by the number of observations. If a Primary Health Centre records the heights of 10 newly recruited Auxiliary Nurse Midwives as 152, 155, 157, 158, 160, 160, 162, 163, 165, and 168 centimetres, the mean height is 1600 ÷ 10 = 160 cm.

The mean uses every value in the dataset, which is both its biggest strength and its biggest weakness. Because it pulls in all the information, it is well-suited to variables that are measured on interval or ratio scales and that follow a roughly symmetrical distribution.

When the mean works well 🔗

A classic example in family health is birth weight. Birth weights in a large population tend to follow an approximately bell-shaped curve, with most babies clustered around a central value and progressively fewer at the very low and very high extremes. According to data from the fifth round of the National Family Health Survey, the prevalence of low birth weight in India was estimated using NFHS-5 data covering nearly 1.5 lakh women in the reproductive age group, with the standard cut-off being a baby weighing less than 2,500 grams at birth. Because birth weight is continuous and reasonably symmetrical around its centre, the mean is a meaningful summary and forms the basis for further statistical analysis.

When the mean misleads 🔗

The mean has a serious vulnerability: extreme values, or outliers, can drag it away from what most people would consider “typical”. Suppose nine households in a village earn ₹15,000 a month and one household earns ₹15,00,000. The mean monthly income is roughly ₹1.6 lakh, a figure that describes none of the ten families accurately. This is why mean income is often a poor representation of how an average family actually lives.

The median: the middle value 🔗

The median is the middle value when all observations are arranged in ascending or descending order. If there is an odd number of values, the median is simply the central one. If there is an even number of values, the median is the average of the two middle ones.

For the height data above (10 values), the median is the average of the 5th and 6th values: (160 + 160) ÷ 2 = 160 cm. In this symmetrical example, the mean and median coincide. But when distributions are skewed, the two diverge sharply.

Why the median wins for income data 🔗

Household income in India is a textbook example of a right-skewed distribution. A small number of very wealthy households pull the upper tail far to the right, while the bulk of households cluster at much lower values. An analysis comparing two national household surveys found that the median worker in India earns around ₹10,000 a month or less, and that anyone earning ₹50,000 per month sits in the top 5 per cent of the income distribution. The mean monthly income, by contrast, is significantly higher because it is pulled upward by the small fraction of very high earners.

This is exactly why the World Bank, the National Sample Survey Office, and most economists prefer the median when describing the financial situation of a “typical” Indian household. As reporting on India’s inequality data highlights, the top 10 per cent of earners receive roughly 57.7 per cent of national income, a concentration that would distort any mean-based summary of how the average family lives.

The median is also robust when data has missing values at the extremes, or when researchers are working with ordinal data such as pain scales (mild, moderate, severe) or wealth quintiles.

The mode: the most frequent value 🔗

The mode is the value that appears most often in a dataset. Unlike the mean and median, it can be used for any type of data, including categorical variables where arithmetic makes no sense.

Mode in family health research 🔗

Consider contraceptive method choice, a key variable in family planning research. The data is categorical: condoms, oral pills, IUDs, female sterilisation, male sterilisation, and so on. You cannot compute an “average” contraceptive method, nor can you find a “middle” one. But you can identify the mode-the most commonly used method. Across India, female sterilisation has historically been the modal method, a finding that has shaped decades of family planning policy.

The mode is equally useful for variables like modal birth order, most common cause of maternal death, or most frequent age at first marriage. In disease surveillance, the modal symptom of a new outbreak often becomes the case definition used by field epidemiologists.

When there is more than one mode 🔗

A dataset can have two modes (bimodal) or more (multimodal). Public health analysts point out that a bimodal distribution of disease onset age might reveal two distinct subgroups within a population, each potentially requiring a different intervention strategy. Far from being a nuisance, multiple modes can be diagnostic clues that a population is not as homogeneous as it first appears.

Choosing the right measure 🔗

The right measure depends on two things: the level of measurement of the data and the shape of the distribution.

Match the measure to the data type 🔗

A useful summary, drawn from standard statistical guidance, is as follows. The mode can be applied to any level of measurement but is most informative for nominal data such as blood type, religion, or contraceptive method. The median requires data that can be at least ranked, so it works for ordinal, interval, and ratio variables. The mean is restricted to interval and ratio data, because it relies on the assumption that the spacing between adjacent values is equal.

For nominal data such as caste category or district of residence, only the mode is meaningful. For ordinal data such as a wealth index or a Likert-scale satisfaction survey, the median is the safest choice. For continuous variables such as haemoglobin levels or systolic blood pressure, all three measures can be calculated, but the mean is typically reported.

Match the measure to the distribution 🔗

When data is symmetrically distributed and free of outliers, the mean, median, and mode are approximately equal, and the mean is usually preferred because it uses every value and feeds into further statistical procedures. When data is skewed, as statistical educators recommend, the median is the better representation of the centre because it is not pulled by extreme values.

This principle has direct policy consequences. Reporting the mean income of an unequal society overstates the well-being of the typical citizen. Reporting the mean length of hospital stay can be distorted by a handful of very long stays. Reporting the modal age at marriage tells you what is most common but says nothing about how spread out the values are.

A practical checklist 🔗

Before choosing a measure, a researcher in population studies might ask: What is the level of measurement? Is the distribution roughly symmetrical or skewed? Are there extreme outliers? Is there a meaningful “most common” category? In well-designed studies, all three measures are often reported together, because each reveals something the others hide.

Why this matters for population and family health 🔗

The choice of central tendency is not just a technical decision; it shapes the story a dataset tells. Public health planners use the mean to estimate average healthcare utilisation and plan staffing, the median to ensure that resource allocation reflects the typical citizen rather than the extremes, and the mode to identify the most commonly needed supplies or the most frequently reported symptoms. A district health officer who uses the mean instead of the median to describe local incomes may end up designing a nutrition programme that misses the families it was meant to help.

In NFHS reports, in census tables, and in evaluations of programmes like Janani Suraksha Yojana or Mission Indradhanush, central tendency measures are the first step toward interpreting any number. They are also the foundation on which more advanced statistics-variance, regression, hypothesis testing-are built. Getting them right is the difference between research that informs policy and research that misleads it.

What do you think? If you were designing a survey to measure the financial burden of out-of-pocket health expenditure on Indian households, would you report the mean, the median, or both, and why? And can you think of a health variable where the mode would be more informative than either the mean or the median?

References

1. https://www.scribbr.com/statistics/central-tendency/
2. https://pmc.ncbi.nlm.nih.gov/articles/PMC10283257/
3. https://pmc.ncbi.nlm.nih.gov/articles/PMC9961298/
4. https://www.indiaspend.com/explainers/explained-why-indias-inequality-is-underestimated-962681
5. https://banotes.org/public-health-epidemiology/measures-central-tendency-health-data-analysis/
6. https://statisticsbyjim.com/basics/measures-central-tendency-mean-median-mode/
7. https://psychology.town/statistics/central-tendency-measures-data-analysis/