When working with data in statistics, one question comes up almost immediately: what does a “typical” value really look like? In the UK education system, from GCSE Maths to A-level Statistics and university research, students are often taught that averages explain data. But not all averages tell the full story. This is where the median in statistics becomes essential.
The median represents the middle value in a data set when the numbers are arranged in order. Unlike the mean, it is not distorted by extremely high or low values, a common issue when analysing real-world data such as household incomes, property prices, exam results, or medical studies in the UK. For this reason, the median is widely used by UK statisticians, researchers, and government bodies to present fair and realistic insights.
What Is the Median
The median is the middle value in a dataset when all observations are arranged in ascending (or descending) order. Exactly half the values in the dataset are below the median and half are above it. It is a measure of central tendency that describes the typical or central value, but unlike the mean, it is not pulled by extreme values at either end of the distribution.
The median is one of three main measures of central tendency alongside the mean and the mode.
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How To Calculate The Median
Let us now look at how you can calculate the median value.
Step 1: Sort Your Data
Arrange all values from smallest to largest. This step is non-negotiable and skipping it may give you the wrong answer.
Step 2: Find the Middle
If you have an odd number of values (n is odd), the median is the value at position (n + 1) ÷ 2.
If you have an even number of values (n is even), there is no single middle value. The median is the average of the two middle values, at positions n ÷ 2 and (n ÷ 2) + 1.
| Dataset | n | Step | Median |
|---|---|---|---|
| 12, 15, 18, 22, 27 | 5 (odd) | Position = (5 + 1) ÷ 2 = 3rd value | 18 |
| 12, 15, 18, 22, 27, 31 | 6 (even) | Average of 3rd and 4th values = (18 + 22) ÷ 2 | 20 |
| 4, 7, 9, 11, 14, 17, 19, 24 | 8 (even) | Average of 4th and 5th values = (11 + 14) ÷ 2 | 12.5 |
Example: A study records waiting times (in minutes) for patients at 7 NHS walk-in centres: 8, 12, 14, 19, 23, 35, 74. Sorted in order, the median is the 4th value: 19 minutes. The mean is (8+12+14+19+23+35+74)÷7 = 26.4 minutes. The single centre with a 74-minute wait pulls the mean away from what most patients experienced. The median is the more representative figure.
Why The Median Is Preferred For Skewed Data
When data is normally distributed, the mean, median, and mode are all approximately equal, and the mean is perfectly fine. But most real-world data is not symmetrical. Income, house prices, hospital waiting times, and test scores on easy tests all tend to be skewed, and in skewed distributions, the mean gets distorted by the long tail.
| Distribution Type | Relationship | When to Use Median |
|---|---|---|
| Symmetric (normal) | Mean ≈ Median ≈ Mode | Not essential, but harmless |
| Positive skew (right tail) | Mean > Median > Mode | Always, mean is inflated by high outliers |
| Negative skew (left tail) | Mean < Median < Mode | Always, mean is deflated by low outliers |
Median Vs Mean
Here is the key distinction: the mean treats every value as equally important; the median treats every observation as a vote on where the centre is. A single extreme value can swing the mean significantly. It barely moves the median.
- UK house prices: Median = £285,000 (England, 2023, ONS). Mean = substantially higher due to multi-million pound properties in London and the South East.
- NHS waiting times: Median wait for a first outpatient appointment gives a clearer picture of the typical patient’s experience than a mean pulled up by a small number of very long waits.
- Student essay grades: If most students score 55-68 and one student scores 22, the median is more representative of what the class achieved.
The Median & Levels Of Measurement
The median requires that you can order your data, so it is appropriate for ordinal, interval, and ratio data. It is not appropriate for nominal data (unordered categories), where the mode is the only valid measure of central tendency.
The Median & Measures Of Spread
When you report the median, always pair it with the interquartile range (IQR), the range of the middle 50% of data. The IQR is to the median what the standard deviation is to the mean: it tells your reader how spread out the data is around the central value. You can read more about this in our guide to the interquartile range.
Student Tip: In your dissertation, if your data is skewed, report both the mean and the median, and explain why you are using the median as your primary measure. Showing that you have checked the distribution and chosen accordingly demonstrates statistical competence that will strengthen your methodology chapter.
Median In Inferential Statistics
The median is the basis in inferential statistics for several important non-parametric statistical tests, tests used when data does not meet the assumptions of parametric methods. Mann-Whitney U, Wilcoxon signed-rank, and Kruskal-Wallis tests all work with ranked data and are appropriate when your outcome variable is ordinal or skewed.
Frequently Asked Questions
Both are accurate, but the choice to use mean or median depends on the kind of datasets available.
No, because mean is simply the average or sum of all the numbers in a dataset, divided by the total number of values in the set. A median, however, is the central value, and that value may not always be one of the values explicitly included in the dataset. Furthermore, the median can be of odd-numbered data sets too.
Median is denoted as either ‘M’ or as ‘X’ which is read as ‘childa.’
Calculating median is preferred most over mean in situations where there are one or more than one outliers in the datasets. The outliers can be either very small or large values either to the left or right. That means, there are either too many numbers on the right of a certain value (the outlier) or to its left. For instance, in the dataset below, there is one outlier, -10, with 6 values to its right. Such a dataset can’t be plotted on a bell graph, either.
-10 10 20 30 40 50 60
Yes, by definition. For an odd number of values, it is literally the middle data point when sorted. For an even number, it is the average of the two middle values. In both cases, half of all observations are below it and half are above it.
It can, but usually less dramatically than the mean. Adding an extreme value to a dataset will barely move the median (it just shifts which values are above and below the midpoint), whereas it could substantially shift the mean.
Yes. Go to Analyze > Descriptive Statistics > Frequencies, move your variable into the box, click Statistics, and tick Median. You can also use Analyze > Descriptive Statistics > Explore for a more complete output including box plots and tests of normality.
The median is not appropriate for nominal data, you cannot meaningfully rank unordered categories. It is also not the best choice for normally distributed interval or ratio data, where the mean provides more statistical power for subsequent tests.
