Use the mean for symmetric numeric data, the median for skewed data or data with outliers, and the mode for categorical data or when you need the most common value. If you're staring at a column of numbers in your thesis dataset and unsure which "average" to report, that one rule solves 90% of cases — but the details matter when a reviewer asks why you chose one over another.
Key Takeaways
- The mean is the arithmetic average (add all values, divide by the count). It works best when data are roughly symmetric and free of extreme outliers.
- The median is the middle value when data are ordered from smallest to largest. It's the right choice for skewed data, income, reaction times, and any dataset with outliers.
- The mode is the most frequently occurring value. It's the only measure of central tendency that works for nominal (categorical) data like eye colour or brand preference.
- A single outlier can shift the mean dramatically while barely moving the median — which is why household income is almost always reported as a median.
- For a normal distribution, the mean, median, and mode are all equal; the further apart they are, the more skewed your data.
What are the mean, median, and mode?
The mean, median, and mode are the three measures of central tendency — three different ways of answering the question "what's the typical value in this dataset?" Each summarises a whole column of numbers with a single representative figure, but they define "typical" differently, which is why they don't always agree.
- Mean: the sum of all values divided by the number of values.
- Median: the middle value once the data are sorted in order.
- Mode: the value that appears most often.
They only diverge when your data are skewed or contain outliers. In a perfectly symmetric distribution, all three land on the same number.
When should I use the mean?
Use the mean when your data are numeric (interval or ratio) and roughly symmetric, with no extreme outliers. The mean uses every data point in its calculation, which makes it the most statistically efficient and the default input for most inferential tests like the t-test and ANOVA.
For example, if five students score 82, 85, 88, 90, and 95 on an exam:
Mean = (82 + 85 + 88 + 90 + 95) ÷ 5 = 440 ÷ 5 = 88
The mean of 88 fairly represents this group because the scores cluster tightly with no wild values. Report exam scores, test measurements, temperatures, and lab readings with the mean when the distribution looks balanced.
The mean's weakness is its sensitivity to outliers. Add one student who scored 20:
Mean = (82 + 85 + 88 + 90 + 95 + 20) ÷ 6 = 460 ÷ 6 = 76.7
That single low score dragged the "typical" value down by more than 11 points, even though five of the six students still scored in the 80s and 90s. When that happens, the median is more honest.
When should I use the median?
Use the median when your data are skewed or contain outliers, because the median is unaffected by extreme values. The median only cares about the position of the middle value, not how large or small the extremes are — so it describes the "typical" case far better in lopsided distributions.
Take the same six scores from above: 20, 82, 85, 88, 90, 95. With an even number of values, the median is the average of the two middle ones:
Median = (85 + 88) ÷ 2 = 86.5
Notice the median (86.5) still reflects where most students actually scored, while the mean (76.7) was distorted by the single outlier. This is exactly why income, house prices, hospital wait times, and reaction times are reported as medians — a handful of billionaires or a few very slow responses would inflate the mean and mislead readers.
Rule of thumb: if the mean and median differ substantially, your data are skewed, and the median is usually the safer summary.
When should I use the mode?
Use the mode when your data are categorical, or when you specifically need the most common value. The mode is the only measure of central tendency that works for nominal data — categories with no numeric order, like eye colour, blood type, or preferred survey response.
If 30 survey respondents choose a favourite brand and 14 pick Brand A, 10 pick Brand B, and 6 pick Brand C, the mode is Brand A — it makes no sense to calculate a "mean brand." The mode also flags the most frequent value in numeric data (e.g. the most common shoe size stocked), and a dataset can have two modes (bimodal) or more.
Mean vs median vs mode: which one do I use?
| Measure | Best for | Data type | Outlier-sensitive? | Example use |
|---|---|---|---|---|
| Mean | Symmetric numeric data | Interval / ratio | Yes — highly | Exam scores, temperatures |
| Median | Skewed data or outliers | Ordinal, interval / ratio | No | Income, reaction times, house prices |
| Mode | Most frequent value | Nominal, ordinal, numeric | No | Survey categories, blood type |
A quick decision path: Is your data categorical? Use the mode. Is it numeric but skewed or full of outliers? Use the median. Is it numeric and symmetric? Use the mean.
A worked example with real numbers
Imagine you survey the annual salaries (in thousands) of 7 alumni from your programme: 38, 42, 45, 47, 50, 52, and 240 (one founded a startup).
- Mean = (38 + 42 + 45 + 47 + 50 + 52 + 240) ÷ 7 = 514 ÷ 7 = 73.4 (i.e. $73,400)
- Median = the 4th value when sorted = 47 (i.e. $47,000)
- Mode = no value repeats, so there is no mode
The mean says the "typical" graduate earns $73,400 — but six of seven earn under $53,000. The $240k outlier inflated the mean by over $26,000. The median of $47,000 is the honest summary here, which is why national statistics agencies report median household income, not mean.
In APA 7 style, you'd write descriptive statistics like this: M = 73.4, Mdn = 47.0, SD = 71.8. Note the italics on M, Mdn, and SD, and that a large gap between M and Mdn signals skew a reviewer will expect you to acknowledge.
How do I report central tendency in APA 7 format?
Report the mean with its standard deviation in parentheses: M = 88.0, SD = 4.9. Use Mdn for the median: Mdn = 86.5. For skewed data, report the median (and often the interquartile range) instead of, or alongside, the mean. Always italicise the statistical symbols and use two decimal places for consistency.
If you're not sure whether your data are skewed enough to warrant the median, checking skewness by hand is tedious and error-prone. StatRyx calculates the mean, median, mode, standard deviation, and skewness for every variable automatically and flags when your distribution is skewed enough that the median is the better summary — then formats it all in APA 7 for you to paste straight into your thesis.
For the next step — deciding which test to run on that data — see our guide on how to choose the right statistical test.
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Frequently Asked Questions
What is the difference between mean, median, and mode?
The mean is the arithmetic average of all values, the median is the middle value when data are sorted in order, and the mode is the most frequently occurring value. The mean uses every data point and is sensitive to outliers, the median ignores extreme values and describes the middle of the distribution, and the mode simply identifies the most common category or number.
Which measure of central tendency is best for skewed data?
The