Five fictional journeys take 10, 11, 12, 13 and 54 minutes. The arithmetic mean is 20 minutes. The median is 12. Both calculations describe the same list, but they draw attention to different features.
The difference is a reason to inspect the data, not to declare one summary universally correct.
Follow each calculation
Add the five times to obtain 100, then divide by five to get the mean of 20. For the median, place the values in order and find the middle one: 12.
NIST’s median reference describes the middle-value calculation and its relative resistance to outlying values. The example here is original and deliberately small.
Ask what the long journey represents
The 54-minute value might be a genuine journey, a recording error or a different kind of trip. Check the collection context before deleting it. An inconvenient value does not become invalid merely because it changes the average.
If it is genuine, the mean reflects its contribution to the total time. The median identifies the central position in the ordered list. Which is useful depends on the question you are trying to answer.
Show the spread as well as a centre
A single number hides that four journeys are close together and one is much longer. For a tiny dataset, displaying the values may be more informative than selecting one summary.
For a larger dataset, a suitable distribution plot and clear definitions can provide context that a headline average lacks.
State the population you are describing
These five invented journeys do not establish a city’s typical travel time. Keep the conclusion tied to the observations and method. Pair this example with our chart-scale guide to see how both numerical summaries and visual choices influence a reader’s impression.