How to choose between the mean and median
The mean and median can describe the same dataset very differently. Before choosing one, look at the values and decide what you want the average to communicate. A useful answer names the measure, gives its value and explains why it fits the question.
Calculate each measure from the actual values
The arithmetic mean is the sum of the values divided by how many values there are. The median is the middle value after you put the values in order. Both keep the unit of the data, such as minutes or centimetres.
For an odd number of values, the median is the single middle value. For an even number, take the mean of the two middle values. For example, the ordered list 4, 6, 8, 10 has median (6 + 8) ÷ 2 = 7. Sorting matters: taking the middle entries in an unsorted list can give the wrong result.
Check what the question actually requests. If it specifies the mean or median, calculate that measure. If it asks you to choose a suitable average, you need to explain your choice using the data and the purpose of the comparison.
See what a large value does
Use this invented practice dataset: five journeys take 5, 6, 7, 8 and 34 minutes. The total is 60 minutes, so the mean is 60 ÷ 5 = 12 minutes. The median is the third value in the ordered list, which is 7 minutes.
The 34-minute journey raises the mean. The median sits among the four shorter journeys and may be a useful description of a typical journey in this small list. If the question concerns the total time across the five journeys, the mean retains that relationship: 12 × 5 = 60 minutes.
Now change only the last value to 64 minutes. The total becomes 90 and the mean becomes 18 minutes. The median stays at 7 because the middle position has not changed. This shows how the two measures respond differently; it does not establish that one is always the better average.
Investigate an unusual value before removing it
A value far from the others may be an error, or it may be a real observation. Check the original record, units and collection method. A journey logged in seconds among values in minutes needs a unit correction. A genuinely long journey needs to remain part of the evidence unless there is a justified reason to exclude it.
Do not remove 34 merely to make the mean closer to the other values. If the question supplies a rule for identifying or excluding outliers, follow it and explain what you did. Otherwise, describe the unusual value and its effect. Reporting both mean and median can make that effect visible.
Use the spread as context too. The practice journeys range from 5 to 34 minutes. Neither an average of 12 nor a median of 7 tells a reader that full range on its own. Two datasets can share an average while having quite different distributions.
Write a choice you can defend
For a question asking about a typical journey in the practice list, you could write: “I would report the median of 7 minutes because four of the five journeys are between 5 and 8 minutes, while the 34-minute journey raises the mean to 12 minutes. I would also give the range so the longer journey remains visible.” This conclusion describes only the supplied data.
For a question about the total time divided equally across the five journeys, write: “The mean is 12 minutes, calculated from a total of 60 minutes across five journeys.” A mean need not be an observed value; none of these journeys lasted exactly 12 minutes.
When comparing groups, use the same measure and unit for each and inspect their values or distributions. Avoid treating an average as a description of every member. Finish with: “Measure: __. Value and unit: __. Why it fits this question: __. Important limitation or unusual value: __.”
