Mean or Median? Compare a Fictional Safety Dataset

Define the observations and their unit

A classroom file contains five elapsed response durations: 2, 3, 3, 4 and 18 days. For this exercise, every duration uses the same start and end event and the same calendar-day convention. No record is missing. These assumptions matter before any average is calculated.

The mean adds the values and divides by their count. The median identifies the middle of the ordered set; for an even number of values, this worksheet averages the two middle values. Neither number explains why an item took longer or whether the response was appropriate.

Calculate both summaries

The mean uses every value. The median locates the centre by order. Here the long duration pulls the mean above four of the five observations. Reporting only “average: six days” leaves that distribution hidden.

Investigate an extreme value before removing it

The eighteen-day entry might be valid, incorrectly entered, or based on a different definition. The short dataset does not tell you which. Check its source before changing it. Deleting an inconvenient value because it weakens the headline would change the dataset without justification.

If it is corrected to eight days after a documented source check, the mean becomes four days and the median remains three. Preserve the correction reason and original record. If eighteen is valid, retain it and explain its context where permitted. A long duration can be important even when a typical-case summary is useful.

Choose a summary for the actual question

To describe the middle observed duration, the median is useful. To describe the total duration divided across these five records, the mean is useful. Neither is automatically the correct measure for every reporting purpose. Include the sample size and, where practical, the range or original values.

For a practice answer, first identify the requested measure, then check the sorting and arithmetic. Keep open records separate from completed durations rather than assigning them zero. A report on completed records alone also cannot establish how long unresolved items have been waiting. That is a separate question requiring separate evidence.