Describe the center and the spread

The arithmetic mean — open definition adds the observations and divides by their number. The median — open definition is the middle value after sorting, or the average of the two middle values for an even count. Both describe a kind of center, but they need not match and neither alone describes the whole distribution.

For fictional sensor readings 2, 3, 3, 4 and 18, the mean is 6 while the median is 3. The high reading pulls the mean upward. Whether 18 is a real event, a different operating condition or an error requires investigation; its effect on a summary is not by itself a reason to delete it.

Compare fictional sets A = 9, 10, 11 and B = 0, 10, 20. Both have mean 10. Their ranges, maximum minus minimum, are 2 and 20. If these were repeat measurements under comparable conditions, the second set would show much greater observed spread.

Standard deviation — open definition uses deviations from the mean to summarize spread in the original units. It is sensitive to distant observations. A histogram or the raw values can reveal clusters and tails that one number hides. State which summary is used and why it suits the question.

Equal means can hide unequal spread

Suppose one fictional instrument is measured twice at 10 units and another eight times at 20. The mean of all ten readings is 18. Averaging the two instrument means equally gives 15, a different quantity with equal instrument weighting. Neither calculation should be described without its weighting rule.

Ask whether the scientific question concerns a typical reading, instrument, location or time period. These may require different groupings. A useful report preserves counts, units, selection rules and the distribution, so a reader can understand what the center summarizes and what variation remains around it.