A sample with a standard deviation of zero means that every value in the sample is exactly the same. There is no variation or spread among the data points, so all measurements or scores in the sample are identical to the mean value. This indicates zero dispersion in the data set, implying complete uniformity in the sample values.
In practical terms, this means that if you measured a characteristic across all elements in the sample, you found no differences at all — each measurement is constant. This is rare in most real-world data unless all observations are controlled or naturally identical. Examples could include measuring the length of identical manufactured parts or recording a constant event count over multiple intervals.
Hence, a zero standard deviation summarizes that the mean fully represents every value in the sample since there is no deviation from it.
