Read mean and SD together
The mean supplies the center used by standard deviation. The SD summarizes the root-mean-square distance from that center. If two groups have the same mean but SDs of 5 and 15, the second group is more dispersed on that scale.
| Result | Defensible reading |
|---|---|
| Mean 50, SD 0 | Every observed value is 50, subject to rounding. |
| Mean 50, SD 5 | Values vary around 50 on a scale of 5 units. |
| Mean 50, SD 20 | Spread is much larger, but shape still needs a plot. |
Sample output may divide by n−1 while a population definition divides by n. Identify the estimator before reproducing the value.1
The 68–95 rule is conditional
For a normal distribution, about 68% of values fall within one SD of the mean and about 95% within two. That is a property of the normal model, not the definition of SD. Do not apply it automatically to skewed, bounded, multimodal, or heavy-tailed data.
Use z-score interpretation when the result expresses a value in SD units. Use confidence interval interpretation when the number describes uncertainty in an estimate rather than spread among observations.
When SD is incomplete
A single SD can hide groups, skew, outliers, or two distinct modes. Inspect a histogram or box plot and report group-specific summaries where aggregation hides structure. Skewness and kurtosis explains why a normal-looking numerical summary cannot establish normality.
Comparing SDs across different units is meaningless. A coefficient of variation can express spread relative to a positive ratio-scale mean, but it adds assumptions; see coefficient of variation interpretation.
A defensible reporting sentence
“Scores averaged 50 with SD 12 points. The SD describes observed spread in the original units; the histogram was inspected because no normal shape was assumed.”