Glossary
Standard Deviation
The standard deviation is the square root of the variance — a measure of how dispersed values are around the mean. A low standard deviation indicates data clustered close to the mean; a high value indicates greater spread. It shares the same units as the original data, making ...
Definition
The standard deviation is the square root of the variance — a measure of how dispersed values are around the mean. A low standard deviation indicates data clustered close to the mean; a high value indicates greater spread. It shares the same units as the original data, making it more interpretable than the variance.
Why It Matters
Standard deviation is the most commonly reported measure of spread because it is expressed in the same units as the original variable. It underpins the calculation of standard errors, confidence intervals, z-scores, and many hypothesis tests. In quality control, finance, and experimental research, standard deviation helps quantify risk, consistency, and measurement precision.
Example
Two classes both have an average exam score of 70%. Class A has a standard deviation of 5 points, while Class B has a standard deviation of 15 points. In Class A, most scores fall between 60 and 80, indicating consistent performance. In Class B, scores are widely scattered, suggesting a diverse range of understanding that may require differentiated teaching strategies.
Related Terms
- Variance (standard deviation is the square root of variance)
- Mean
- Normal Distribution
- Standard Error (standard error is the standard deviation of the sampling distribution)
- Outlier
Software Notes
- SPSS: Analyze > Descriptive Statistics > Frequencies or Descriptives — check "Std. deviation" under Statistics.
- R:
sd(x, na.rm = TRUE). For grouped data:aggregate(y ~ group, data = df, sd). - Stata:
summarize varname, detailreturns standard deviation among other descriptive statistics.