What is the standard deviation?

• A. Average of the variance
• B. Square root of the variance
• C. Variance divided by the mean
• D. Mean of the squared differences

Answer: (B)

The standard deviation is defined as the square root of the variance. This relationship is fundamental in statistics because it provides a measure of how spread out the values in a data set are around the mean.

Variance itself is calculated by taking the average of the squared differences between each data point and the mean of the data set. Since variance is expressed in squared units, taking the square root transforms it back into the original unit of measure, which makes the standard deviation a more interpretable statistic for describing variability.

By providing a clear gauge of data dispersion, the standard deviation is crucial for understanding the distribution of data points around the mean, making it easier to compare spread across different datasets.