What is the relationship between standard deviation and variance?

The correct answer is that standard deviation is the square root of the variance. This relationship is fundamental in statistics as it connects two important measures of dispersion within a dataset.

Variance measures how far a set of numbers is spread out from their average value. It is calculated by taking the average of the squared differences from the mean. Since variance uses squared differences, its units are different from those of the original data. This can make variance less intuitive to interpret when discussing the spread of data in the same units as the original dataset.

Standard deviation addresses this issue by taking the square root of the variance, returning the measure to the same units as the data itself. This makes standard deviation a more interpretable and practical measure for understanding variability in the context of the data being analyzed. For example, if you are measuring the heights of students in centimeters, while variance will be in square centimeters, standard deviation will similarly be in centimeters, making it easier for analysis and comparison.

Thus, the relationship is crucial for statistical calculations and for interpreting data effectively. By utilizing both metrics, one can attain a comprehensive understanding of how data varies around its mean.