What is the relationship between variance and standard deviation?

What is the relationship between variance and standard deviation?

• A. Standard deviation is double the variance
• B. Variance is the square root of the standard deviation
• C. Standard deviation is the square root of variance
• D. Variance and standard deviation are not related

Answer: (C)

The relationship between variance and standard deviation is that standard deviation is the square root of variance. Variance measures the dispersion of a set of data points around their mean, represented mathematically as the average of the squared differences from the mean. Standard deviation, on the other hand, is a measure of that dispersion expressed in the same units as the original data, which makes it more interpretable. By taking the square root of the variance, one converts the squared units back to the original units, allowing for a more intuitive understanding of variability in the data set. This foundational relationship highlights how these two statistics are connected, bringing clarity to the analysis of data spread.

The relationship between variance and standard deviation is that standard deviation is the square root of variance. Variance measures the dispersion of a set of data points around their mean, represented mathematically as the average of the squared differences from the mean. Standard deviation, on the other hand, is a measure of that dispersion expressed in the same units as the original data, which makes it more interpretable. By taking the square root of the variance, one converts the squared units back to the original units, allowing for a more intuitive understanding of variability in the data set. This foundational relationship highlights how these two statistics are connected, bringing clarity to the analysis of data spread.