What is the formula for standard deviation?

The formula for standard deviation is defined as the square root of the variance, which is precisely what is stated in the correct choice. Variance measures how spread out the values in a data set are—specifically, it quantifies the average of the squared differences from the mean (denoted as μ). Taking the square root of the variance allows you to express the spread of data in the same units as the original data, making the standard deviation a more interpretable measure of dispersion.

For instance, if the variance of a dataset is 25, the standard deviation would be √25 = 5, providing a clear understanding of how much the values deviate, on average, from the mean. This measurement is widely used in statistics to express the variability or uncertainty involved within a set of values.

Using the square root in this way ties the concept of standard deviation back to the spread of the original data, facilitating better insights into data characteristics. The other options involve either incorrect relationships or incomplete formulations related to standard deviation.