What is the square of the standard deviation called?

The square of the standard deviation is referred to as variance. This concept is fundamental in statistics as it provides a measure of the dispersion or spread of a set of data points around the mean. While the standard deviation itself indicates the average distance of each data point from the mean, squaring the standard deviation results in the variance, which can sometimes simplify the analysis—especially in the context of further statistical calculations and interpretations.

In practical applications, variance is used to understand how much variation exists in a dataset, with larger values indicating greater spread among the data points. It's essential for various statistical methodologies, including hypothesis testing and the estimation of confidence intervals.

The other options pertain to different statistical concepts that do not represent the square of the standard deviation. The standard error relates to the accuracy of a sample statistic. The mean is the average of a dataset, and the coefficient of variation is a normalized measure of dispersion relative to the mean, often expressed as a percentage. Thus, recognizing and understanding variance is crucial for analyzing data effectively in various fields, including surveying and engineering.