What is standard deviation a measure of in statistical analysis?

Standard deviation is indeed the square root of variance, which makes the answer correct. Variance itself measures the average of the squared differences from the mean, reflecting how spread out the numbers in a data set are. By taking the square root of the variance, standard deviation provides a measurement of dispersion that is expressed in the same units as the original data, making it easier to interpret in relation to the data set.

This property of standard deviation is particularly useful in statistical analysis because it allows for a more intuitive understanding of variability. For example, a low standard deviation indicates that the values tend to be close to the mean, while a high standard deviation indicates that the values are more spread out.

The other choices address different concepts in statistics. The average of all observations refers to the mean, not standard deviation. The correlation between different observations measures the relationship between two variables, and the highest value in a data set refers to the maximum value, which does not relate to standard deviation at all. Thus, the definition of standard deviation as the square root of variance accurately captures its role in statistical analysis.