What is the positive square root of the variance?

The positive square root of the variance is known as the standard deviation. Variance measures the dispersion of a set of data points, indicating how far each data point is from the mean. By taking the square root of the variance, you convert this measure of dispersion back to the original units of measurement, resulting in the standard deviation.

Standard deviation provides a clearer understanding of data variability because it expresses the spread of the data in the same units as the original data set, making it easier to interpret. For instance, if the variance of a data set is 16, the standard deviation would be 4, indicating that most data points deviate from the mean by this amount, on average.

The other options—mean, median, and quartile deviation—do not represent the positive square root of the variance. The mean is a measure of central tendency, the median is the middle value in a data set, and the quartile deviation is a measure of dispersion that focuses on the interquartile range. Thus, the standard deviation provides the precise relationship to variance as its positive square root, confirming its role as the correct answer.