Definition of the Standard Deviation:
The standard deviation is a measure of the dispersion or variability of a set of values. It quantifies the amount by which the values deviate from the mean.

Calculating the Standard Deviation:
To calculate the standard deviation, we first need to find the mean of the data set. Then, for each value in the data set, we calculate the difference between the value and the mean, square that difference, and sum up all of these squared differences. Finally, we take the square root of the mean of these squared differences.

Mean of Squared Deviations from Mean:
The mean of squared deviations from the mean is the average of the squared differences between each value in the data set and the mean. It is a measure of the average squared distance between each value and the mean.

Positive Square Root:
Taking the positive square root of the mean of squared deviations from the mean is necessary to ensure that the standard deviation is always a positive value. Since we are measuring the deviation from the mean and squaring the differences, we end up with positive values. Taking the square root of the mean of these squared deviations gives us a positive value that is representative of the amount of dispersion in the data set.

Why Standard Deviation is the Correct Answer:
The standard deviation is widely used in statistics and data analysis as a measure of variability. It provides valuable information about the spread of the data set and how closely the values are clustered around the mean. It is a fundamental concept in understanding the distribution of data and is used in various statistical calculations and models.

Alternatives:
The other options presented in the question are not correct because they do not accurately describe the concept of the positive square root of the mean of squared deviations from the mean.

- Central tendency refers to measures such as the mean, median, and mode that represent the "center" or average value of a data set.
- Quartile deviation is a measure of the spread of the data based on the quartiles, which divide the data set into four equal parts.
- Mean deviation is a measure of the average absolute difference between each value in the data set and the mean. It does not involve squaring the differences.

Therefore, the correct answer is option 'D', standard deviation.