Which type of deviation is defined as the square root $\sqrt{\mathrm{variance}}$ of the variance in a set of numerical data?

• A. Absolute deviation
• B. Standard deviation $\sqrt{\mathrm{variance}}$
• C. Mean deviation
• D. Relative deviation

Answer: (B)

Verified step by step guidance

1. Understand the concept of variance: Variance measures the average of the squared differences between each data point and the mean of the data set. It gives an idea of how spread out the data points are.
2. Recall the definition of standard deviation: Standard deviation is defined as the square root of the variance. It provides a measure of dispersion in the same units as the original data, making it easier to interpret.
3. Compare with other types of deviation: Absolute deviation is the average of the absolute differences from the mean, mean deviation is similar but sometimes refers to the average absolute deviation, and relative deviation is the deviation relative to some reference value, often expressed as a percentage.
4. Identify that the question asks for the deviation type that is the square root of the variance, which matches the definition of standard deviation.
5. Conclude that the correct answer is standard deviation, as it is the only deviation type defined as the square root of the variance.