Question

The ........... is directly related to the variance and is figured by taking the square root of the variance.

• A. Average Deviation
• B. Quartile Deviation
• C. Standard Deviation
• D. Range

Hint:

The name itself gives a clue. The {standard deviation} represents the "standard" or typical amount that scores deviate from the mean. Taking the square root of the variance returns the measure to the original, non-squared units, making it more intuitive to interpret.

Answer 1

The Correct Option is C

Step 1: Concept Clarification:
The query requires identifying the statistical measure of dispersion derived from the square root of the variance.
Step 2: Relevant Formula/Method:
In statistics, variance and standard deviation are the primary metrics for assessing variability or spread within a dataset.

Variance (\(\sigma^2\)): Represents the mean of the squared deviations from the average. Its units are the square of the original data's units.

Standard Deviation (\(\sigma\)): Calculated to revert the measure of spread to the original data's units. It is defined as the positive square root of the variance.

\[ \text{Standard Deviation} = \sqrt{\text{Variance}} \] Step 3: Conclusion:
The standard deviation is formally defined as the square root of the variance.