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: Understanding the Concept:
The question asks to identify the statistical measure of dispersion that is calculated as the square root of the variance.
Step 2: Key Formula or Approach:
In statistics, variance and standard deviation are the two most common measures of variability or spread in a dataset.
Variance (\(\sigma^2\)): This is the average of the squared differences from the mean. It is measured in squared units of the original data.
Standard Deviation (\(\sigma\)): This is calculated to bring the measure of spread back into the original units of the data. Its definition is the positive square root of the variance.
\[ \text{Standard Deviation} = \sqrt{\text{Variance}} \] Step 3: Final Answer:
The standard deviation is defined as the square root of the variance.