ACtE08 · Chapter 8Demo2 · Set 2🏛️ Past Licensure QuestionID: a67b060c

In probability and statistics, standard deviation ( $\sigma$ ) is mathematically defined as:

Multiple Choice Options

A
Variance^(1/2)
✓ Correct Option
B
Variance^2
C
Variance / 2
D
Variance^(0.25)

Detailed Technical Solution & Explanation

Standard deviation ( $\sigma$ ) is a statistical measure of the dispersion or spread of a dataset relative to its arithmetic mean. By mathematical definition, the standard deviation is the positive square root of the variance ( $Var(X)$ ):

\sigma = \sqrt{\text{Variance}} = (\text{Variance})^{1/2}

\text{Variance} = \sigma^2 = E[(X - \mu)^2]

Option Analysis:

•

Option A (Variance^(1/2)): Correct;

\sqrt{\text{Variance}} = \text{Variance}^{1/2}

•

Option B (Variance^2): Incorrect; represents variance squared (fourth central moment normalized).

•

Option C (Variance / 2): Incorrect; halving variance does not restore original units.

•

Option D (Variance^(0.25)): Incorrect; fourth root of variance.

Reference: Demo2 · Set 2NEC Licensure Syllabus

In probability and statistics, standard deviation ( $\sigma$ ) is mathematically defined as:

Multiple Choice Options

Detailed Technical Solution & Explanation

Option Analysis:

Want to practice this topic interactively?

In probability and statistics, standard deviation ( $\sigma$ ) is mathematically defined as:

Multiple Choice Options

Detailed Technical Solution & Explanation

Option Analysis:

Want to practice this topic interactively?