Questions: Which of these is the most precise definition of a Z score? a measure of where a score falls in the population relative to the mean value a measure of a score's variance relative to other scores a measure of how many standard deviations a score is above or below the mean a measure of how far a score is from the mean a measure of how extreme a value is

Solution Steps

The most precise definition of a Z score is "a measure of how many standard deviations a score is above or below the mean."

A Z score, also known as a standard score, indicates how many standard deviations an element is from the mean. The formula for calculating a Z score is:

\[ Z = \frac{X - \mu}{\sigma} \]

where:

• \( X \) is the value of the element,
• \( \mu \) is the mean of the population,
• \( \sigma \) is the standard deviation of the population.

We need to determine which option best matches the definition of a Z score. Let's analyze each option:

1. A measure of where a score falls in the population relative to the mean value: This is a general description but not precise enough.
2. A measure of a score's variance relative to other scores: This describes variance, not the Z score.
3. A measure of how many standard deviations a score is above or below the mean: This is the precise definition of a Z score.
4. A measure of how far a score is from the mean: This is a general description and does not specify the use of standard deviations.
5. A measure of how extreme a value is: This is a qualitative description and not precise.

Final Answer