Question

Which of the following is true about a z-score?

A. It specifies the precise location of each score within a distribution of scores.
B. The sign of the z-score indicates whether the score is above or below the mean.
C. The numerical value of the z-score specifies the distance of a score from the mean by counting numbers of standard deviations between the score and the mean.
D. All of the above.

Answer 1

The true statement about a z-score is D. All of the above. A z-score indicates the precise location, direction, and distance of a score from the mean in standard deviation units.

Step-by-step explanation:

The correct answer to the question is D. All of the above. A z-score is a statistical measurement that describes the position of a raw score in terms of its distance from the mean, measured by the number of standard deviations away from the mean. Specifically:

• It specifies the precise location of each score within a distribution.
• The sign of the z-score (whether positive or negative) indicates whether the score is above or below the mean.
• The numerical value of the z-score specifies the distance of the score from the mean in units of standard deviations.

Z-scores are essential when we seek to normalize the scores from different datasets, allowing comparison on the same scale, particularly the standard normal distribution. This standardization is achieved via the transformation z = (x - μ) / σ, where x is the raw score, μ is the mean of the distribution, and σ is the standard deviation. The standard normal distribution is denoted as Z ~ N(0, 1), indicating a normal distribution with a mean of 0 and a standard deviation of 1.