Final answer:
The Z value, or Z-score, indeed indicates the number of standard deviations a value X is from the mean in a data set, with positive values indicating a position above the mean and negative ones below. It is a standardized measure that makes it possible to compare different data sets.
Step-by-step explanation:
The statement that the Z value tells us the number of standard deviations that a value X is from the mean is true. When we talk about Z-scores in the context of a standard normal distribution, we are effectively measuring how many standard deviations a raw score is above or below the mean (μ) of a dataset. Z-scores are particularly useful because they allow us to compare scores from different datasets, regardless of their individual means and standard deviations.
A positive Z-score indicates that the value is above the mean, while a negative Z-score indicates that it's below. For example, if we have a normal distribution N(μ, σ) and a value x from this distribution, we can calculate the corresponding Z-score. This helps us understand where x falls in relation to the overall distribution. The formula for calculating a Z-score is Z = (X - μ) / σ.