Question

Write the formula for changing a raw score to a Z score and define each of the symbols.

a) Z = (X - μ) / σ, where Z is the Z score, X is the raw score, μ is the mean, and σ is the standard deviation.
b) Z = (X + μ) * σ, where Z is the Z score, X is the raw score, μ is the mean, and σ is the standard deviation.
c) Z = (X - μ) * σ, where Z is the Z score, X is the raw score, μ is the mean, and σ is the standard deviation.
d) Z = (X / μ) - σ, where Z is the Z score, X is the raw score, μ is the mean, and σ is the standard deviation.

Answer 1

The correct formula for converting a raw score to a Z score is Z = (X - μ) / σ, where Z is the Z score, X is the raw score, μ is the mean, and σ is the standard deviation.

Step-by-step explanation:

The correct formula for converting a raw score to a Z score is option a), which is Z = (X - μ) / σ. This formula represents the process of standardizing a score within a set of data. Here, Z is the Z score itself, X is the raw score that we want to convert, μ (mu) is the mean of the dataset, and σ (sigma) is the standard deviation of the dataset. By using this equation, we can determine how many standard deviations the raw score is away from the mean of the data set. A positive Z score indicates the score is above the mean, while a negative Z score indicates it's below.