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z-Score: tells where a score is located relative to the mean - Coggle…
z-Score: tells where a score is located relative to the mean
Location: a z-score identifies a score’s exact relative position in a distribution
Mean (μ or M): the center of the distribution
Above the Mean: represented by a positive z-score
Below the Mean
Represented by a negative z-score.
Distance from Mean: measured in standard deviation units by a z-score
Raw Score (X): the original score before it is transformed
Magnitude of z: shows how many standard deviations a score is from the mean
Deviation Score: the distance and direction of a score from the mean: X − μ
Positive z-Score: the score is above the mean
Negative z-Score: the score is below the mean
Calculating z
z-Score Formula:
z = (X − μ) / σ for a population
Standard Deviation (σ or s): the typical distance scores are from the mean
z = 0: the raw score is exactly at the mean
Transforming z Back to X: Use X = μ + zσ to recover a population raw score
Why It Matters
Comparing Distributions: z-scores allow scores from different distributions to be compared
Representative Score": a z-score near 0 means the score is typical of the population
Extreme Score: a z-score around ±2 or beyond indicates an unusually distant score
Inferential Statistics: z-scores help judge how typical or unusual a score is within its population
Standardized Distribution: a distribution transformed to a common scale
z-Score Transformation: converting raw scores into z-scores
Mean of z-Scores = 0: every complete z-score distribution has a mean of zero
SD of z-Scores = 1: every complete z-score distribution has a standard deviation of one
Distribution Shape: a z-transformation does not change the shape of the distribution
Standardized Score: a transformed score that allows meaningful comparisons