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z-Scores - measures exactly how many standard deviations a specific data…
z-Scores - measures exactly how many standard deviations a specific data point is from the mean of a dataset.
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First purpose of z-scores tell exactly where within a distribution the original scores are located by transforming raw scores into z-scores.
Raw Scores = original, unchanged scores that are the direct result of measurement.
The sign of the z-score (+ or −) signifies whether the score is above the mean (positive) or below the mean (negative). The numerical value of the z-score specifies the distance from the mean by counting the number of standard deviations between X and μ.
Positive z-score: The data point is above the mean (e.g. z = +1.5).
Negative z-score: The data point is below the mean (e.g. z = -2.0).
Zero z-score: The data point is exactly at the mean.
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Population z-Scores
Deviation Score - the numerator of the equation, X-μ.
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In inferential statistics, z-scores provide an objective method for determining how well a specific score represents its population. A z-score near 0 indicates that the score is close to the population mean and therefore is representative. A z-score beyond +2.00 (or −2.00) indicates that the score is extreme and is noticeably different from the other scores in the distribution.
Outliers - In a normal distribution, z-scores beyond +/- 3.0 are typically flagged as outliers, as they represent only 0.3% of the total data.
Calculate Probabilities -you can determine the exact probability of a specific event occurring or the percentage of data that falls above or below your data point by looking at z-score table.
