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lecture 7 zscore and normal distribution

# lecture 7 zscore and normal distribution - Dimensionless...

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Dimensionless Statistics Permit comparisons between distributions with different means and standard deviations, or which are based on different units of measurement Coefﬁcient of Variation Coefﬁcient of Quartile Variation Standard (z) Scores 1

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Coefﬁcient of Variation Useful for comparing the degree of dispersion in two or more distributions that have widely divergent means Generally only used with data sets having a mean considerably larger than zero c v = σ / µ Expressed as a percentage = (c v ) x 100 c v = s / X 2
Coefﬁcient of Quartile Variation Similar logic to Coefﬁcient of Variation, but less affected by extreme observations Roughly (but not exactly) a measure of how how large the Quartile Deviation is relative to the median CQV = (Q3 - Q1)/(Q3 + Q1) Expressed as a percentage = (CQV) x 100 3

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Standard (z) Scores Characterize scores according to how many standard deviations they’re located above or below the mean. Facilitate comparisons among scores from distributions with different means and/or standard deviations Permit the re-scaling of scores to a unit that is easy to interpret (e.g., IQ scores) Facilitate the determination of relative standing (e.g., percentile ranks) 4
Standard (z) Scores z = ( x - μ )/ σ Negative values of z indicate that the score lies below the mean Positive values of z indicate that the score lies above the mean 5

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Properties of z Scores Any distribution of z Scores composed of all the elements from the original distribution of raw scores will have the following properties: The shape of the distribution of z Scores
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lecture 7 zscore and normal distribution - Dimensionless...

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