Lesson 8 - Variation, Deviation, & Z-Scores

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University of Toronto *

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2120

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Geography

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Oct 30, 2023

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pdf

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1

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Measures Of Variation (Dispersion) - How scores differ in terms of their spread around the center - Range - The most basic measure of dispersion - A range of dispersion for one variable, indicating the highest and lowest scores - Percentiles - The percentage of scores that fall at or below a certain score - Ex - we can see how many scores ball below a 90 - Standard Deviation - A measure of dispersion for one variable that tells us the average distance between the scores and the mean - Z-Scores - A way to locate a score in a distribution of scores by determining the number of standard deviations it is above or below the mean Standard Deviation - First, calculate the mean (Add all the numbers together and divide by the number of numbers) - Second, take the scores and subtract the mean from each score (it can be negative) - Third, Square the new values (the score after the mean has been subtracted) - Fourth, add all of the scores together - Fifth, divide the sum of the scores by the number of numbers minus 1 (Ex - 12 - 1) - The standard deviation will always be positive - That Is How To Get The Standard Deviation Z-Scores (Standardized Score) - Every observation can be converted into a Z-score - 1 - allows us to compare 2 or more distributions or groups - 2 - Z-scores can indicate whether an observation is statistically significantly different from the average - Make both groups have the same average (take 50, and 90, and make them both 0) - The formula for Z-Scores is - Z-Score = (Score - Mean) / Standard Deviation - Score minus mean, divided by the standard deviation - A score is X standard deviations above or below the average
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