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8-3 Statistics: Range and Standard Deviation statisticians need to know what the central tendency of a set of scores is: mean, median they also want to know how “spread out” the scores are statistics that measure the spread are called measures of dispersion RANGE The range of a set of scores is the distance from lowest to highest score: range = (high score – low score) STANDARD DEVIATION the most commonly used measure of dispersion notation (for the whole population): (“sigma”) notation (for a sample): s Here’s the formula for s, the sample standard deviation of a set of n scores: x1, x2, x3, … , xn with sample mean: x n 2 ( xi x ) s= i 1 n 1 why will data that is more “spread out” give a larger standard deviation? 8-3 p. 1 A distribution with “large” standard deviation: -100 100 0 One with “small” standard deviation: -20 8-3 0 20 p. 2