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Understanding z scores Standard scores Standard scores assume a normal distribution They provide a method of expressing any score in a distribution in terms of its distance from the mean in standard deviation units 2 Z-score A raw score by itself is rather meaningless. What gives the score meaning is its deviation from the mean A Z score expresses this value in standard deviation units 3 Z-score z= X = Raw score X = Mean s = x= X-X s or x s Standard deviation (X - X ) 4 Z score formula z= X-X s or x s X = 76 X = 82 s =4 5 Z score computation z= X-X s or x X = 76 s X = 82 s =4 76 - 82 - 6 z= = = -1.50 4 4 6