STAT 2004 Lecture Notes - Lecture 6: Normal Distribution, Standard Deviation, Unimodality
14 Oct 2018
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Z-scores: a z-score is a statistical measurement of a score"s relationship to the mean in a group of scores. A z-score of 0 means the score is the same as the mean. A z-score can also be positive or negative, indicating whether it is above or below the mean and by how many standard deviations. (wikipedia) Standardizing distributions: shape same as original, center mean = 0, spread sx becomes equal to 1. Shifting (adding/subtracting: measures of position will change accordingly center, maximum, minimum quartiles, measures of spread will not change whatsoever range, iqr, sx. Rescaling (multiplying/dividing) changing units: measures of position change accordingly, measures of spread change accordingly. Represented as (cid:4666),(cid:4667) representing the mean and the standard deviation, respectively (these numbers are referred to as the model"s parameters, as they do not help summarize a given model, but rather come from such. Standard normal model: represented as n(0,1), but also referred to as the standard normal distribution (***this does.
