# Exam 2 stats.docx - A Z score is the number of standard...

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A Z score is the number of standard deviations a particular score deviates from the mean . Z = +1.00, a particular raw score is one standard deviation above the mean, Z = -1.00, a particular raw score is one standard deviation below the mean. Raw score = ordinary score, Z score = standardized raw score. The purpose of z -scores , or standard scores, is to identify and describe the exact location of each score in a distribution. A second purpose for z-scores is to standardize an entire distribution. A common example of a standardized distribution is the distribution of IQ scores. of 15. A z -score specifies the precise location of each X value within a distribution. + or − z score, signifies whether the score is above the mean (positive) or below the mean (negative). The numerical value of the z-score specifies the distance from the mean by counting the number of standard deviations between X and μ. In most cases, we simply transform scores ( X values) into z -scores, or change z -scores back into X values. However, a z -score establishes a relationship between the score, mean, and standard deviation. If every X value is transformed into a z -score, then the distribution of z -scores will have the following properties: (1) The distribution of z -scores will have exactly the same shape as the original distribution of scores. (2) The z -score distribution will always have a mean of zero. (3) The distribution of z-scores will always have a standard deviation of 1. A standardized distribution is composed of scores that have been transformed to create predetermined values for μ and σ. One advantage of standardizing distributions is that it makes it possible to compare different scores or different individuals even though they come from completely different distributions. Normally, if two scores come from different distributions, it is impossible to make any direct comparison between them, Using z -scores makes such comparisons possible. Transforming a distribution of raw scores into z -scores will not change the shape of the distribution. Although z -scores are most commonly used in the context of a population, the same principles can be used to identify individual locations within a sample. If all the scores in a sample are transformed into z -scores, the result is a sample of z -scores. (1.) The transformed distribution of z -scores will have the same properties that exist when a population of X values is transformed into z -scores. (2.) The sample will have the same shape as the original sample. (3) The sample will have a mean of M z = 0. (4) The sample will have a standard deviation of s z = 1. A theoretical distribution with data that are symmetrically distributed around the mean, median, and mode. - Scores closer to the mean are more probable, or likely, than scores further from the mean. -Behavioral data that researchers measure often tend to approximate a normal distribution Characteristics of normally distributed data sets (Mean, median, and mode are all located at the 50th percentile, Half of the data (50%) in a normal distribution fall