mgf1107lecture35 - MGF 1107 EXPLORATIONS IN MATHEMATICS...

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MGF 1107 – EXPLORATIONS IN MATHEMATICS LECTURE 35 Standardizing Data Values If you score 90 on an exam with a mean of 80 and a standard deviation of 10, and then score 75 on an exam with a mean of 70 and a standard deviation of 5, then in relative terms your performance on the two exams relative to your classmates was identical. This notion of comparing performances from different experiments is what leads us creating standardized data. In order to do this we use z-scores to determine how far, in terms of the standard deviation, a given score is from the mean. For example, a piece of data having a z-score of 2 lies two standard deviations above the mean, and a piece of data having a z-score of –2 lies two standard deviations below the mean. In the scenario described at the top of the page, both exam scores result in a z-score of 1, indicating scores one standard deviation above the mean. In general, the z-score for a piece of data is calculated as follows.
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Ex. (16.B.15)
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