Lecture%208-2

Lecture%208-2 - Measures of Relative Standing: Consider the...

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Unformatted text preview: Measures of Relative Standing: Consider the following scenario: In Sec. 1 of a statistic course, Jack scored 86 out of 100 in Exam 1, where the mean and the standard deviation of the class were gG = 80 and s = 4. In Sec. 2 of the same course, Jill scored 15 out of 20 in Exam 1, where the mean and the standard deviation of the class were gG = 12 and s = 1.5. Can we say who did better? z score (or the standardized value): The z score of a data value x is the number of standard deviations that the data value x is above or below the mean. z = g G g (z-score of the data x in the sample ) z-score of a data x in the population : z = g G Recall the example: In Sec. 1 of a statistic course, Jack scored 86 out of 100 in Exam 1, where the mean and the standard deviation of the class were gG = 80 and s = 4. In Sec. 2 of the same course, Jill scored 15 out of 20 in Exam 1, where the mean and the standard deviation of the class were gG = 12 and s = 1.5. z-score of Jack is z = G = = 6/4 = 1.5 Jacks score 86 is ``1.5 standard deviation , i.e., (1.5)*4 above the mean gG = 80 z-score of Jill is z = G = . = 3/(1.5) = 2 Jills score 15 is ``2 standard deviation , i.e., (2)*1.5 above the mean gG = 12 Therefore Jills score is ``better. Example:...
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This note was uploaded on 12/27/2011 for the course MATH 121 taught by Professor Banerjee during the Fall '11 term at Syracuse.

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Lecture%208-2 - Measures of Relative Standing: Consider the...

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