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Lecture%208-2

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

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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 g1876 g1191 = 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 g1876 g1191 = 12 and s = 1.5. Can we say who did better?

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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 = g3051 g2879 g3051 g1191 g3046 (z-score of the data x in the sample ) z-score of a data x in the population : z = g3051 g2879 g3091 g3097
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 g1876 g1191 = 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 g1876 g1191 = 12 and s = 1.5. z-score of Jack is z = g3051 g2879 g3051 g1191 g3046 = g2876g2874g2879g2876g2868 g2872 = 6/4 = 1.5 Jack’s score 86 is ``1.5 standard deviation’’ , i.e., (1.5)*4 above the mean g1876 g1191 = 80 z-score of Jill is z = g3051 g2879 g3051 g1191 g3046 =

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

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