M119L07to08

M119L07to08 - (Lesson 7 Measures of Relative Standing or...

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(Lesson 7: Measures of Relative Standing or Position; 3-4) 3.30 LESSON 7: MEASURES OF RELATIVE STANDING OR POSITION (SECTION 3-4) How high or low is a data value relative to the others? We want standardized measures that will work for practically all populations involving quantitative data. PART A: z SCORES z = x ± mean SD Idea: ² new mean = 0 ² new SD = 1 ³ ´ µ · ¸ We are transforming the original data set of x -values into a new data set of z -values. x 1 x 2 x 3 etc. ±±± z 1 z 2 z 3 etc. Subtracting off the mean from all of the original x -values recenters the data set so that the new mean will be 0. Then, dividing by the SD rescales the data set so that the new SD will be 1. Notation Population (Size N ) z = x ± μ ² ± Sample (Size n ) z = x ± x s Round off z scores to two decimal places. They have no units, because we divide by the SD. We will be able to use z scores in many different applications where different units are involved. If we are studying heights, for instance, we may use inches, feet, meters, etc. and still obtain the same z scores.

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M119L07to08 - (Lesson 7 Measures of Relative Standing or...

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