Section 2.5 Spotlight on Statistics Objective 1 – Compute z-scores and Standardized Scores Objective 2 – Explore the Normal Distribution Objective 1 – Compute z-scores and Standardized Scores Key Terms 𝑧-scores Chebychev’s Theorem: Summary In the last chapter’s Spotlight on Statistics we introduced the basic measures of central tendency and spread. The mean is the arithmetical average of the data set and the standard deviation is the “average distance from the mean.” Given these two descriptive statistics we can put into perspective the location of individual data points within the overall distribution of values. As explained in the beginning of this chapter, absolute numbers are virtually meaningless without comparison. The age distribution of the U.S. shows a mean age 38.5 in 2016 with a standard deviation of 23.1 years. Thus someone who is 15 years old will be about one standard deviation below the mean and someone who is 62 is one standard deviation above the mean. These ages represent the average distance away from the mean. One of the fundamental statistical questions we will ask is whether or not a data value is unusual. A z-score will tell how many standard deviations away from the mean a given data value is. Copyright © 2020 Pearson Education, Inc. 106 U.S. Age Distribution 2016 5,000,000 FREQUENCY 4,000,000 3,000,000 2,000,000 1,000,000 0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 75 78 81 84 87 90 93 96 99 AGE IN ...
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