# 3.3 - Measures of Relative Standing and Boxplots.pdf -...

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Measures of Relative Standing and BoxplotsSection 3.3Objectives:𝑧𝑧-Scores.Percentiles.Quartiles.5-Number Summary and BoxplotDef:Az-score (or standardized value)is the number of standard deviations that a given value𝑥𝑥is aboveor below the mean. The z-score is calculated by using the following:Note:z- scores are always rounded to two decimal places. This is standard format for tables of z-scores.We can use z-scores to compare two values from different sets of data.Ex: 1) As of this book's writing, the tallest living man is Sultan Kosen, who has a height of 247 cm. Thetallest living woman is De-Fan Yao, who is 236 cm tall. Heights of men have a mean of 175 cm and astandard deviation of 7 cm. Heights of women have a mean of 162 cm and a standard deviation of 6 cm.Relative to the population of the same gender, who is taller? Explain.Note: Aside, from just using different data sets, we can compare values that have different units as well.

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