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Section 3.4: “Measures of Position and Outliers”

Section 3.4: “Measures of Position and Outliers”. Calculate and interpret z-scores Interpret percentiles and quartiles Interpret interquartile range Interpret boxplots Note: We will not worry about calculating percentiles nor quartiles (besides median).

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Section 3.4: “Measures of Position and Outliers”

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  1. Section 3.4: “Measures of Position and Outliers” • Calculate and interpret z-scores • Interpret percentiles and quartiles • Interpret interquartile range • Interpret boxplots • Note: We will not worry about calculating percentiles nor quartiles (besides median)

  2. Suppose men have a mean height of 70 inches (sd=3). Women have a mean height of 63 inches (sd=2). Relative to people their own gender, who is taller a 73 inch tall man or a 67 inch woman? • The man • The woman • They are equal

  3. Suppose the mean amount of luggage per a airline passenger is 34 pounds (s=10). What is the z-score for a passenger with 64 pounds of luggage? • 3 • 3.4 • 6.4 • 30

  4. Suppose the mean amount of luggage per a airline passenger is 34 pounds (s=10). How many standard deviations from the mean is a passenger with 64 pounds of luggage? • 3 • 3.4 • 6.4 • 30

  5. Suppose the mean rainfall for Arcata is 43 inches (sd=4). Calculate the z-score for a year with 30 inches of rain. • -13 • -3.25 • 7.5 • 13

  6. Z-score = In statistics, differences are often measured in terms of standard deviations from the mean!

  7. If you exam score is at the 78th percentile then: • You did better than 22% of the test takers. • You did better than 78% of the test takers. • You did worse than 78% of the test takers. • You scored a 78% on the exam.

  8. The 50th percentile can also be called the: • Mean and 1st quartile • Mean and 2nd quartile • Median and 2nd quartile • Median and 3rd quartile

  9. The 75th percentile can also be called the: • 1st quartile • 2nd quartile • 3rd quartile • 4th quartile

  10. IQR is an abbreviation for… • Intelligence Quotient Ratio • Interrupted Question Request • Integrated Quality Ratio • Interquartile Range

  11. What percent of the data lies within the IQR? • 25% • 50% • 75% • 80%

  12. Boxplots show • Boxes defined by 25th & 75th percentiles (half of data lies within) • Middle line is 50th percentile • “Fences” or “Whiskers” stretch no further than1.5 IQR from box • Any point beyond reach of whiskers is plotted individually • Excellent tool for visual comparison of different groups of quantitative data. • “Outlier” is a subjective term – much more complicated than just saying it lies outside of whiskers.

  13. What is the interquartile range for El Nino rain? A) 10 B) 12.5 C) 17 D) 22.5

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