Section 3.4: “Measures of Position and Outliers” Calculate and interpret z-scores Interpret...

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)

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?A. The manB. The womanC. They are equal

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?A. 3B. 3.4C. 6.4D. 30

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?A. 3B. 3.4C. 6.4D. 30

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

Z-score =

In statistics, differences are often measured in terms of standard deviations from the mean!

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

The 50th percentile can also be called the:A. Mean and 1st quartileB. Mean and 2nd quartileC. Median and 2nd quartileD. Median and 3rd quartile

The 75th percentile can also be called the:A. 1st quartileB. 2nd quartileC. 3rd quartileD. 4th quartile

IQR is an abbreviation for…A. Intelligence Quotient RatioB. Interrupted Question RequestC. Integrated Quality RatioD. Interquartile Range

What percent of the data lies within the IQR?A. 25%B. 50%C. 75%D. 80%

ElNino LaNina neutral

51

01

52

02

53

03

5

Los Angeles Rainfall by Ocean Conditions

Ocean Conditions

ElNino LaNina neutral

51

01

52

02

53

03

5

Los Angeles Rainfall by Ocean Conditions

Ocean Conditions

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.

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