Section 3.4: “Measures of Position and
Outliers”
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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 man
B. The woman
C. 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. 3
B. 3.4
C. 6.4
D. 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. 3
B. 3.4
C. 6.4
D. 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. -13
B. -3.25
C. 7.5
D. 13
Z-score =
𝑥−𝑚𝑒𝑎𝑛
𝑠𝑑
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 quartile
B. Mean and 2nd quartile
C. Median and 2nd quartile
D. Median and 3rd quartile
The 75th percentile can also be called the:
A. 1st quartile
B. 2nd quartile
C. 3rd quartile
D. 4th quartile
IQR is an abbreviation for…
A. Intelligence Quotient Ratio
B. Interrupted Question Request
C. Integrated Quality Ratio
D. Interquartile Range
What percent of the data lies within the IQR?
A. 25%
B. 50%
C. 75%
D. 80%
5
10
15
20
25
30
35
Los Angeles Rainfall by Ocean Conditions
ElNino
LaNina
Ocean Conditions
neutral
5
10
15
20
25
30
35
Los Angeles Rainfall by Ocean Conditions
ElNino
LaNina
neutral
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