Question 1.59

1.59 Discovering outliers.

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Whether an observation is an outlier is a matter of judgment. It is convenient to have a rule for identifying suspected outliers. The is in common use:

  1. The interquartile range is the distance between the first and third quartiles, . This is the spread of the middle half of the data.
  2. An observation is a suspected outlier if it lies more than below the first quartile or above the third quartile .

The stemplot in Exercise 1.31 (page 22) displays the distribution of the percents of residents aged 65 and older in the 50 states. Stemplots help you find the five-number summary because they arrange the observations in increasing order.

  1. Give the five-number summary of this distribution.
  2. Does the rule identify any outliers? If yes, give the names of the states with the percents of the population over 65.

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The following three exercises use the Mean and Median applet available at the text website to explore the behavior of the mean and median.

1.59

(a) , , , , . (b) . . So, Utah with 9.5 percent and Alaska with 8.5 percent are low outliers. . So, Florida with 18.2 percent is a high outlier.