Supplementary Exercises 1.42 and 1.72 of IPS7e
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1.42:
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For this exercise, we will work with the stemplot provided in the
problem. We will use the actual data for the follow-up questions in
1.72.

(a)
Because the stems are whole percents and the leaves are tenths of a
percent, we can approximate the values to within one decimal by reading
off the numbers from the stemplot. A stem value of 17 and a leaf value
of 6 corresponds to 17.6% (Florida). In the same way, the approximate value 
for Alaska equals 5.7%.

(b)
The distribution appears as unimodal and left-skewed, centered at 13%
and with a fairly narrow spread: almost all the states have values
between 11% and 15%.


1.72:
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We prefer to use statistical software to compute numerical summaries 
for the distribution, despite that the problem suggests the 5-number 
summary to be computed from the stemplot. 

MTB > WOpen "H:\VHM\VHM801\Datasets\Minitab\Chapter 1\ex01_042.mtw".
Retrieving worksheet from file: ‘H:\VHM\VHM801\Datasets\Minitab\Chapter
1\ex01_042.mtw’
Worksheet was saved on 28/08/2014

MTB > Describe 'over65'.
Descriptive Statistics: over65 

Variable   N  N*    Mean  SE Mean  StDev  Minimum      Q1  Median      Q3  Maximum
over65    50   0  12.538    0.269  1.905    5.700  11.675  12.750  13.500   17.600


Comments:
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The 5-number summary is 5.7 - 11.7 - 12.8 - 13.5 - 17.6. 
For the 1.5*IQR rule we further calculate:
  IQR = 13.5-11.7 = 1.8
  Q1 - 1.5*IQR = 11.7-2.7 = 9.0
  Q3 + 1.5*IQR = 13.5+2.7 = 16.2

Both of the two extreme states (Alaska and Florida) are beyond this
range, so they would indeed be identified as suspected outliers. Another
state with a value around 8.5% would however also be identified as a
suspected outlier. This may seem unnatural because that value does not
differ that much from several values between 9% and 10%. In a left-
skewed distribution, the rule will tend to identify too many outliers in
the left tail, with the converse happening in a right-skewed
distribution. This is because the rule is symmetrical and does therefore
not account for one tail being naturally larger than the other one.

In practice we would always have to use our judgement to decide whether
suspected outliers should be regarded as real outliers.