PROBLEMS 61largest X, whichever is lower. The lower fence is at (Q1 - 1.5(IQR)) or the smallest
X, whichever is higher. Values that are outside the fences are considered possible
extreme values, or outliers. Here, we have depicted a box plot of the hemoglobin levels
for mine workers at high elevations. Had the distribution of hemoglobin levels been
skewed to the right, the portion of the box between the median and Q3 would have
been larger than the portion between the median and Q1. There is one observation
of 26.2 that is beyond the upper fence and two observations, 12.2 and 13.1, that are
below the lower fence. These values are possible outliers or extreme values.
Since box plots are used frequently some statistical software programs will offer
numerous options on how the box plots are displayed. They are often used to see
if the data are skewed. Note in Figure 5.1 that the median is almost in the middle
of the box and the fences are almost the same distance from the median. This is an
indication that the data are distributed symmetrically.
Often, several box plots are displayed side by side so that information concerning
different groups can be compared. An example would be blood pressure for patients
who are assigned one of three drugs. Plots of box plots are available in Minitab,
SAS, SPSS, and Stata. Graphical methods of comparison are especially useful for a
presentation of data to an audience since most viewers can see the results in a graph
more easily than in searching through a table.
PROBLEMS5.1 In a study of nursing home patients, the following data were obtained for each
patient; age, gender, previous smoking status (smoker or nonsmoker), reason
for admission, nursing wing housed in, length of stay, and four-point scale
rating of health status. Classify each variable by whether it is nominal, ordinal,
interval, or ratio according to Stevens’ classification.
The following data are ordered systolic blood pressures in millimeters of mer-
cury (mmHg) from 48 young adult males:
5.2
87 106 114 120 129 140 155 183
93 107 116 122 133 141 155 194(^101 107 117 122 133 146 162 197)
104 109 118 125 134 146 167 204
105 110 118 125 135 148 173 212
105 114 119 128 138 152 176 230
(a) Compute the mean and standard deviation using the formulas given in this
book. Check your results by entering the data into a statistical package and
obtain their results for the means and standard deviations.
(b) Compute the median and quartiles.
(c) Display a histogram and a box plot of the data above using a statistical
package. Check if your median and quartiles coincide with the box plot
obtained from a statistical package.
(d) State whether or not you think the data follow a symmetric distribution, and
give the reason for your answer.