The remission times of 42 patients with acute leukemia were reported from
a clinical trial undertaken to assess the ability of the drug 6-mercaptopurine
(6-MP) to maintain remission. Each patient was randomized to receive either
6-MP or placebo. The study was terminated after one year; patients have dif-
ferent follow-up times because they were enrolled sequentially at di¤erent
times. Times to relapse in weeks for the 21 patients in the placebo group were
1 ; 1 ; 2 ; 2 ; 3 ; 4 ; 4 ; 5 ; 5 ; 8 ; 8 ; 8 ; 8 ; 11 ; 11 ; 12 ; 12 ; 15 ; 17 ; 22 ; 23
The mean is
x¼P
x
n
¼ 8 :67 weeksand on the log scale we have
P
lnx
n¼ 1 : 826
leading to a geometric mean of 6.21, which, in general, is less a¤ected by the
large measurements.
2.2.2 Other Measures of Location
Another useful measure of location is themedian. If the observations in the
data set are arranged in increasing or decreasing order, the median is the mid-
dle observation, which divides the set into equal halves. If the number of
observationsnis odd, there will be a unique median, the^12 ðnþ 1 Þth number
from either end in the ordered sequence. Ifnis even, there is strictly no
middle observation, but the median is defined by convention as the average of
the two middle observations, the^12 n
th and^12 ðnþ 1 Þth from either end. In
Section 2.1 we showed a quicker way to get an approximate value for the
median using the cumulative frequency graph (see Figure 2.6).
The two data setsf 8 ; 5 ; 4 ; 12 ; 15 ; 7 ; 28 gandf 8 ; 5 ; 4 ; 12 ; 15 ; 7 ; 49 g, for exam-
ple, have di¤erent means but the same median, 8. Therefore, the advantage of
the median as a measure of location is that it is less a¤ected by extreme
observations. However, the median has some disadvantages in comparison
with the mean:
- It takes no account of the precise magnitude of most of the observations
and is therefore less e‰cient than the mean because it wastes information. - If two groups of observations are pooled, the median of the combined
group cannot be expressed in terms of the medians of the two component
76 DESCRIPTIVE METHODS FOR CONTINUOUS DATA