Exercise 3.30:
The paper "Lessons from Pacemaker Implantations" (Journal of the
American Medical Association [1965]: 231-232) gave the results of
a study that followed 89 heart patients who had received electronic
pacemakers. The time (in months) to the first electrical malfunction
of the pacemaker was recorded:
| 24 |
20 |
16 |
32 |
14 |
22 |
2 |
12 |
24 |
6 |
10 |
20 |
| 8 |
16 |
12 |
24 |
14 |
20 |
18 |
14 |
16 |
18 |
20 |
22 |
| 24 |
26 |
28 |
18 |
14 |
10 |
12 |
24 |
6 |
12 |
18 |
16 |
| 34 |
18 |
20 |
22 |
24 |
26 |
18 |
2 |
18 |
12 |
12 |
8 |
| 24 |
10 |
14 |
16 |
22 |
24 |
22 |
20 |
24 |
28 |
20 |
22 |
| 26 |
20 |
6 |
14 |
16 |
18 |
24 |
18 |
16 |
6 |
16 |
10 |
| 14 |
18 |
24 |
22 |
28 |
24 |
30 |
34 |
26 |
24 |
22 |
28 |
| 30 |
22 |
24 |
22 |
32 |
a. Summarize these data in the form of a frequency distribution, using
class intervals of 0 to <6, 6 to <12, and so on.
b. Compute the relative frequencies and cumulative relative frequencies
for each class interval of the frequency distribution of Part (a).
c. Show how the relative frequency for the class interval 12 to <18 could
be obtained from the cumulative relative frequencies.
d. Use the cumulative relative frequencies to give approximate answers to
the following:
i. What proportion of those who participated in
the study had pacmakers that did not malfunction within the first
year?
ii. If the pacemaker must be replaced as soon as
the first electrical malfunction occurs, approximately what proprtion
required replacement between 1 and 2 years after implanation?
e. Construct a cumulative relative frequency plot, and use it to answer
the following questions.
i. What is the approximate time at which about 50% of
the pacemakers had failed?
ii. What is the approximate time at which only about
10% of the pacemakers initially implanted were still functioning?
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