What is the maximum dispersion in the registration of patients in the two…
2009
What is the maximum dispersion in the registration of patients in the two hospitals in a year?
Answer: A. 8000 — Concept: For two data series recorded over the same years, the dispersion in a given year is the absolute difference between the two values plotted for that…
- A.
8000
- B.
6000
- C.
4000
- D.
2000
Show answer & explanation
Correct answer: A
Concept: For two data series recorded over the same years, the dispersion in a given year is the absolute difference between the two values plotted for that year, |X − Y|. The maximum dispersion over a period is therefore the largest of those year-wise absolute differences: difference the two series year by year, then take the greatest of those differences. It is not read off either series' own highest or lowest point.
Application: Reading both curves at each year mark and differencing them:
Year | Hospital X | Hospital Y | Dispersion |X − Y| |
|---|---|---|---|
2001 | 8,000 | 6,000 | 2,000 |
2002 | 10,000 | 4,000 | 6,000 |
2003 | 8,000 | 6,000 | 2,000 |
2004 | 4,000 | 6,000 | 2,000 |
2005 | 12,000 | 4,000 | 8,000 |
2006 | 2,000 | 4,000 | 2,000 |
The greatest entry in the last column is 8,000, recorded in 2005, where hospital X stands at 12,000 and hospital Y at 4,000.
Cross-check:
On the graph the widest vertical separation between the two plotted lines occurs at 2005: hospital X touches its peak of 12,000 while hospital Y sits at its floor of 4,000, four grid divisions of 2,000 apart.
Everywhere else the lines are closer, three grid divisions apart in 2002 and a single division apart in 2001, 2003, 2004 and 2006.
A peak in one series alone does not settle the matter: 2005 gives the largest gap only because hospital X is at its highest while hospital Y is simultaneously at its lowest. Had hospital Y also read 10,000 that year, the dispersion there would have been 2,000.
Answer: The maximum dispersion in the registration of patients in the two hospitals in a year is 8,000.