International Tourist Arrivals, in millions Country 2012 2013 France 83.0 84.7 United States 66.7 69.8 Spain 57.5 60.7 China 57.7...
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
International Tourist Arrivals, in millions
| Country | 2012 | 2013 |
|---|---|---|
| France | 83.0 | 84.7 |
| United States | 66.7 | 69.8 |
| Spain | 57.5 | 60.7 |
| China | 57.7 | 55.7 |
| Italy | 46.4 | 47.7 |
| Turkey | 35.7 | 37.8 |
| Germany | 30.4 | 31.5 |
| United Kingdom | 26.3 | 32.2 |
| Russia | 24.7 | 28.4 |
The table above shows the number of international tourist arrivals, rounded to the nearest tenth of a million, to the top nine tourist destinations in both 2012 and 2013. Based on the information given in the table, how much greater, in millions, was the median number of international tourist arrivals to the top nine tourist destinations in 2013 than the median number in 2012, to the nearest tenth of a million?
1. TRANSLATE the problem information
- Given information:
- Table showing tourist arrivals (in millions) for 9 countries in both 2012 and 2013
- Need to find how much greater the 2013 median was than the 2012 median
- Answer should be to the nearest tenth of a million
2. INFER the approach needed
- To find medians, I must order each year's data from least to greatest
- The median will be the middle value (5th out of 9 values) for each year
- Then subtract: \(\mathrm{2013\ median - 2012\ median}\)
3. SIMPLIFY by organizing the 2012 data
- From the table: 83.0, 66.7, 57.5, 57.7, 46.4, 35.7, 30.4, 26.3, 24.7
- Ordered from least to greatest: 24.7, 26.3, 30.4, 35.7, 46.4, 57.5, 57.7, 66.7, 83.0
- \(\mathrm{2012\ median = 46.4\ million}\)
4. SIMPLIFY by organizing the 2013 data
- From the table: 84.7, 69.8, 60.7, 55.7, 47.7, 37.8, 31.5, 32.2, 28.4
- Ordered from least to greatest: 28.4, 31.5, 32.2, 37.8, 47.7, 55.7, 60.7, 69.8, 84.7
- \(\mathrm{2013\ median = 47.7\ million}\)
5. SIMPLIFY the final calculation
- Difference:
\(\mathrm{Difference = 47.7 - 46.4}\)
\(= 1.3\ \mathrm{million}\)
Answer: 1.3 (or \(\frac{13}{10}\))
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak INFER skill: Students often try to find the median by looking at the middle country in the table as presented, rather than recognizing that the data must first be ordered from least to greatest.
For example, they might look at the table and think Italy (46.4 in 2012, 47.7 in 2013) is the "middle" since it appears roughly in the middle of the table. This would still give the right answer by coincidence, but shows they don't understand the median concept.
Second Most Common Error:
Poor TRANSLATE execution: Students may misread decimal values from the table or transpose digits when copying numbers. For instance, reading 26.3 as 63.2 or 32.2 as 23.2 would throw off the entire ordering process and lead to an incorrect median calculation.
This leads to confusion when their calculated medians don't make sense or don't match any reasonable answer pattern.
The Bottom Line:
The core challenge is recognizing that median requires ordering data, not just identifying a middle position in the given table format. Students must actively reorganize the information rather than work with it as presented.