The table above shows the land area, in square kilometers, of the five smallest countries of the world in 2016....

1. TRANSLATE the problem information

• Given information:
  • Land areas of 5 countries: Monaco (2.0), Nauru (21), San Marino (61), Tuvalu (26), Vatican City (0.44)
  • Need to find: mean land area rounded to nearest square kilometer
• What this tells us: We need to calculate the arithmetic average and then round appropriately

2. SIMPLIFY by calculating the mean

• First, find the sum of all land areas:
  \(2.0 + 21 + 61 + 26 + 0.44 = 110.44 \mathrm{\ km}^2\)
• Then divide by the number of countries (5):
  \(110.44 \div 5 = 22.088 \mathrm{\ km}^2\)

3. APPLY CONSTRAINTS for the final answer

• The problem asks for the answer 'to the nearest square kilometer'
• 22.088 rounds to 22 km²

Answer: B. 22

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students might misunderstand what 'mean' means and instead select the largest value or middle value from the data set.

This leads them to scan the table and pick San Marino's area of 61 km² as their answer, selecting Choice C (61).

Second Most Common Error:

Incomplete SIMPLIFY execution: Students correctly understand they need to find the mean but stop after calculating the sum without dividing by the number of countries.

They calculate \(2.0 + 21 + 61 + 26 + 0.44 = 110.44\), round to 110, and select Choice D (110).

The Bottom Line:

This problem tests whether students truly understand the concept of arithmetic mean versus other measures of central tendency, and whether they can complete all steps of a multi-step calculation including proper rounding.