A survey was given to residents of all 50 states asking if they had earned a bachelor's degree or higher....

1. INFER what the problem is asking

• Given information:
  • 7 states with their bachelor's degree percentages
  • National median for all 50 states: \(\mathrm{26.95\%}\)
  • Need to find the difference between the 7-state median and national median

• Key insight: To find median, we must arrange data in order first

2. SIMPLIFY by ordering the data

• Arrange the 7 percentages from least to greatest:
  • 19.5%, 21.9%, 25.9%, 27.9%, 30.1%, 35.5%, 36.4%

• Since we have 7 values (odd number), the median is the middle value
• The 4th value is the median: \(\mathrm{27.9\%}\)

3. SIMPLIFY the final calculation

• Difference = 7-state median - national median
• \(\mathrm{27.9\% - 26.95\% = 0.95\%}\)

Answer: B. \(\mathrm{0.95\%}\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Students forget to order the data before finding the median and instead use the middle value from the original unordered list (which would be State D at \(\mathrm{19.5\%}\) or calculate incorrectly).

When data isn't properly ordered first, they might grab the middle position from the table as given, leading to an incorrect median calculation. This may lead them to select Choice D \(\mathrm{(7.45\%)}\) or causes confusion leading to guessing.

Second Most Common Error:

Conceptual confusion about median vs mean: Students calculate the average (mean) instead of the median.

They add all seven percentages and divide by 7, getting approximately \(\mathrm{28.17\%}\), then subtract \(\mathrm{26.95\%}\) to get about \(\mathrm{1.22\%}\). This may lead them to select Choice C \(\mathrm{(1.22\%)}\).

The Bottom Line:

The key challenge is remembering that median requires ordered data - it's not just "the middle number in the list as given." Students who rush through without the ordering step will struggle with this foundational statistics concept.