The box plots summarize the masses, in kilograms, of two groups of gazelles. Based on the box plots, which of...

1. TRANSLATE the box plot information

When you look at a box plot, the vertical line inside the box represents the median of the data set.

• From Group 1's box plot:
  • The vertical line within the box is at \(\mathrm{25\ kilograms}\)
  • This is the median mass for Group 1

• From Group 2's box plot:
  • The vertical line within the box is at \(\mathrm{24\ kilograms}\)
  • This is the median mass for Group 2

2. INFER which answer choices are even possible

Before comparing specific values, recognize what box plots can and cannot tell you:

• Box plots show the five-number summary (min, Q1, median, Q3, max)
• Box plots do NOT show the mean directly
• You cannot calculate or reliably estimate the mean from a box plot alone

This means:

• Choices A and B (about means) cannot be determined from this information
• Choices C and D (about medians) can be evaluated using the data we translated

3. Compare the medians

Now TRANSLATE the comparison into a mathematical statement:

• Group 1 median: \(\mathrm{25\ kg}\)
• Group 2 median: \(\mathrm{24\ kg}\)
• Is \(\mathrm{25\ kg \gt 24\ kg}\)? Yes!

Therefore, the median mass of Group 1 IS greater than the median mass of Group 2.

This matches Choice C exactly.

4. Verify the other choices

Choice D states the opposite (Group 1 median < Group 2 median), which is false since \(\mathrm{25 \gt 24}\).

Answer: C

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill - Not knowing what information box plots provide: Many students either don't remember or never learned that box plots show medians but not means. They might see answer choices A and B about means and think "Well, I can see the data distribution, so I should be able to figure out which group has a higher mean."

They might reason: "Group 1's box extends further to the right, so it must have a higher mean" or "Group 2 looks more compact, so it might have a lower mean."

This faulty reasoning could lead them to select Choice A (thinking they can determine that Group 1's mean is greater) or cause confusion and guessing between all four choices.

Second Most Common Error:

Weak TRANSLATE skill - Misidentifying the median in the box plot: Some students confuse which line represents the median. They might think:

• The left edge of the box is the median (it's actually Q1)
• The right edge of the box is the median (it's actually Q3)
• The middle of the whisker is the median (whiskers show min/max range)

If they misread Group 1's median as being at the left edge of its box (\(\mathrm{approximately\ 23\ kg}\)) while correctly reading Group 2's median as \(\mathrm{24\ kg}\), they might conclude that Group 1's median is less than Group 2's median.

This may lead them to select Choice D (incorrectly concluding that Group 1's median is less than Group 2's median).

The Bottom Line:

This problem tests whether you understand box plot structure and can extract the correct information. The key is knowing that the vertical line inside the box is always the median, and recognizing that box plots don't give you enough information to determine means. Once you know what to look for, it's just a simple comparison: \(\mathrm{25 \gt 24}\).