A group of paleobotanists collected samples of sediments containing pollen and spores from various plant species. Each sample was analyzed...

Phase 1: Owning the Dataset

Visualization Selection

We'll use a comparison table since we're comparing properties of two distinct samples.

Creating Our Visual

Phase 2: Understanding the Question

Breaking Down the Statement

We need to complete: "S1 had the greater ratio of total number of 1 to total number of 2"

This means we're looking for: \(\frac{\mathrm{Something\ in\ S1}}{\mathrm{Something\ else\ in\ S1}} > \frac{\mathrm{Same\ something\ in\ S2}}{\mathrm{Same\ something\ else\ in\ S2}}\)

Key Insight

For S1 to have a greater ratio than S2:

• The numerator (position 1) should be something S1 has MORE of than S2
• The denominator (position 2) should be something S1 has LESS of than S2
• OR a combination that makes S1's ratio larger

What We Know for Certain

From our visualization:

• S1 has MORE total spores than S2 ✓
• S1 has FEWER species represented than S2 ✓
• S1 has pollen from Species P (S2's pollen status not mentioned)

Phase 3: Finding the Answer

Applying Our Logical Framework

Let's check which combination gives S1 a definitively greater ratio:

For position 1 (numerator): We need something S1 has more of

• "spores" - S1 has more ✓
• "pollen grains from Species P" - S1 has these, S2 not mentioned to have any

For position 2 (denominator): We need something S1 has less of

• "species represented" - S1 has fewer ✓

The Winning Combination

\(\mathrm{Ratio} = \frac{\mathrm{total\ spores}}{\mathrm{species\ represented}}\)

For S1: \(\frac{\mathrm{Many\ spores}}{\mathrm{Few\ species}} = \mathrm{Large\ ratio}\)

For S2: \(\frac{\mathrm{Few\ spores}}{\mathrm{Many\ species}} = \mathrm{Small\ ratio}\)

This perfectly satisfies our requirement that S1 has the greater ratio!

Phase 4: Solution

Position 1: spores
Position 2: species represented

This gives us: "S1 had the greater ratio of total number of spores to total number of species represented."

This answer emerges naturally from our data - S1 has both more spores (making the numerator larger) AND fewer species (making the denominator smaller), guaranteeing a greater ratio.