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I totally understand why the data might look scattered at first glance. Key Insight: negative correlation does NOT mean a perfect downward line — it just means that, overall, as one variable increases, the other tends to decrease.
Let me sort the data by self-check unlimited lanes so the pattern becomes clear:
0 unlimited lanes: Store D (50.5), Store G (38.8), Store I (56.7) — average age around 48.7
4 unlimited lanes: Store A (34.5), Store C (32.0), Store E (42.5) — average age around 36.3
6 unlimited lanes: Store B (28.4), Store F (34.6) — average age around 31.5
8 unlimited lanes: Store H (29.9) — age 29.9
Now look at the group averages as unlimited lanes increase: 48.7 → 36.3 → 31.5 → 29.9. That is a clear downward trend!
Yes, there is scatter within each group — for example, at 0 lanes, ages range from 38.8 to 56.7. But correlation measures the overall tendency, not perfection. Think of it this way: if you plotted all 9 points on a graph with unlimited lanes on the x-axis and age on the y-axis, the best-fit line would clearly slope downward. That is what makes it a negative correlation.
The GMAT trick here is that you do not need to calculate a correlation coefficient. You just need to observe: stores with MORE unlimited lanes consistently tend to have LOWER average customer ages, and stores with FEWER unlimited lanes tend to have HIGHER ages. Every single store with 6 or 8 unlimited lanes has a below-average customer age (under 38.66), while every store with 0 unlimited lanes has an above-average or near-average customer age. That overall pattern is enough to confirm a negative correlation.
Answer: True, True, False
Let me sort the data by self-check unlimited lanes so the pattern becomes clear:
0 unlimited lanes: Store D (50.5), Store G (38.8), Store I (56.7) — average age around 48.7
4 unlimited lanes: Store A (34.5), Store C (32.0), Store E (42.5) — average age around 36.3
6 unlimited lanes: Store B (28.4), Store F (34.6) — average age around 31.5
8 unlimited lanes: Store H (29.9) — age 29.9
Now look at the group averages as unlimited lanes increase: 48.7 → 36.3 → 31.5 → 29.9. That is a clear downward trend!
Yes, there is scatter within each group — for example, at 0 lanes, ages range from 38.8 to 56.7. But correlation measures the overall tendency, not perfection. Think of it this way: if you plotted all 9 points on a graph with unlimited lanes on the x-axis and age on the y-axis, the best-fit line would clearly slope downward. That is what makes it a negative correlation.
The GMAT trick here is that you do not need to calculate a correlation coefficient. You just need to observe: stores with MORE unlimited lanes consistently tend to have LOWER average customer ages, and stores with FEWER unlimited lanes tend to have HIGHER ages. Every single store with 6 or 8 unlimited lanes has a below-average customer age (under 38.66), while every store with 0 unlimited lanes has an above-average or near-average customer age. That overall pattern is enough to confirm a negative correlation.
Answer: True, True, False
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