The NYT posted reasonably detailed data for colleges about 5 years ago. Wake and Colgate were pretty comparable from a socioeconomic standpoint at the time, though the admissions landscape has changed since, as @Bill_Marsh noted above.
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Median family income: $221,500 Wake, $270,200 Colgate
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Average income percentile: 83rd Wake, 84th Colgate
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Students from top 0.1%: 2.7% Wake, 2.9% Colgate
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Students from top 1%: 22% Wake, 23% Colgate
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Students from top 5%: 49% Wake, 58% Colgate
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Students from top 10%: 61% Wake, 66% Colgate
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Students from top 20%: 71% Wake, 77% Colgate
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Students from bottom 20%: 2.3% Wake, 2.5% Colgate
I’ll add that Wake is arguably the most LAC-like of the national universities (yes, even more so than Dartmouth). In fact, it has fewer large classes (50+ students) than many of the elite liberal arts colleges.