In a set of 24 positive integers, exactly 12 are less than 50 and the remaining 12 are all greater than 50 (none equals 50). Compare:
Quantity A: The median of the 24 integers
Quantity B: $50$
The median of 24 values is the average of the 12th and 13th values when sorted.
12 values are below 50 and 12 values are above 50 (none equals 50).
When sorted, values 1–12 are all less than 50, and values 13–24 are all greater than 50.
The 12th value $< 50$ and the 13th value $> 50$.
Median $= \dfrac{\text{12th value} + \text{13th value}}{2}$.
This could be less than, equal to, or greater than 50 depending on the specific values.
For example: 12th value $= 49$, 13th value $= 51$ → median $= 50$ (equal). But 12th $= 1$, 13th $= 51$ → median $= 26 < 50$. The relationship cannot be determined.
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