Median and mode conjecture for crosscap number and unoriented genus of prime alternating knots

Let $c$ be the crossing number of a prime alternating knot. For each $c$, consider the distributions of its crosscap number $4\gamma$ and unoriented genus $\Gamma$ among all $c$-crossing prime alternating knots.

Median and mode conjecture. For any $c\geq 12$, the medians and modes for $\gamma$ and $\Gamma$ among all $c$-crossing prime alternating knots equal

$$\left\lfloor\frac{c}{2}\right\rfloor-1.$$

This conjecture extrapolates a pattern observed in the tabulated data; its status is open, and no proof or disproof is supplied.