5 is exactly halfway, that's not random enough either, that's out.

2, 4, 6, 8 are even and even numbers are round and friendly and comfortable, those are out too.

9 feels too close to the boundary, it's out.

That leaves 3 and 7, and 7 is more than 3 so it's got more room for randomness in it right?

Therefore 7 is the most random number between 1 and 10.