In perfectly symmetrical distributions is the distance from smallest observation to Q2 the same as the distance from Q2 to the largest observation?

Yes, in perfectly symmetrical distributions, the distance from the smallest observation to the median (Q2) is equal to the distance from the median to the largest observation. This symmetry ensures that the distribution is balanced around the median, making the two distances identical. Consequently, the values are distributed evenly on either side of the median.