Have you watched the video? It almost explains everything about monopole antenna.
Your monopole is 60cm, then the first resonant frequency is 3e8/2.4=125MHz, this is theory which is assuming the wire has no thickness.
Now your wire has a thickness of 5mm, then it will introduce extra capacitance, this is commonly known as "stretching effect" (Watch the videos in post #2). So your real resonant frequency will drop for sure, and you see that as 115MHz against 125MHz.
Now when you check the radiation pattern, its really highly depending on your ground plane, the larger of the ground plane, the closer it will match the theory. However, if you say your ground is only 20*20*8cm. Then the theory prediction is not valid, since 20cm compare with 60cm is not a ground reflector at all, it will totally change your radiation pattern. (Watch the second video in post #2), I've shown you why this is happening and how to explain it completely.