Sample Size Justification

‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ The mean tells us that for 3x3, the average of all of my times is 22.9 seconds. This makes sense as chronologically, I started off being able to solve a cube in 30-40 seconds, and can now solve one in roughly 15 seconds. Near the chronological middle between then and now, I was able to solve 3x3 cubes for over 20 seconds. The median for 3x3 is 20.9 seconds, which relatively speaking, is a very similar value to the mean. Both the mean and median for 3x3 show the gradual improvement of my times across official solves.

‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ As for 2x2, my mean time is 7.9 seconds, which does not exactly correlate the midway point of my solves. Due to the more abrupt drop-offs in my solving times as seen in the scatter plot below at the 11th, 22nd, and 33rd solves, this mean is mainly being pulled up by my earlier solves from before the first abrupt drop-off. Likewise, it is also being pulled up by the extreme outlier time of the 41st solve. This time was caused my one of the pieces of the cube during that solve having accidentally been misaligned in a way that made it impossible to solve, which resulted in a lot of confusion where I ended up having to take out the piece and reinsert it in order to be able to solve the cube. Due to these reasons, the median for 2x2 solves is in this case the superior way of fairly representing my overall average. As for the mode, it does not mean much here. However, it is an interesting coincidence that the 2x2 times have a mode due entirely to the fact that I ended up solving one in 8.18 seconds twice.