Based on the discussion with Spieghalter, I found three main examples that give a good representation of the "theory to data" spectrum.
On the far left of the spectrum of "pure theory", Cromwell's Law is a good representation of a pure theory. Cromwell's Law states that when dealing with probabilities unless it is a logical statement, humans must assign the unknown a probability. An example is that we believe the probability of the positioning of a bottle landing to be 1/3 upright, 1/3 downright, or 1/3 sideways. However, there is a really small chance that the bottle lands in a diagonal manner due to some force of the bottle or nature that can't be ignored despite how unlikely it might be. Therefore, Cromwell's Law states that you must assign some probability for those unlikely leaning towards improbable outcomes in the case that it does occur since it isn't impossible. Cromwell's Law is a pure theory because there is no feasible way to test his theory because it banks on the idea of unknown or improbable events occurring which is rare. Thus, his law is simply a way to think about probability. On the far right of the spectrum of "just Data", ancient star-tracking is a great example. In the past, there were people who noticed that stars tend to be in a certain location. With this, these people began to draw those stars and their relative location to other celestial bodies; however, aside from this data collection, no theories and hypotheses were explained on why these stars may be there. Thus, star-tracking was a pure data activity. Note that this doesn't mean people didn't use the data from these tracking to come up with laws and theories, but the act of writing down the geographical positioning of these stars, themselves, are pure data. In the middle of the spectrum with both aspects of data and theory is the Gaussian distribution. The Gaussian distribution is a statistical model that shows that many data will fall near the mean of the data instead of the extremes of the data, creating a bell-shaped model. The Gaussian distribution has aspects of theory because of the logic of the distribution itself. The distribution simply suggests that logically if there were 1000 outcomes in a situation, there would still be a 1/1000 possibility that it is a certain outcome despite the model showing that a vast majority of outcomes fall in the mean. The reason this occurred is the outcome themselves are independent of other outcomes; therefore, the likelihood of you having outcome #51 is the same as the likelihood of you having outcome #812 because you don't know where those outcomes fall in the model. Therefore, the Gaussian distribution is simply a way of thinking about probability; however, the distinction between the Gaussian distribution and Cromwell's law is that there is data to back up this model distribution of outcomes. There is a toy that holds 100 small beads and allows you to flip it around so that you can see where the small beads end up at. The vast majority of the time, the beads fall in a manner that creates the shape of a bell. While each iteration of this simulation creates a different variation of the bell, it still follows the logical manner that Gaussian predicted which shows that the Gaussian distribution has aspects of data collection within it.