After taking all the undergraduate courses in statistics, I enrolled in a graduate course in mathematical statistics at Columbia with the eminent Harold Hotelling, one of the founders of modern mathematical economics. I walked out of the Hotelling course, and out of the world of statistics, never to return. Statistics, of course, is far more than the mere collection of data.
Statistical inference is the conclusions one can draw from that data.
After taking our sample or samples, we have to find a way to make statements about the population as a whole. For example, suppose we wish to conclude something about the average height of the American male population. Since there is no way that we can mobilize every male American and measure everyone's height, we take samples of a small number, say 500 people, selected in various ways, from which we presume to say what the average American's height may be. The normal curve is a symmetrical, bell-shaped curve familiar to all statistics textbooks. These precise figures are arrived at simply by assuming that all samples are distributed around the population according to this normal curve.