Histograms showing the distribution of radius for two individual grains

Creating a histogram by hand as we did in class is educational (avoiding the black box syndrome), but luckily there are a variety of tools that make for much quicker and better results. The middle and right grain images in your exercise were pasted into a digitizing program, and x and y coordinates for the grain center (selected by eye) and for semi-regularly spaced points along the grain margin were obtained simply by clicking away on the positioned mouse. The resulting values were pasted into an Excel sheet, and then radius values were calculated, and a histogram made of the resulting values. The two resulting images are shown below, and from start to finish the exercise took about 40 minutes (mainly for digitizing).

Below is the image used in digitizing.

What can we learn from this exercise?? First, a number as simple as the radius of an individual grain of sand is more complex, and can be considered as representing a family of numbers. Second, the shape of the histogram, the population distribution, of those numbers is different for different grains, and is often not symmetric (and is not 'normal'). We can then ask the question, why are the distributions different - what information is in this data? Some thought suggests that the histogram reflects in some manner the grain shape. This opens all sorts of new avenues of thought.

@Harmon D. Maher Jr., 2010.