Graphing (One of the Secrets of Good Experimental Science)

Graphs allow us to see trends in our data. Seeing trends is almost always how we understand anything. (If you notice that you're almost always miserable the day after you drink a lot of alcohol, and more miserable when you've drunk more, you will understand that drinking a lot is dangerous for you. You'll understand this even if you occasionally drink and then feel OK the next day.)

We will use “scatter plots,” or “y vs x plots.” In one of our first labs, we're letting a ball roll down a ramp and off the edge of a table, and then measuring how far away from the table the ball lands. So, we might choose to hold the ramp at a fixed angle and use the same ball, and vary only how far up along the ramp we've placed the ball. For each of these starting distances (These are our x's.), we record how far away the ball lands (These are our y's.) On our graph paper, we mark off, along the bottom edge, an x scale, and along the left-hand edge, a y scale. Then we make a dot at each measured pair of x & y values. We should see, I think, that the bigger x is, the bigger y is. That's a trend. (Hurrah!)

The nicest trend is a “linear” trend, in which we can draw a straight line through all the plotted data points, or almost through them, or through almost all of them, or almost through almost all of them. If that straight line goes through the “origin”, which is the point where x=0 and y=0, then we know that y is proportional to x. This means, if x is doubled, then y is doubled. For many experiments, you won't get a linear relationship between x and y. But you might get something very pretty if you try plotting y vs x-squared or y-squared vs x. You could try that. (But first think about which one you might want to square; do this by looking at your data.) Or maybe you should cube x or y. We may even do some experiments where the relationship between x and y is exponential; we'll save that for when you're more sophisticated.