Bad Graphs part II: don't force the best-fit through the origin

In today's episode of Bad Graphs, we begin with another poor scale.

BAD GRAPH #4:  Scaled to less than one-quarter page

As you can see -- or maybe you can't, it's so small -- these data points are plotted correctly, but in a teeny weeny portion of the page provided.  A proper graph takes up well over half the available room on the page.  The standard for credit on this particular AP problem (2010 B2) was for the graph to take up more than 1/4 page.  Scaling across a whole page is a skill that must be taught -- it does not come naturally out of math classes.

BAD GRAPH #5:  Can't see the data points without a magnifying glass

If you want to get extra-technical, the size of the data points on the graph should reflect the experimental uncertainty in each quantity measured.  That is, if you could measure to the nearest milliliter, than the data points should be as big as half of a box in the vertical direction.  (And if large uncertainty would make the points ridiculously big, then you're supposed to use error bars.)

For the purposes of AP exam questions or labs within my course, all I ask is that the data points be clearly visible, as in all of the other BAD GRAPHS shown in this post.  The graph above, though, shows itty bitty dots and a nice best-fit.  Sure, the best-fit will yield a reasonable slope, but without easily seen evidence of where that slope came from.

BAD GRAPH #6:  best-fit line forced through the origin

A best-fit line should reasonably indicate the trend of the data.  There is no one "best" best-fit, but rather a range of allowable best-fits.  I've occasionally had my class draw the steepest possible best-fit, then the shallowest, and note that the value of the slope is somewhere between these two extremes. 

The problem with the graph above is much more subtle than with some of the other BAD GRAPHs.  This student has drawn the best-fit line by starting at the origin of coordinates, and only then trying to approximate the trend of the graph.  Problem is, for one thing, the origin is not a special spot on the graph.  The point (0 kg, 0 m³) is no more important than the point (.04 kg, .000054 m³).  Even in the case where (0,0) is a data point, it's a data point like any other.  Would you insist that the best-fit line always go through the third data point?

In this particular experiment from the 2010 AP exam, the y-intercept of the graph was explicitly non-zero.  (In fact, the last part of the question demanded students to figure out that the y-intercept represented the volume of fluid displaced by the floating cup alone, without any additional mass.)  Forcing the best-fit through the origin not only artifically steepens the graph's slope, but it obscures the physically meaningful y-intercept.

Of course, forcing best-fits through the origin isn't always as subtle.  Trust me.  When we graded this problem, we saw the not-totally-unreasonable version above, but also we saw plenty of these:

BAD GRAPH #7:  Curved to get to the origin

 Yuk.  But this one takes the cake...

BAD GRAPH #8:  Forced through the origin that isn't even the origin

It's perfectly acceptable, and sometimes desirable, not to begin an axis at zero.  However, you gotta recognize that what looks like the origin isn't necessarily the actual origin, in that case.  This grapher would have been fine, except for forcing that line through the origin that, after all, isn't the origin.  Boux.

One more set of BAD GRAPHs tomorrow.  But I promise, I'll include a couple of GOOD GRAPHs as well.