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23 June 2011

GOOD GRAPHS: a sequel to BAD GRAPHS

I do have a couple more BAD GRAPHS.  These are utterly obvious, so I won't post pictures:

(BAD GRAPH #9) Failure to draw a best-fit at all means the slope cannot be taken properly
(BAD GRAPH #10) Failure to label the axes of the graph and to include units means the graph is worthless.

Now that we've washed our hands of those, it's time for some GOOD GRAPHS. 

GOOD GRAPH #1: y-intercept is clear

The y-intercept may have physical significance.  Often it's useful to be sure that the y-intercept can be recognized by inspection.  However, this is not the only GOOD GRAPH.

GOOD GRAPH #2:  You don't HAVE to start scaling from the origin
This graph is just dandy.  In fact, there has been at least one AP question (2005 problem 6) on which the scale could not have begun at the origin in order to scale the data to at least half a page.  Students will attempt to demand a hard-and-fast rule about scaling graphs from the origin, but such a rule does not exist.  The scaling of a graph depends on the circumstances of the data.

One warning, though, while we wrap up today's feel-good episode of GOOD GRAPHS:

GOOD GRAPH #3:  If you don't scale from the origin, be careful about the y-intercept.

This graph is quite fine.  Proper labels, scale, points, and best-fit.  However, gotta be careful... the circled point looks to be the y-intercept.  But no!  The horizontal scaling starts from .01 kg.  The actual y-intercept has to be extrapolated.

BAD GRAPHS:  Summation
I've created this series of posts on request from several teachers.  Our students come to us with essentially zero experience making useful graphs of experimental data.  We have to bust all sorts of misconceptions. 

Ideally, we bring our class to an understanding of the purpose of an experimental graph.  A graph communicates not just the result of the experiment, but also the data acquired, the calculational methodology behind that result, the precision of the result.  A scientist who says merely "From my data, I conclude that the density of this oil is 0.9 g/ml" must be taken at his word.  It is so much more transparent to say, "The density of this oil is 0.9 g/ml, as determined by the reciprocal of the slope of this graph here."  Of course, a BAD GRAPH undermines this point.

It's great if you can get your class to see why they should not make BAD GRAPHS.  But the other usefulness of this series of posts is more functional.  When your student tries to argue that his graph is okay, and when he's not listening to or believing your rationale, you can point him here:  "Johnny, look at BAD GRAPH #5.  That's why you're going to redo the graph you submitted."

1 comment:

  1. How then do we find the intercept when we are not starting from the origin?

    ReplyDelete