Questions (and answers) about graphing

In the past, people have asked me many questions about how to make a good graph.  If you’ve got questions, maybe one of these will help.

Question:  Do the lines on graphs need to go through the origin?

Answer:  Not necessarily.

Consider my weight (again).  When I was 30 I weighed 85 kg.  When I was 20 I weighed 80 kg.  And when I was ten I weighed 35 kilograms.  These all make sense, right?  Unfortunately, for this graph to go through the origin, I’d have to draw a point that shows (0 years old, 0 kilograms), which indicates that I weighed nothing when I was born. Not so awesome, eh?

That’s not to say that some graphs can’t go through the origin.  If I’m graphing the distance I’ve walked vs. time, it would be absolutely vital to draw the line through the origin because the distance I traveled in zero time would obviously be zero.

Question:  What happens if the data in a graph don’t fit a straight line?

Answer:  It depends.  

If the data clearly don’t show a straight line, there could be many different causes:

  • The data follow a curve.  If the data don’t follow a line but do seem to curve in some fashion, that might be the trick.
  • The data have some sort of discontinuity.  It could be that there isn’t one line, but two lines in the data.  One example would be if I were to make a graph of my weight over a timespan of 40 years… and at year 20 my arms and legs were both cut off in a terrible accident.  Clearly, it would be appropriate to have two separate lines, because something interesting and meaningful has happened to warrant it.
  • There’s no relationship between the independent and dependent variable.  If I’m making a graph that shows the effect of my burping on the temperature outside, we wouldn’t see any straight line because the variables aren’t related.

Question:  What if my teacher told me to make graphs differently than you described here?

Answer:  It’s probably not a big deal.

There are many different ways of doing the same thing, and I’d guess that your teacher simply prefers the data to be shown in some slightly different format.  However, if your teacher tells you something crazy like “use bar graphs” or “always go through the origin”, he or she is wrong.  Though, for the sake of your grade, I’d probably keep that to myself.

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