City F C
Amsterdam, Netherlands 73 23
Atlanta, USA 88 31
Dhahran, Saudi Arabia 100 38
Moscow, Russia 48 9
New Delhi, India 84 29
Sydney, Australia 53 12
Vladivostok, Russia 62 17

The usual convention is to put the variable that is being
controlled on the horizontal axis, and the response on the vertical
axis. A common example would be a graph showing how the
temperature varied throughout a school day.
Here time is on the horizontal axis (we can’t
control time, but it
controls everything else), and the temperature
on the vertical axis.

In the C and F problem, we can chose our axes any way we like, since we don’t know which is “cause” and which is “effect.” (This example is a little unusual, in that the data is given in an order that has nothing to do with the C or F values. This doesn’t prevent us from looking for a relationship between C and F). So let’s choose the horizontal axis to be the “C” value and the vertical axis is the “F” value. Here’s what this looks like for Amsterdam:
Repeating this process for each city gives a set of dots.
It’s possible we would have to stop here. For example, if you
were to graph the high and low temperatures at each city this way,
you would just get a cloud of dots.
The two values do tend to go up and down together, but no
strong pattern emerges.

However, in the case
of the “F” and “C” data we see a strong relationship — in fact,
we can draw a line that goes very close to all of them.

Note that I have drawn a single line, rather than many segments that connect the dots. This means that I think there is a simple relationship (the line) and that the data may be slightly inaccurate for some reason (in the present case, they have been rounded off to the nearest degree). It generally is proper to draw the smooth curve that goes near the points in preference to a bumpy one that goes right through them.
The line is very interesting, because it proposes that there is a relationship that goes beyond the data at hand. It predicts that if we ever find a city where the “F” value is 41, the “C” value will be 5.
The line appears to be straight, and for this example it should be. However, we should realize that over short ranges of data, a smooth curve may look straight even though it really isn’t. Going beyond the range for which data is available can be dangerous for this reason.
When you make line graphs of data you have taken, they might not look as pretty as this. Sometimes it is hard to read the measuring apparatus accurately; sometimes you read the number wrong or wrote it down incorrectly or misplotted the point. Making a line graph is a good way of discovering errors of this sort. However, if you are careful in measuring, you should have confidence in your data; don’t assume that the line has to be straight or smooth. In the end, what you have measured is reality; if it looks differently than you expected, it may mean that your expectations were wrong, or that what you measured differs in some way from what you thought you were measuring. Graphs that “do the wrong thing” can be very interesting, because they hint at a way that nature is different from our understanding of it.
Happy graphing! To help, we include three pieces of graph paper that you can print out and use. 10 x 10 15 x 15 20 x 20
Graphs can also be constructed using Microsoft Excel. Click here for an example with brief explanation.
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