Using graphs
What is the point of drawing a graph?
Sometimes it is easy to see
patterns in a set of results.
Time
(s)
1
2
3
4
5
Size
(m)
2
4
6
8
10
Sometimes it is not as easy.
Time
(min)
Temperature
(oC)
2
9.45
4
21.21
6
29.98
8
40.01
10
49.69
Graphs help us see patterns
Temperature graph
Is there a pattern in these results?
50
45
Temperature
(oC)
2
9.45
4
21.21
6
29.98
40
35
Temperature (degC)
Time
(min)
30
25
20
15
10
8
10
40.01
49.69
5
0
0
1
2
3
4
5
6
Time (min)
It is hard to see a pattern in this
set of results but if you draw a
graph then it is much easier to
see if there is a pattern.
With a graph it is very easy to see a pattern
that is not clear from the table.
Drawing the right axes for your graph
This can be quite tricky and will always depend upon the results you have
to plot. Three points to try and consider when working out the size of a
graph are.
Try and make sure the
graph fills the at least half
the page.
Make sure that all your
points fit on the scale.
Try and make the scales
go up in easy numbers
(like twos, fives or tens).
0
3.5
7
10.5
14
17.5
0
2
4
6
8
10
Drawing a best fit line
One of the most common mistakes is joining the dots up one by one.
Try and draw a smooth line near to as many points as possible.
This gives a very uneven line
and doesn’t really show if
there is any pattern.
This gives a much clearer line.
More about drawing a best fit line
When drawing a best fit line it is important to try and get the same
number or points above the line as below.
Each of the graphs below are the same
Line too low.
Line too high.
Line just right.
Even more about drawing a best fit line
Not all best fit lines have to go through the origin (0,0).
This line goes through the
origin but is not right.
A much better best fit line that
doesn’t go through the origin.
Spot the best fit line
In each of the cases below try and imagine where the best
fit line will go before it appears.
Best fit lines can
be curved.
Best fit lines can
change shape.
Best fit lines can
go down as well
as up.
Describing the pattern
If there is a pattern then it is important to try and describe it.
A
A increases as B increases up
to point X.
A decreases
increases as
asBBincreases.
increases.
After this point as B increases A
does not change.
B
Are all best fit lines as good as each other?
Different sets of results may show the same pattern but some sets of
results look ‘better’ than others.
In both cases the best fit line is exactly the same.
If the points are all close to the line of best fit then we say that they are reliable.
The results in both graphs show the same pattern but the results on the first
graph are more reliable than the results in the second.