Arithmetic versus Logarithmic Graphs



Arithmetic versus
Logarithmic Graphs
1
100
2
200
3
400
4
800
5
1,600
6
3,200
7
6,400
8
12,800
9
25,600
10
51,200
11
102,400
12
204,800
13
409,600
14
819,200
15
1,638,400
16
3,276,800
17
6,553,600
18
13,107,200
19
26,214,400
20
52,428,800
21
104,857,600
22
209,715,200


Microsoft Excel Chart
Microsoft Excel Chart


For some types of analysis, particularly for long-term trend analysis, there is an advantage to using logarithmic charts. Look at the above two graphs - they plot the same exact data (the data on the left) - but look quite different.

The arithmetic chart makes the growth rate appear as so it is increasing. On an arithmetic graph, the vertical price scale from say 10 to 100 would be plotted with an "equal distance" as 1000 to 10,000, bringing about the distortion in the later years. Equal distance means that the vertical price scale shows an equal distance for each price unit of change.

Price plotted on log (logarithmic) scales show equal distances for similar "percentage" moves. 10 to 100 would be the same vertical "%" distance as 1000 to 10,000.

They say "a picture is worth a thousand words". It is however important that the picture accurately depicts what you are studying. For examples look at the Dow Jones Industrial long term charts.