I have 6 different data sets which I need to compare. I am able to compare five of them by plotting graphs, but when I include the sixth dataset, it tanks the other datasets because while the maximum value of the other five datasets is in thousands, for the sixth dataset, the maximum values is in billions. So I get one straight line for the first five datasets and some graph for the sixth. Therefore, I am unable to compare the first five together with the sixth. How should I visualize the data so that I can differentiate between them.
That would depend on what you're trying to show. If it's just the means being different, then that IS the graph you want because it shows that one of the data sets has a very large mean. Just like statistical questions, visualization questions should provide the questioner's objective as well for them to be well answered.
If you're trying to show distribution, and the poor five other variables from the five corresponding datasets are being squished together, then try first standardizing the values into z-score, then visualize them. The picture will be much better. This would work on most tools such as scatter plot, error bar plot, and box plot.
Standardization can be generalized into unit as well. If some of them are in milligram and one is in kilogram, unify them to either one. If some of them are in Japanese Yen, and some of them are in US Dollar, convert them into some common currency equivalence.
If your audience can take some mathematics, then you can try performing some transformation to bring the values closer. E.g. Logarithmic transformation can be a potential candidate.
Use a broken y-axis
For graphs like bar chart, histogram, etc. you can also consider a broken y-axis, it allows the user to omit a chunk of the graph so that most of the graphical area can be preserved for the shorter bars.
Use animated graphics
Animate your graphics in a way that when the first 5 data sets are being shown, you keep the frame to show their details. And when the 6th is introduced, you can zoom out to show the contrast.
Be a bit "out there" and use some creative graphics
It's not a good advice according to Wilkinson's Grammar of Graphics, but I'll just suggest that anyway. If you turn the billions into area or volume on a graph, the contrast will be dampened. It'd still be giant, but not as much when they are expressed in length. It's probably going to be a disaster, but a job done is a job done.
Rethink if visualization is the right tool
If most are in thousands and one is in billions, I can't think of any reason to downplay it because it's perhaps the major or even only thing that deems interesting. Instead of tweaking them to go with each other on a graph, I'd suggest also reconsider if visualization is the way to go. You can also consider tabulation or text. Numerical expression is actually a great tool, for each 10-fold increase, the expression only increase by one digit; a very efficient tool to deal with numbers with huge differences.
Depends upon what you are trying to communicate. If you are trying to highlight differences or similarities in trajectories over time, say, then a logarithmic scale could be helpful.
Another option is to just use two graphs, one with the five similar data sets and one with the sixth data set. It's hard to say without more information.