Axis scale for scatter plots

Question

I'm trying to create a specialized scatter plot, which functions similar to Excel's scatter plot. I'm having problems determining what the min and max values should be for the axes. I would like the program to determine from the input data what the initial min and max values should be on the x- and y-axis, the user can adjust later.
So, I don't want the program to just look at the maximum value imported and round up. For instance, data = {523.7, 514.4, 271.8, 128.5}. The max value is 523.7, round up to 524. Instead, I would like to program to make 600 the largest value on the axis, because that makes it nice round number for the user to view the dataset.
Then, I thought it really depends on the range of the data. For instance, data = {523.4, 523.8, 523.2, 522.8, 523.9}. Here, the range is very small, so it doesn't make sense to have 600 the largest value on the scale. The largest value should be 524 or 525, and the small value on the axis scale should be 521 or 522.
Has anyone else ever worked with this problem, or have a good solution? I would really appreciate it, I've spend way too many days working on this.
Thank you,
Joe

Answer 1

This is off the top of my head and based on a slight variation of your data.
data: 52.34, 52.38, 52.32, 52.28, 52.39
min=52.28 max=52.39 range=0.11
Looking at the range we see it is "on the order of" 0.1. Ie, it is closer to the next lower power of 10 (0.1) than it is to the next higher one (1.0). So we round min down to the next lowest multiple of 0.1 (52.2) and round max up (52.4). 52.2 and 52.4 can serve as the nice numbers.
The range is just a little bigger than a power of 10, so it might be a good idea to check what happens when it's a little less.
data: 135 226 141 143 etc
min=135 max=226 range=91
range is on the order of 100, and the nice numbers are 100 and 300.
As a variation on this strategy if we always find the power of 10 below the range (10 in the second example) we get a tighter fit but the numbers are slightly less nice - 130 and 220.
(I'm pretty sure I've seen - and used! - some java software from the Internet somewhere to find the best scale for axes, so it might pay to look around)
Had to edit my second example and, while I was waiting, found what I have used for this sort of thing: http://geosoft.no/software/index.html (The NiceNumbers class - it finds numbers along a range suitable for major and minor "ticks" but, if memory serves me correctly it extends the range so that the ends are nice too.)