# Designing legends to handle overlapping/sequential values

I'm moving this question from gis.stackexchange to UX, as UXD's, I think, are better equipped to answer this question. I have always struggled to come up with a great solution to handle quantitative intervals or dataset classifications in a map legend where the numbers are non-integer and sequential.

For instance: here is the ArcGIS default legend, which is a bit gaudy and what's the real cuttoff? .55000000001 or .5501 or what?:

Set notation { x| 55 < x <= 67} would work as well, but I'm worried that people won't always understand these methods.

Anyway, I'd like to hear your solutions to this to help figure this out.

EDIT: My question is not on classification - there are no overlapping values in classifying the data, my question is how best to design the legend labels

Totally see your point in the second instance, but in the first, isn't the problem, as you stated it, endlessly recursive?

[0-.999],[1-1.999].

"Ah, but what if I have a value of 0.9992?"

Ok, [0-.9999],[1-1.9999].

"Ah, but what if I have a value of 0.99923?" : /

You have to draw a line somewhere.

Where exactly you draw that line and how thoroughly you explain it, depends entirely on the situation.

Delivering results of analysis to Molecular Biologist PhDs - it's probably worth being decisive and clear in your categorization rationale.

Delivering poll results on network news - not so much.

• This is probably the best answer that anyone can give. Certainly the audience is the most important thing to consider. In this case, it's actual election data for officials and staff to help plan campaign strategy - But whether it is designed for experts or general public, I am looking for a 'sweet spot' in legend design that leaves out all ambiguity for all audiences. I'll leave the question open for awhile for someone to blow my mind Apr 26, 2016 at 21:25

Taking continuity into acount I would go with something like this:

• Good Point - I like this May 12, 2016 at 19:01

It doesn't matter where the cutoff is. 55.0000000000000000000000001 is still over 55.

As for how to count 45-55 vs 55-65; you generally start counting at whole integers. We tend to start (things of unknown length) however it's easy, because we can't yet know where the end is, so you can't adjust for the unknown end. This influences our thinking so that we tend to start at integers regardless if we know the end, unless otherwise specified.

You don't specify 45-<55, 55-<65 or 45>-55, 55>-65, so by default it's the former. Which means that 55 would be placed under 55-65.

Why your example uses 'unclear' cutoffs is truncation. The cutoff in this case would be .55005. .55004999999 gets rounded down to .5500, .55005 gets rounded up to .5501.

They're not so much overlapping, they simply are rounded.

A plurality winner would be filed under tie-55.

• So you would say #2 for the legend labeling strategy? I only used 3 examples on one image due to low reputation, but I could have used many more examples of labeling strategies, such as: tie - 54.9, 55 - 66.9, 67-100 or given actual breaks like: tie - 54.7, 56.2 - 66.8, 71.1 - 100.... I think my question was a bit misleading, I have edited it. Apr 26, 2016 at 20:58

A general comment (but one that doesn't fit well in the comment section with links etc before anyone gets on their high horse) is that inequality symbols >, <, >=, <= get introduced in maths syllabuses a lot earlier than interval notations so I'd expect more people to understand >TIE - 55 than (TIE -55] and >55 - 67 than (55 - 67] - I remember using >, >= etc on numbers in junior school

e.g. Inequalities covered at UK KS3 (Kids aged 11-14): http://www.bbc.co.uk/bitesize/ks3/maths/algebra/inequalities_simultaneous/revision/3/

and Interval notation covered at undergraduate level syllabuses: http://math.hawaii.edu/~don/syllabus_134_fall14.pdf https://www.unr.edu/Documents/provost/assessment/core/approved%20core%20courses/CO2/MATH%20126e_silver_syllabus.pdf