# Best way to display ranges where end range is inclusive

I have a table with one column displaying a range of values where the end range value is inclusive, but the start range value is exclusive.

I'm having a hard time figuring out how to succinctly and effectively convey that in the table.

This is what I've settled on so far:

``````| Average Usage | Average Score |
| ------------- | ------------- |
| 0 - 1 days    | 23.1          |
| > 1 - 2 days  | 120           |
| > 2 - 3 days  | 312           |
| > 3 days      | 521           |
``````

Can anyone think of a better way to get this across?

If the expected audience is math savvy, this is how you could represent an interval:

``````| Average Usage | Average Score |
| ------------- | ------------- |
| (0 - 1] days  | 23.1          |
| (1 - 2] days  | 120           |
| (2 - 3] days  | 312           |
| > 3 days      | 521           |
``````

Parenthesis denote exclusiveness, brackets inclusiveness. https://undergroundmathematics.org/glossary/interval-notation

Then, of course you could

``````| Average Usage | Average Score |
| ------------- | ------------- |
| ≤ 1     days  | 23.1          |
| ≤ 2     days  | 120           |
| ≤ 3     days  | 312           |
| ≥ 4     days  | 521           |
``````

Provided you are not allowed to add natural language, otherwise you could insert "up to 1" or "from 1 to 2" or the likes.

But if that table is made of real data, couldn't it be expressed as something like this?:

``````| Average Usage | Average Score |
| ------------- | ------------- |
|   1 day       | 23.1          |
|   2 days      | 120           |
|   3 days      | 312           |
|   4 + days    | 521           |
``````

Not really advocating the 4 +, just that (0-1] could be 1 and (1-2] is 2 if we are treating days as basic units.

• The expected audience isn't math savy, but that'd be a good idea if so. I think your other two examples are too vague. The second example a user might think that people with average Usage <= 1 days would be included in the <= 2 days category as well. And the last example a user might think the same or be confused about specific cases (like if a user with 1.9 days be categorized rounded up or down). Oct 6, 2017 at 19:35

Have you considered defining the range by using precision, like this?

``````| Average Usage      | Average Score |
| ------------------ | ------------- |
| 0.001 - 1.000 days | 23.1          |
| 1.001 - 2.000 days | 120           |
| 2.001 - 3.000 days | 312           |
| 3.001 - ∞ days     | 521           |
``````
• Seems cluttered and what if someone has `1.0001` average usage? Oct 6, 2017 at 17:52
• Increase your precision... Try `1.000000000000000000000000000000001 - 2.000000000000000000000000000000000 days` ;) Oct 6, 2017 at 18:42

I'd use :

``````| Average Usage    | Average Score |
| ---------------- | ------------- |
|   1 day          | 23.1          |
|   2 days         | 120           |
|   3 days         | 312           |
|   4 days or more | 521           |
``````

And include a note that "part-days" are rounded up - which is what a lot of people would assume anyway.

We decided to do like this, for ranges that are multiple of 100:

``````<100
100-200
200-300
300-400
>=400
``````

This way, you just use two symbols, you avoid adding a lot of characters and the first and the last contain enough information to allow the user understand how to interpret the rest of the ranges. This example is of course for left end included and right end exluded.