Application Variables always present themselves as "Text", so depending on the result the formula is meant to display, you would need to indicate the format in the Formula field you're using to call upon that app variable by name - for the following example we'll say your app variable name is "Variable"
if you were to want to use this app wide variable on a form, you would need to use a formula type field, and in that formula you need to indicate the format the variable should result in, followed by the the variable name enclosed in brackets, just as you would when referencing any other field on that form.
Ex. ToNumber([Variable])
or ToText([Variable])
or ToDate([Variable]) etc.
Hope this helps, although I'm still really curious about your specific use-case for the app-wide formula variable.