If the data are not ordered pairs, or the {min, max} are not in range, the function should just echo back what you initially typed into it.
This requires that no definition match under the given condition. For example
foo[data : {{_, _} ..}, min_, max_] /; max >= min := "some action"
Now if any part of this pattern including the Condition does not match the input is returned:
foo[{{1, 2}, {3, 4}}, 5, 2]
foo[{1, 2, 3}, 3, 5]
foo[{{1, 2}, {3, 4}}, 5, 2] foo[{1, 2, 3}, 3, 5]
A valid input evaluates:
foo[{{1, 2}, {3, 4}}, 3, 8]
"some action"
If your condition depends on the output of the function then you need a very specific use of Condition
lhs := Module[{vars}, rhs /; test] allows local variables to be shared between test and rhs. You can use the same construction with Block and With.
So maybe you want something like this:
Clear[foo]
foo[data : {{_, _} ..}, min_, max_] :=
Module[{mean},
mean = Mean[ data[[All, 2]] ];
mean /; min <= mean <= max
]
Now:
foo[{{1, 2}, {3, 4}}, 1, 5]
3
But:
foo[{{1, 2}, {3, 4}}, 5, 7]
foo[{{1, 2}, {3, 4}}, 5, 7]
And any other bad input is returned as-is:
foo["not good data", 5, 7]
foo["not good data", 5, 7]
Additional reading:
