Continuous scale definition:
On a continuous scale respondents rate the objects by placing a mark at the appropriate position on a line that runs from one extreme of the variable to the other. The form of the continuous scale may vary considerably.
A continuous scale should not be confused with a continuous sum. A continuous sum lets the respondent give a score to items which add up to a predefined total. This question type allows respondents to add a certain weight to each item.
Continuous scale example: