Is a Likert scale ordinal or interval?
It is important to clarify the difference between the item scale and the total score scale. The item scales are ordinal as they represent distinct ordered categories. While a number is typically assigned to these categories, the numbers represent the first, second, third, etc., ordered categories.
The Likert scale represents the range of all possible total scores, with the total score itself comprised of the sum of the item scores. The Likert scale can be treated as an interval scale, under certain conditions. This was an important element of Likert's contribution. While these total scores are discrete and not continuous, under the Likert perspective, these total scores are treated as adhering to an interval scale.
To recap: Likert item scores, ordinal. Likert scale as the sum of Likert item scores, interval.