Subject in the sentence

The most common kind is the curves.

The data is pairs of y and x.

Are subjects of these sentences kind and data, which means that is is the predicator (not are), right? I am confused by the following plural (but these are objects, right?). Thank you

Solution 1:

Until the question is closed (it is a duplicate of Is "data" treated as singular or plural in formal contexts?), consider this:

Data singular or plural is now a matter of choice.

Data is the Latin plural of datum, so your teacher is fundamentally wrong.

However, usage has shifted because of general ignorance of Latin, to use data as singular.

Data - Usage: In Latin, data is the plural of datum and, historically and in specialized scientific fields, it is also treated as a plural in English, taking a plural verb, as in the data were collected and classified. In modern non-scientific use, however, it is generally not treated as a plural. Instead, it is treated as a mass noun, similar to a word like information, which takes a singular verb. Sentences such as data was collected over a number of years are now widely accepted in standard English

Oxford Lexico

We have to move with linguistic shift, so data is now often used as singular; in that sense your teacher is correct.

The important thing is to use one or the other consistently in whatever is written. Mixing them in the same prose is a mark of poor style and sloppy thinking.