Learn Russian: Мы пригласили того известного социолога, с которым вы анализировали данные. - We invited that famous sociologist with whom you analyzed the data.

They are actually in the accusative case because they are the direct object of the verb пригласили (invited). Remember that for animate masculine nouns (like a person), the accusative case endings are identical to the genitive case endings.

How does the relative pronoun которым work here?

The word который (which/who) matches the gender and number of the noun it refers to (the masculine singular социолог). However, its case is determined by its role in the second half of the sentence: "with whom". The preposition с (with) requires the instrumental case, making it с которым.

The word данные looks like an adjective. Is it acting as a noun?

Yes! Данные (data) is originally an adjective but functions as a noun in Russian, and it is almost exclusively used in the plural. Here it is the direct object of анализировали (analyzed). Because "data" is inanimate, its accusative plural form is identical to the nominative plural.

If I wanted to say "analyzed some data" using the quantifier несколько, how would that change the sentence?