I am not sure if I should use plural or singular. I have many responses. I have a sentence like:
We summarise the responses data
We summarise the response data
Which one should I use?
the term is response data. The data received as responses to a survey, for example.
The data from the response is written as: response data. This is a common phenomenon in English. Results of the tests becomes: test results. These are not formal compound nouns. They are noun phrases using two nouns in order to shorten text.
1) View Survey Data When participants complete a survey, you can view the response data [bolding mine] on the Analyze tab of the Survey Builder. If you don’t see the information that you need on the Analyze tab, you can create a custom report type for survey responses.
REQUIRED EDITIONS AND USER PERMISSIONS
2) Exporting Response Data [bolding mine]
Regardless of whether we think of data as singular or plural, the word response in OP's example is an (adjectival) noun adjunct / attributive noun usage.
Attributive nouns are usually singular, as in He bought a car radio, but in certain contexts, such as They met in a singles bar, the plural form has become idiomatically established.
Things get more complicated because possessive forms can also be used instead of "unvarnished" (singular or plural) attributive nouns, such as New students must enroll on a beginner's course. Where in speech, no-one really knows whether that s represents a possessive apostrophe attached to singular beginner (the "Saxon genitive" form), or a morphological inflection creating the plural noun beginners. So there's often confusion about whether to write that apostrophe.
Not all permutations of singular / plural / possessive work in all contexts though - "acceptable" usages include, for example,...
1: a student workbook ("student" = attributive noun, "workbook" = head noun)
2: a students workbook
3: a student's workbook
4: a students' workbook (we don't write/say the implied possessive s after the apostrophe here)
5: a children's book (but this example shows that we do if the plural doesn't already end in s)
Doubtless some prescriptive grammarians would argue about the "correctness" of some of the above examples, but they certainly all occur. If this seems a bit daunting, you might find it comforting to know that Linguists have been trying to figure out what’s going on with singulars and plurals inside English compound nouns for at least 30 years ("Quick & Dirty Tips" from Grammar Girl).
Returning to OP's specific example, all the following are syntactically valid...
6: We summarise the response data
7: We summarise the data
8: We summarise the responses
9: We summarise the response
Strictly speaking, I think I could argue for "possessive" forms of the above (We summarise the response's data, We summarise the responses' data) being at least "syntactically valid". They might even be "idiomatically acceptable" in a contrived context where the response / responses have some other relevant "attribute" besides "data" - in which case the word data would likely be heavily stressed to accentuate the contrast with other attributes (such as fonts)...
10: We record the response data [content], but we don't record things like the font it was written in
I realise this isn't what most learners want to hear, but the awkward truth of the matter is that (style guides and opinionated grammarians excepted) there isn't really a consensus on which permutations of the above (singular or plural, possessive or not) are "syntactically valid" and/or "idiomatically established / acceptable". I think all you can really hope to do is learn which combinations are specifically not idiomatically acceptable for specific pairs of "attributive" and "head" nouns.
To pour a bit more "petrol on the flames", I'll just present this final example which I personally would consider "more or less" acceptable with the first instance of response replaced by plural responses OR by the singular / plural possessive forms response's, responses'...
We analyse the response method of collection, not the response data [content] itself
(Where the highlighting in that example indicated heavy spoken stress in the actual utterance - it's not me calling attention to those specific words because they're particularly relevant to my analysis.)
TL;DR: In OP's specific context, his first version is idiomatically unacceptable. Several other versions besides his second suggestion are acceptable, but this doesn't mean the same combinations of singular / plural, with / without a Saxon genitive will necessarily be seen as "okay" or not with different pairs of attributive + head nouns used in this way.