Are there significant differences in people's hearing responses or do majority have vary similar responses?
Anybody have links to papers or sites showing statistical data of people's hearing response?
Sure. This has been studied extensively by Harman when it comes to speaker evaluation. The answer is that we are remarkably similar to each other when it comes to such assessments.
Please see the peer reviewed Journal of AES paper,
Differences in Performance and Preference of Trained versus Untrained Listeners in Loudspeaker Tests: A Case Study, by Dr. Sean Olive
The data and statistical analysis in the paper is quite extensive. But here is the summary data you are asking about:
The horizontal axis is the different group of listeners performing the double blind listening test of four different speakers. Horizontal axis is different listening groups. HAR for example is Harman's trained listeners. Reviewers is what it says: audio magazine reviewers.
The vertical axis is the preference score. As we see the scores for speakers within a group does not change from any other. For example speaker "M" is the lowest graph and is rates as such by every category of listeners.
There are variations on how harsh the scoring is done (e.g. Harman listeners are much more ruthless and give much lower scores to poor speakers), but overall ranking does not change.
In all, 268 listeners participated in the test. Here is the high-level breakdown:
In a follow up test conducted on younger listeners by Dr. Olive, similar outcome was seen:
Note that the only way to achieve these results is by hiding the identity of the loudspeakers. Once people see the product, preferences shift due to prejudices regarding brand, looks, design, etc.
So as a whole, we like similar characteristics in loudspeakers which bodes well for designings speakers that appeal to large group of people. It may seem non-intuitive at first but if you think about the fact that vast majority of us like chocolate, and steak, it is not that hard to imagine it being correct

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Now your question was about headphones. Again Dr. Olive (and Todd Welti) have conducted good research there. See AES paper
The Relationship between Perception and Measurement of Headphone Sound Quality
This double blind listening test paper is also quite extensive. The results here are not quite as cut and dry as loudspeakers:
We see some agreement among listeners but also exceptions. Authors dig further and find that some listeners are just not consistent in their scoring. But also, rated headphones on other factors such as the fit.
Indeed that remains a problem with studying headphones as it is impossible to conduct a true blind test. Even though headphones were placed on the listener head by a proctor, listeners quickly learn which is which based on feel of headphones on their heads and that can and likely biases their scores. There is also the inconsistency of measurements (to correlate with subjective results).
Here is part of the conclusions of note:
#4 matches what the research says about loudspeakers. That smooth (not flat) frequency response is desirable.
Probably more than you wanted to know but I figured better be more complete than not.
