Suzied that is a very useful explanation - sadly probably not to be read by those taking offence where no such thing is given.
I do not believe that the "lies, damn lies" is helpful as it proposes and untruth. Statistics, those inanimate figures, cannot lie, only people can. So it is the way people use the statistics and why they use them in that way that needs careful watching not the statistics themselves.
Simplified the stats relating to education and voting in the referendum are:
Of those who left school at 15/16 - 3 out of 4 voted 'out'.
Of those who achieved the equivalent of 'A' - 50/50 in/out
Of with Higher Education - 3 out of 4 voted in
So Education did play a part. It is what part they played that is interesting. I found Suzied's point "So older people with higher education more likely to vote remain than older people without." gives us something to think about.
My feeling is that those whose life had been or would be influenced by lower (I wish there was another word but there isn't) education levels believe what we had does not work in their favour and, they may possibly believe it works or has worked, against them. On the other side those who life had been or would be influenced by higher education levels did believe that what we had worked for them.
I could be wrong, any interpretation could be wrong but if I am right we need to work out how the country can work for all - and I do not believe Brexit will, or was even intended to do that by those leading the campaign.