It’s sad to read about the family splits that the referendum has caused, where some young people say they are disgusted with the fascist stupid older generation, including their parents.   Could they have made a difference if they had all bothered to vote?

Some rough calculations which I admit do have to make some assumptions as the available data are not exact:

According to the Office for National Statistics projections of UK demographics from 2014, the following numbers are given:

20-24 age group – 4.253 million

15-19 age group – 3.755 million

In the latter 5 year group an approximate estimate of 18-19 year olds would be 40% of 3.755 million = 1.502 million

So total of 18-24 age group ≈ 5.755 million

It has been estimated that only 36% of the 18-24 age group bothered to vote.

http://www.independent.co.uk/voices/eu-referendum-brexit-young-people-upset-by-the-outcome-of-the-eu...

IF the other 64% had registered and voted (either directly or by proxy), that would be 3.68 million more votes. 

But wait, not all of the population above 18 years old here can be eligible to vote.  I suppose some can’t be eligible to register for various reasons as well as those who haven't bothered. From the ONS in 2016 the population aged 18 and above is ≈ 51.39 million, and the total electorate in the referendum was 46.50 million, which is 90.5% of the population above 18 years old.

There is no way of knowing what proportion of 18-24 year olds here aren’t qualified to register even if they wanted to, or haven't registered by choice, but if  we take  90.5% of the 3.68 million potential extra votes that would leave approximately 3.33 million unused votes in this age group.

Obviously not all of the 64% that didn’t bother to vote would have voted 100% to leave.  If we assume that the percentage of results from the non-voters in that age group would be similar to the estimates of the ones that did turn out to vote (75% remain : 25% leave)  there would be approximately another 2.5 million more votes to remain, and 0.83 million more to leave.  That would make the Total votes 18.2 million to Leave, 18.6 million to Remain.  Perhaps too close to call, only 0.4 million difference, and 0.01% of the total vote (0.4 out of 36.8 million), but Remain could have won.

A lot of assumptions I know, and no doubt some flaws which I would be happy for anyone to correct me on, but given that the difference between Leave and Remain was only 1.27 million votes it seems quite feasible that the 18-24 year olds could have swung the vote and made a difference if far more of them had participated in the process.