Official statistics show nearly 9% of higher education students who went to a Scottish university in 2010/11 dropped out, compared to a UK average of 7.4%.
The highest drop-out rate in Scotland was the 23% recorded for the University of the West of Scotland, which has campuses in Paisley, Hamilton, Ayr and Dumfries.
Edinburgh Napier University, Queen Margaret University in Edinburgh, and Highlands and Islands University all recorded drop-out rates of more than 10%.
The lowest drop-out rate was at St Andrews University in Fife, where just 1.5% failed to finish the first year of their course.
The figures from the UK-wide Higher Education Statistics Agency (Hesa) also show the proportion of state school and private school pupils at university.
Some 12% of students at Scottish universities in 2011/12 were educated in the independent sector, despite the fact fewer than 5% of the school population go to a private school.
The university with the highest proportion of private school pupils is St Andrews, with just 59% from state schools, while Edinburgh University takes 70% of its students from comprehensive schools. Glasgow University recruits 80% of students from the state sector.
On widening access, figures produced by the Scottish Funding Council (SFC) show 22.5% of students came from the 40% most deprived areas in 2011/12, compared to 22.9% the previous year.
Although drop-out rates and figures on access will cause concern, they come before the impact of new agreements between the SFC and universities which give institutions targets on improving the position. Improving retention is part of the new deals.
Michael Russell, the Education Secretary, said the statistics proved the Scottish Government was right to legislate on widening access under the Post-16 Education (Scotland) Bill.
He said: "We have already added places for students from disadvantaged backgrounds through an investment of £10 million in 2000 extra places for 2013/14, including over 700 targeted at widening access schemes. We will continue to work with universities.
"We have already taken action to ensure access is based on the ability to learn, not to pay.
"On top of this, the best package of student support in the UK will come into force this year, ensuring students from the poorest families receive an income of at least £7250 a year."
Robin Parker, president of NUS Scotland, called the figures "really disappointing".
He said: "We know universities can't do it all on fair access. But they can, and must, do a great deal more than this.
"Scotland remains the worst in the whole of the UK and this is a record we simply cannot tolerate any more.
"Without legislating on widening access, we could easily make no progress at all for many years to come."
However, Alastair Sim, director of Universities Scotland, which represents university principals, said it was unfortunate the data did not reflect recent improvements.
He said: "Every university is committed to widening access and has signed up to an outcome agreement including goals for progress.
"Universities are also working hard to recruit 700 additional places which have been set aside for students from the poorest neighbourhoods who we hope to see on university campuses from the autumn onwards.
"We can project that the impact of the additional access places is likely to mean as much as a 15% increase in university students from the most disadvantaged areas of Scotland, but frustratingly this won't show up in the figures for another two years."
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