The BBC's Sunday Politics breached broadcasting rules with misleading claims made by presenter Andrew Neil, a watchdog has found.
The host claimed during an interview with former Scottish National Party leader Alex Salmond that "after a decade of SNP rule, one in five Scots pupils leave primary school functionally illiterate".
Media watchdog Ofcom has found that his statistical claim was not accurate or based on any official source.
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Following a complaint about the false statistic, an investigation found that the claim misled viewers during the build-up to elections in 2017.
Neil said his claim was "all too credible, even if not exactly accurate, as I now realise".
It was also found that the BBC attempted to find a source to back up Neil's inaccurate claim, before conceding it was inaccurate and had no basis.
'False' claim about illiteracy
Ofcom is "greatly concerned" with the BBC's handling of the complaint, and the time taken to admit the error.
A spokeswoman for Ofcom said: "We expect the BBC to take careful note of its errors in the handling of this case to ensure they don't recur.
"The length of time it took the BBC to admit there was no factual source to support the statement made in this programme was deeply unsatisfactory.
"We expect better standards from the BBC, both in its handling of viewer complaints and in its interactions with Ofcom."
Neil conducted an interview with former Scottish first minister Salmond in 2017, ahead of the local elections in Scotland and a UK general election.
He asked the politician: "If services have been so well protected, why, after a decade of SNP rule, do one in five Scots pupils leave primary school functionally illiterate?"
Neil then repeated: "Why are one in five functionally illiterate?"
This, Ofcom has ruled, gave a "false impression that Mr Neil's question was founded on an established fact or source".
The BBC's subsequent handling of the complaint has also been criticised by Ofcom.
The watchdog found that not only was the claim unfounded, but that the BBC has erroneously pointed to sources to try and give it some factual basis, and offered "conflicting explanations on the source from which Mr Neil's statement was derived".
The BBC also pointed to the fact that first minister Nicola Sturgeon did not rebut the statistic in a Scottish parliamentary debate as backing their case that it was not materially misleading.
Ofcom's findings stated that: "The BBC now accepts that it was not based on any such source and that it was therefore not accurate."
The watchdog has said that it is concerned that the misleading claims were made during a sensitive election period.
Neil said in his representations to Ofcom: "Questions can always be better framed in retrospect. But I refute Ofcom's draft conclusion that my question seriously misled viewers about literacy problems."
He added: "Evidence is strong that illiteracy in Scottish schools is still deeply embedded in the system and that, far from improving, is likely getting worse, even after 10 years of SNP government."
A BBC spokesman said: "The BBC has already upheld a complaint on this issue in 2017 and we will study Ofcom's findings."