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A review by the BBC's governing body, the BBC Trust, concluded the British broadcaster must be "braver" in guiding audiences towards the credible facts in an argument, rather than leaving them to make up their own mind.
The recommendation comes after the BBC was criticised for being "too timid" during the EU referendum.
Timothy Garton Ash, a professor of European studies at Oxford University, suggested in a Guardian comment piece that the BBC gave "equal airtime to unequal arguments."
The 86-page BBC Trust review, led by former National Statistician Dame Jil Matheson, highlighted an article on the BBC website in March in which it examined a London School of Economics (LSE) claim that Brexit would cost British households £850 ($1,100).
The article provided a counter view from Vote Leave chief executive Matthew Elliott, who said the LSE's claim was "ridiculous" and lacked credibility.
The BBC piece concluded: "Nobody knows what would happen if the
The BBC Trust review said the article "did not go far enough in weighing the available evidence."
It added: "Simply pitching one challenging statistical claim against another without providing any kind of 'refereeing' voice will rarely be sufficient to ensure audiences reach a full understanding of the relevance of the numbers."
The BBC Trust report accepted that journalists "might feel constrained" by the BBC's responsibility to impartiality, but it argued that audience research has shown that the corporation's current approach caused "considerable frustration."
It stressed: "The BBC needs to get better and braver in interpreting and explaining rival statistics and guiding the audience."
But in a response, published within the BBC Trust review, BBC News said:
"We note that the review is critical about presenting different sets of statistics, and claims based on them, presented by those on either side of political arguments, without interpretation or guide. It is our role to give our audiences the best information so that they can form their own judgments."
Overall, the BBC Trust report - which was titled Making Sense of Statistics - praised the broadcaster's "strong record" on reporting statistics, but said it could also do more to contextualise data and go "beyond the headlines" of press releases.
Matheson said: "I have been impressed by the BBC's commitment to helping audiences understand the world we live in, and helping them navigate through complex data and statistics. The public trusts the BBC to do it well, and we found that they often do a very good job - but it is frustrating that they don't do this consistently."
BBC News has committed to reviewing its progress on reporting statistics every six months, starting with Radio 4's "Today" programme, "BBC Breakfast," and Radio 5Live's drive time show.