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How do we know what we don't know? How do some people use ignorance, or claim ignorance, to mislead (e.g., by claiming that we are ignorant of the causes of climate change)? How do we navigate claims when two sides are in direct opposition? Radio national discuss the study of ignorance, and how it relates to evidence and arguments

Journalists often make mistakes when reporting on data such as opinion poll results, federal jobs reports and census surveys because they don't quite understand - or they ignore - the data's margin of error. Data collected from a sample of the population will never perfectly represent the population as a whole. The margin of error, which depends primarily on sample size, is a measure of how precise the estimate is. The margin of error for an opinion poll indicates how close the match is likely to be between the responses of the people in the poll and those of the population as a whole. To help journalists understand margin of error and how to correctly interpret data from polls and surveys, we've put together a list of seven tips, Look for the margin of error - and report it. It tells you and your audience how much the results can vary. Remember that the larger the margin of error, the greater the likelihood the survey estimate will be inaccurate. Make sure a political candidate really has the lead before you report it. Note that there are real trends, and then there are mistaken claims of a trend. Watch your adjectives. (And it might be best to avoid them altogether.) Keep in mind that the margin of error for subgroups of a sample will always be larger than the margin of error for the sample. Use caution when comparing results from different polls and surveys, especially those conducted by different organizations.

It's not just disadvantaged and vulnerable groups that struggle with financial decision-making. People who are highly educated in finance also make poor decisions - for instance, by focusing too much on growing their assets and ignoring risks. But studies show that when regulation is effective and the financial system can be trusted, even consumers with limited financial knowledge and information-processing capabilities have the potential to deal with complex financial decisions. For example, when considering mortgage protection insurance, applicants stand to benefit from knowing the actual risk of events like serious illness or injury that can affect their ability to meet monthly loan repayments.

how could two groups of 'experts' come up with such different conclusions, given they broadly agree of the evidence? David Aaronovitch in the Times identified the critical underlying issue behind the ensuing conflict: whether we take an individual- or a population-based approach. Essentially, the authors point out that any absolute risks are small from an individual perspective, and may generally be cancelled out by the enjoyment of eating, and the bother of changing habits. But these small benefits can be important from a public-health, population-wide perspective, since a lot of people making a small change, that only reduces their risk by a personally-negligible amount, can add up to thousands fewer cases of disease. That's what has generated the disagreement. It can be perfectly reasonable for guidance to be given by authorities, and it can also be perfectly reasonable for individuals to ignore it. Both can be 'right'.

'Middle Australia' earns much less than the government would have you believe and women continue to earn much less than men. ...The 2014-15 taxation statistics released last week revealed that the median taxable income of the 9.95m Australians with a taxable income was just $54,543. If you earned more than that, then you earned more than at least half of Australians.

The Supreme Court does not compute. Or at least some of its members would rather not. The justices, the most powerful jurists in the land, seem to have a reluctance - even an allergy - to taking math and statistics seriously. For decades, the court has struggled with quantitative evidence of all kinds in a wide variety of cases. Sometimes justices ignore this evidence. Sometimes they misinterpret it. And sometimes they cast it aside in order to hold on to more traditional legal arguments. (And, yes, sometimes they also listen to the numbers.) Yet the world itself is becoming more computationally driven, and some of those computations will need to be adjudicated before long. Some major artificial intelligence case will likely come across the court's desk in the next decade, for example. By voicing an unwillingness to engage with data-driven empiricism, justices - and thus the court - are at risk of making decisions without fully grappling with the evidence. This problem was on full display earlier this month, when the Supreme Court heard arguments in Gill v. Whitford, a case that will determine the future of partisan gerrymandering - and the contours of American democracy along with it. As my colleague Galen Druke has reported, the case hinges on math: Is there a way to measure a map's partisan bias and to create a standard for when a gerrymandered map infringes on voters' rights?

There is a black hole in our knowledge of women and girls around the world. They are often missing from official statistics, and areas of their lives are ignored completely. So campaigners say - but what needs to be done?