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This task encourages students to engage with statistics without them needing to carry out detailed calculation. Discussing these statements will lead to a better understanding of statistical ideas (such as averages, expectation and sampling), as well as helping students to see the importance of stating ideas clearly when working with statistics.
This question gives students the opportunity to encounter the power of counter-examples in a mathematical analysis: for example, constructing a single example in which 'Half of the students taking a test DON'T score less than the average mark' shows that the statement 'Half of the students taking a test score less than the average mark' cannot ALWAYS be true.
Can you think of a situation when this statement isn't true?
Can you think of a situation when this statement is true?
How can you convince me that this will never happen?
How can you convince me that this will always happen?
Pose these two questions to students who are finding it difficult to decide which category each statement falls into:
"Can you think of a situation when this statement isn't true?"
"Can you think of a situation when this statement is true?"
For similar statements using statistical ideas at a more advanced level, see Stats Statements.