It means "multiplied by itself".
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In mathematics, the term "squared" refers to multiplying a number by itself. For example, if a number x is squared, it is equivalent to x multiplied by x, or x^2. It is a way of indicating that a number is being raised to the power of 2.
The mathematical term for "mean" is "mean".The popular, or colloquial term for "mean" is "average".
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Mean is the mathematical term for average.
Convention is not a mathematical term: it means what is generally done or an accepted way of doing something.