In mathematics, "extreme" typically refers to the maximum or minimum values of a function or dataset. The maximum is the highest point within a given set, while the minimum is the lowest point. These extreme values are crucial in optimization problems and can be found using techniques such as calculus, specifically through finding critical points where the derivative is zero or undefined.
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the mean (in math) is the average of all the numbers in the problem
It cannot be used for qualitative data. The mean is affected by extreme values. It may not be represented anywhere in the population - for example, in most places, the average number of children per family will be a mixed fraction. There are no fractional children, though!
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An extreme value will drag the mean value towards it.
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Communitive means of, or belonging to, a community. It has no meaning in math. Communative does not mean anything - in math or elsewhere.
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the mean (in math) is the average of all the numbers in the problem
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It cannot be used for qualitative data. The mean is affected by extreme values. It may not be represented anywhere in the population - for example, in most places, the average number of children per family will be a mixed fraction. There are no fractional children, though!
In short, math extreme is the highest (or lowest) value of a math function on an interval (a,b). For example, function y=x2 has minimum (extreme) for x=0 on interval (minus infinity, plus infinity). Similarly, function y=-x2 has maximum (extreme) for x=0 on the same interval. Some functions have multiple extremes, which are called local extremes, but this is enough for basic understanding of the principle.