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The mean of a set of numbers is the sum of their values divided by their number. The mode is the value that features most often in the observed set.

Every set of observations will have a mode though it may have more than one. By definition, the modal value must appear in the observations. A mode can be at an extreme end of a distribution.

Not all sets of observations have a mean. When collecting information about favourite fruit, you cannot have a mean for 3 apples and 4 bananas. A mean may not have a realistic value - (eg each family had 1.8 children - there never was a 0.8 of a child anywhere). However, the mean will be at the centre of the distribution and it also has statistically useful properties.

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