It is misleading to use the mean as a descriptor of a data set when the median or mode would be more representative of the data set as a whole.
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No. Here's one set of data where the mean is not one of the values: a set of 250,000 numbers. 125,000 of them are "1", 125,000 are "3". The mean of this data set is "2", which is not among the data.
The mean of the new data set is shifted from the mean of the original set, in the direction of the added cluster. We note that the same would be true if only a single new element were added.
the mean.
First, you add all of the numbers in the set together. Then, you divde the sum by however many numbers there are in the set of data. Your quotient is the average/mean.
The Mean.