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The mean of a data set is found by summing all the elements, then dividing by the number of elements in the set. This is also called the "average."
The mean of set set {1,2,3,4,5} is (1+2+3+4+5) / 5 = 3
That is correct, but to be more specific, there are several kinds of mean: the most common are arithmetic and geometric. The geometric mean is the nth root of the product of the numbers, where n is the number of elements (numbers) in the set. When the kind of mean is not given, it usually means the arithmetic mean, which is defined as above.
Also, there are several kinds of averages: mean, median, and mode, where by mean is meant the arithmetic mean. But we are getting way outside the scope of the question so I will end my answer here.
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Is it true that in large data sets the mean is always one of the data values?
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.
When is it misleading to use the mean as a descriptor of a data set?
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.
The average of a set of data is called what?
the mean.
What happens to the mean of a data set when you add a cluster near one end of the original data set?
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.
How do you find the average or mean in a set of data?
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.
