Question

a comprehensive example (not just a data set - a concept) showing how the mean is effected by outliers, and the effect that number close to the mean have on it

Answer 1

Outlier An extreme value in a set of data which is much higher or lower than the other numbers.Outliers affect the mean value of the data.

As we have seen in data collections that are used to draw graphs or find means, modes and medians the data arrives in relatively closed order. In other words, each element of the data is closely related to the majority of the other data. If not, the data set may have information that is too scattered to be useful in any analysis.

In some data sets there may be a point or two that can be out of context with the bulk of the data. These are referred to as outliers, which are out of line with the normal data set. The outlier can push the mean of the data out of its usual position.
For example, the data set 3,4,5,6,7 has a mean of 5, found by dividing the sum of the data by the number of data elements:

mean=(3+4+5+6+7)/5=5

If the 4 was mistakenly recorded as a 14, the 14 would be unusual for the data set and it would be an outlier.

Then: mean=(3+14+5+6+7)/5=7

And we can see the outlier has moved the mean of the data set.
To solve this problem the unusual data element can either be re-investigated and corrected, or removed from the data set with an explanation.

The former solution may bring back our original 4 after error checking is completed. The latter will return our mean closer to a representative evaluation of the data.

Mean=(3+5+6+7)/4=5=25

Another example

Let's say we have some data. 1,2,3. The mean of this is 2. But if we add an outlier of 94 to the data set, the mean will become 25. As you can see, the mean moved towards the outlier.