# How does an outlier affect the mean of a data set?

May 17, 2017

The mean will move towards the outlier.

#### Explanation:

The mean is non-resistant. That means, it's affected by outliers. More specifically, the mean will want to move towards the outlier.

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.

Jul 22, 2017

An outlier can affect the mean of a data set by skewing the results so that the mean is no longer representative of the data set. There are solutions to this problem.

#### Explanation:

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:

$m e a n = \frac{3 + 4 + 5 + 6 + 7}{5} = \frac{25}{5} = 5$

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: $m e a n = \frac{3 + 14 + 5 + 6 + 7}{5} = \frac{35}{5} = 7$

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.

$m e a n \left(n o \cancel{14}\right) = \frac{3 + \cancel{14} + 5 + 6 + 7}{\left(\cancel{5}\right) 4} = \frac{21}{4} = 5.25$

There are pictures and graphs here:
https://www.mathsisfun.com/data/outliers.html