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

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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.

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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

If the

Then:

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

There are pictures and graphs here:

https://www.mathsisfun.com/data/outliers.html

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The mean will move towards the outlier.

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

Think about it this way:

Let's say we have some data.

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