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

Last updated date: 13th Jun 2024
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Hint: We first describe the concept of mean and the use of outliner and its effects on the mean. We take an example to understand the concept better. The smaller the sample size of the dataset, the more an outlier has the potential to affect the mean.

Complete step by step solution:
In statistics, the mean of a dataset is the average value. It’s useful to know because it gives us an idea of where the “centre” of the dataset is located.
Sample mean can be expressed as $\overline{x}=\dfrac{\sum{{{x}_{i}}}}{n}$ for inputs as ${{x}_{i}},i=1(1)n$.
But while the mean is a useful and easy to calculate, it does have one drawback: It can be affected by outliers. In particular, the smaller the dataset, the more that an outlier could affect the mean.
Outliner skews the results so that the mean is no longer representative of the data set.
We take an example: Ten students take an exam and receive the following scores of $0,88,90,92,94,95,95,96,97,99$.
The mean is \[\overline{x}=\dfrac{0+88+90+92+94+95+95+96+97+99}{10}=\dfrac{846}{10}=84.6\].
Now if we remove 0 from the sample means the means becomes 94.
The one unusually low score of one student drags the mean down for the entire dataset.

An outlier can affect the mean by being unusually small or unusually large. The mean is non-resistant. That means, it's affected by outliers. More specifically, the mean will want to move towards the outlier.