The mean is the measure of center most affected by outliers. This is because the mean is calculated by adding up all the data points and then dividing by the total number of data points, so outliers can greatly impact the sum and therefore the mean.
For example, consider the following data set: 2, 3, 4, 5, 6, 7, 8, 9, 10, 100. The mean of this data set is 14.4. However, if we remove the outlier of 100, the mean becomes 5.5, a significant difference. This shows how outliers can greatly influence the mean.
In contrast, the median and mode are less affected by outliers. The median is the middle value of a data set when the values are ordered from smallest to largest, so outliers do not impact it as much. The mode is the value that appears most frequently in a data set, so outliers do not have as much influence on it.
Of the mean, median, and mode, which measure of center is most affected by outliers? Explain your reasoning including an example with at least 10 data points.
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