The measure of center most affected by outliers is the mean. This is because the mean takes into account every data point in the set and is therefore highly sensitive to outliers, which can drastically affect the overall average.
For example, consider the following data set of 10 students' test scores:
80, 85, 90, 92, 93, 95, 98, 99, 100, 120
The median score is 94 (the middle value when the scores are listed in order), and the mode is also 94 (since 94 appears twice, more than any other score). However, the mean score is 94.2, which is significantly influenced by the outlier score of 120.
If we remove the outlier from the set, the mean drops to 93.1, which is much closer to the median and mode. This illustrates how outliers can heavily skew the mean and make it a less reliable measure of central tendency.
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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