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Question
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.

Explain why the Correct Answer
is the only Correct Answer

Answer 1

[AI-generated answer — Bot GPT 3.5]

The correct answer is the mean.

The mean is most affected by outliers because it takes into account every value in the data set when calculating the average. This means that a single outlier that is significantly higher or lower than the rest of the data can greatly skew the mean.

For example, consider the following data set: 1, 2, 3, 4, 5, 6, 7, 8, 9, 100. The mean of this data set is 15.5, which is heavily influenced by the outlier value of 100. If we were to remove the outlier, the mean would be reduced to 5.5, a significant difference.

On the other hand, the median and mode are less affected by outliers. The median is the middle value when the data is arranged in ascending order, so outliers do not have as much impact on it. Similarly, the mode is the most frequently occurring value in the data set, so outliers do not affect it unless they are the mode themselves.

In conclusion, the mean is the measure of center that is most affected by outliers due to its sensitivity to extreme values in the data set.