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.(4 points).
The mean is the measure of center most affected by outliers because it takes into account all values in the dataset when calculating the average. This means that extreme values have a large impact on the mean, pulling it towards the outlier.
For example, let's consider the following dataset of 10 numbers: 5, 6, 7, 8, 9, 10, 11, 12, 13, 100. The median of this dataset is 9.5 (the average of the 5th and 6th values), the mode is 5 (as it is the most frequent value), and the mean is 21.1. The outlier of 100 greatly influences the mean, pulling it far away from the majority of the values in the dataset. In this case, the mean is not a good representation of the central tendency of the data due to the outlier.