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.

Answer 1

The measure of center that is most affected by outliers is the mean. This is because the mean is calculated by adding up all the data points and dividing by the total number of data points. If there are outliers in the data set, they can significantly influence the value of the mean, pulling it in their direction.

For example, let's consider the following data set:

2, 3, 4, 5, 6, 7, 8, 9, 10, 100

If we calculate the mean of this data set, it would be (2+3+4+5+6+7+8+9+10+100)/10 = 15.4. However, the presence of the outlier "100" causes the mean to be much larger than the rest of the data points, making it an inaccurate representation of the central tendency of the data set.

On the other hand, the median is less affected by outliers because it only considers the middle value of the data set when arranged in order. In this example, the median would be 6.5, which is a more reasonable representation of the central tendency of the data set given the outliers present. Similarly, the mode would not be affected by outliers at all, as it only represents the value that occurs most frequently in the data set. In this example, the mode would be 2.