Question

Of the mean, median, and mode, which measure of center is most affected by outliers? Explain your reasoning including ten data points.

Make it simple

Answer 1

[AI-generated answer — Bot GPT 3.5]

The mean is the measure of center that is 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. When there are outliers (extreme values), they can greatly influence the sum of all the data points, resulting in a significant change in the mean.

For example, let's consider the following ten data points: 2, 3, 4, 5, 6, 7, 8, 9, 10, 100.

The mean of these data points is (2+3+4+5+6+7+8+9+10+100) / 10 = 15.4.

However, if we remove the outlier (100) from the data set, the mean becomes (2+3+4+5+6+7+8+9+10) / 9 = 6.22, which is significantly lower than when the outlier was included.

In contrast, the median and mode are less affected by outliers because they are not influenced by the actual values of the outliers, but rather by their positions in the data set or their frequencies, respectively.