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). SIMPLE IT

Answer 1

The measure of center that is most affected by outliers is the mean.

Let's consider the following set of data:

10, 12, 12, 13, 14, 15, 16, 17, 18, 100

The mean of this data set is calculated by summing all the values and dividing by the number of data points:

(10 + 12 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 100) / 10 = 32.7

Now, let's say we introduce an outlier to this data set:

10, 12, 12, 13, 14, 15, 16, 17, 18, 500

The mean of this new data set would be:

(10 + 12 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 500) / 10 = 84.7

As we can see, the mean of the data set with the outlier has significantly increased compared to the data set without the outlier. This shows that the mean is heavily influenced by outliers and can be skewed by extreme values.