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.(4 points)

Answer 1

SIMPLE IT

Answer 2

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, so outliers can have a large impact on the overall calculation.

For example, let's consider the following data set: 1, 2, 3, 4, 5, 6, 7, 8, 9, 100. The mean of this data set is (1+2+3+4+5+6+7+8+9+100)/10 = 45.5. The median of this data set is the middle value when the data is arranged in ascending order, which is 5.5, and the mode is the number that appears most frequently, which in this case is 1.

Now, if we add an outlier to this data set, such as 1000, the new data set becomes: 1, 2, 3, 4, 5, 6, 7, 8, 9, 100, 1000. The mean of this new data set is now (1+2+3+4+5+6+7+8+9+100+1000)/11 = 104.1. As we can see, the presence of the outlier 1000 has significantly increased the mean from 45.5 to 104.1, demonstrating how outliers can greatly impact the mean.