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

The measure of center that is most affected by outliers is the mean. The mean is calculated by adding up all the data points and dividing by the total number of data points. This means that even one extremely high or low data point can greatly skew the mean, pulling it in the direction of the outlier.

For example, consider the following set of data points: 2, 3, 4, 5, 6, 7, 8, 9, 10, 40. The mean of this data set is 8.4. Now let's introduce an outlier by changing the last data point to 100. The new mean becomes 19.4, which is significantly higher than the mean without the outlier. This shows how outliers can have a strong influence on the mean compared to the median and mode.

In contrast, the median is less affected by outliers because it only looks at the middle value(s) of the data set, regardless of how extreme the outliers are. The mode is the least affected by outliers because it simply identifies the most frequently occurring value(s) in the data set, which might not change at all regardless of the presence of outliers.