The measure of center most affected by outliers is the mean. This is because the mean is calculated by adding all the numbers together and dividing by how many there are. If a very high or very low number (an outlier) is included, it can significantly change the mean.
For example, consider the following data points:
1, 2, 2, 3, 4, 5, 5, 6, 7, 100
- Mean: (1 + 2 + 2 + 3 + 4 + 5 + 5 + 6 + 7 + 100) ÷ 10 = 13.5
- Median: The middle numbers are 4 and 5, so (4 + 5) ÷ 2 = 4.5
- Mode: The number that appears most is 2 and 5.
In this example, the mean (13.5) is much higher because of the outlier (100). The median (4.5) and mode (2 and 5) are not affected as much. That's why the mean is the most affected by outliers!