The mean is the measure of center that is most affected by outliers. The mean is calculated by adding all the numbers together and then dividing by how many numbers there are. If there’s a really big or really small number (an outlier), it can change the mean a lot.
For example, let’s say we have this set of numbers: 2, 3, 4, 5, 5, 6, 7, 8, 9, 100.
- To find the mean, add them up: 2 + 3 + 4 + 5 + 5 + 6 + 7 + 8 + 9 + 100 = 149.
- Then divide by 10 (because there are 10 numbers): 149 ÷ 10 = 14.9.
Now, if we remove the outlier (100), we have: 2, 3, 4, 5, 5, 6, 7, 8, 9.
- Adding them gives: 2 + 3 + 4 + 5 + 5 + 6 + 7 + 8 + 9 = 49.
- Dividing by 9 gives: 49 ÷ 9 ≈ 5.4.
So, the mean changed a lot because of that one big number (100). The mode (the number that appears most) and the median (the middle number when arranged) stay the same or change less with outliers. That's why the mean is the most affected by outliers!