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. make it super short and as a 4th grader would with grammar that's a little bad but not very bad

Answer 1

The mean is the measure of center most affected by outliers. The mean is when you add all the numbers and divide 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.

Let’s look at this example:

Data points: 2, 3, 4, 5, 6, 7, 8, 9, 10, 100

1. First, find the mean:
   (2+3+4+5+6+7+8+9+10+100) = 154
   Then divide by 10 (the number of data points):
   154 ÷ 10 = 15.4

2. Now, find the median (the middle number):
   When you put them in order: 2, 3, 4, 5, 6, 7, 8, 9, 10, 100, the middle numbers are 6 and 7, so…
   (6+7) ÷ 2 = 6.5

3. Finally, the mode (the number that happens most):
   There is no number that repeats, so there is no mode.

So with the outlier 100, the mean is 15.4 but the median is just 6.5. That’s why the mean is most affected by outliers!