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 extremely short and as a 4th grader would with grammar that's a little bad but not very bad

Answer 1

The mean is most affected by outliers. The mean is the average of all the numbers, so if one number is really big or really small, it can change a lot.

For example, let's look at these 10 numbers: 2, 3, 4, 4, 5, 5, 5, 6, 7, and 100.

To find the mean, you add all the numbers:

2 + 3 + 4 + 4 + 5 + 5 + 5 + 6 + 7 + 100 = 141.

Then you divide by 10 (because there are 10 numbers):

141 ÷ 10 = 14.1.

Now, if we just took out the 100, the numbers are 2, 3, 4, 4, 5, 5, 5, 6, 7.

Adding these gives:

2 + 3 + 4 + 4 + 5 + 5 + 5 + 6 + 7 = 41.

Then divide by 9 (there are 9 numbers):

41 ÷ 9 = about 4.56.

See? The mean changed a lot because of that one big number!

The median and mode are not changed much by just one outlier. So the mean is the most affected.