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 thats a little okay

Answer 1

The measure of center that is most affected by outliers is the mean.

Let’s see an example:

Imagine we have these 10 test scores:
90, 85, 88, 92, 87, 90, 91, 89, 70, 100.

Now, if we find the mean (average), we add all the scores:
90 + 85 + 88 + 92 + 87 + 90 + 91 + 89 + 70 + 100 = 921.
Then we divide by 10 (the number of scores):
921 ÷ 10 = 92.1.

Now, let’s say the score of 70 is an outlier (much lower than the others). If we change it to a higher score, like 95:
90 + 85 + 88 + 92 + 87 + 90 + 91 + 89 + 95 + 100 = 917.
917 ÷ 10 = 91.7.

So, the mean changed because of the outlier, but the median and mode stayed more the same!

That’s why the mean is most affected by outliers!