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 good but not too good grammar

Answer 1

The mean is the measure of center most affected by outliers. The mean is found by adding up all the numbers and dividing by how many there are. If one number is really big or really small (like an outlier), it can change the mean a lot.

For example, let's say we have these 10 numbers:
2, 3, 4, 5, 6, 7, 8, 9, 10, 100.

First, we find the mean:
(2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 100) / 10 = 154 / 10 = 15.4.

Now, if we look at the median (the middle number), we put the numbers in order:
2, 3, 4, 5, 6, 7, 8, 9, 10, 100. The middle numbers are 6 and 7, so the median is (6 + 7) / 2 = 6.5.

The mode is the number that appears the most, which is none in this case because all numbers are different.

So, the mean is 15.4, but the median is just 6.5. The big number (100) made the mean much bigger, showing that the mean is very affected by outliers!