Question

Answer in a 6th graders words
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

Answer 1

The measure of center that is most affected by outliers is the **mean**. The mean is what you get when you add up all the numbers and divide by how many numbers there are. If there’s a really big or really small number (which we call an outlier), it can change the mean a lot!

Let’s look at an example with 10 numbers:

Let’s say we have these numbers:
3, 4, 4, 5, 5, 6, 6, 7, 8, and **100**.

1. First, we add them up:
3 + 4 + 4 + 5 + 5 + 6 + 6 + 7 + 8 + 100 = 143.

2. Now we divide by how many numbers there are (10):
143 ÷ 10 = 14.3 (this is the mean).

Now, let’s look at the median and the mode:

- **Median**: To find the median, we put the numbers in order and find the middle one. Our ordered list is:
3, 4, 4, 5, 5, 6, 6, 7, 8, 100. Since there are 10 numbers, the median is the average of the 5th and 6th numbers:
(5 + 6) ÷ 2 = 5.5.

- **Mode**: The mode is the number that appears the most often. In this case, it's 4 and 5, since they both appear twice.

So here are the three measures of center:
- Mean: 14.3
- Median: 5.5
- Mode: 4 and 5

You can see that the mean (14.3) is really high because of that big number (100). The median (5.5) and mode (4 & 5) didn’t change much because they aren’t affected by the outlier as much. That’s why the mean is the most affected by outliers!