Outliers are those oddball numbers that are very different from the rest in a set of data. It's important to see how these outliers can change average values like the mean, median, and mode in statistics.

1. Mean:

• The mean is the average. To find it, you add up all the numbers and then divide by how many there are.
• Here’s how it looks: [ \text{Mean} = \frac{\text{Total of all values}}{\text{Number of values}} ]
• Outliers can really change the mean. For example, if we have the numbers {2, 3, 4, 5, 100}, the mean would be: [ \text{Mean} = \frac{2 + 3 + 4 + 5 + 100}{5} = 22.8 ]
• If we take away the outlier (100), the calculation changes to: [ \text{Mean} = \frac{2 + 3 + 4 + 5}{4} = 3.5 ]
• So, that one big number really raised the mean a lot!

2. Median:

• The median is the middle number when you arrange the data in order. If there is an even number of values, you take the average of the two middle ones.
• Here’s how to find it:
  • If there are an odd number of values, it’s the middle one.
  • If there are an even number, it’s the average of the two middle ones.
• In our same example {2, 3, 4, 5, 100}, when arranged in order, the median is 4.
• The cool thing about the median is that it doesn’t change much when we have outliers.

3. Mode:

• The mode is the number that shows up the most often. For our set {2, 2, 2, 3, 100}, the mode is 2.
• Outliers don’t usually affect the mode, because it depends on how often a number appears, not how big or small it is.

In Summary:

The mean can change a lot if there are outliers, while the median and mode stay more steady. This makes the median and mode better choices when you’re looking for a good average in a set of data with extreme values.