Outliers are special numbers that can really change how we understand data and statistics. Let’s break down some important ideas:

1. Mean vs. Median:

   • The mean is the average of a group of numbers, but it can be thrown off by outliers.
   • For example, if we have the numbers {2, 3, 3, 4, 100}, the mean would be $22.4$.
   • But if we look at the median, which is the middle number, it’s just $3$.

2. Standard Deviation:

   • Standard deviation tells us how spread out the numbers are.
   • Outliers can make this value much higher, which can make it seem like there's more variety in the data than there really is.
   • In our previous example, the standard deviation is around $43.1$, but this doesn’t really show what most of the numbers look like.

3. Correlation:

   • Correlation shows how two things relate to each other.
   • Outliers can change this relationship a lot.
   • For example, two things might seem to be strongly related at first ($r = 0.9$). But if an outlier pops up, that might drop to $r = 0.2$, showing a weaker connection.

By understanding outliers, we can make sure we correctly interpret and represent data statistics.