Definition: An outlier is a data value that lies unusually far from the other values in a data set.
What is an outlier?
An outlier stands apart from the pattern. On a dot plot, it is a lone dot far from the cluster.
How do you spot one?
Look for a gap. In the quiz scores 72, 75, 78, 80, 81, 83, 12, the score 12 is far below the rest. A formula check uses the IQR: a value more than 1.5 times the IQR beyond Q1 or Q3 is flagged.
What does it do to the statistics?
The mean moves toward the outlier, while the median barely shifts. With the 12 included, the mean is 481 / 7, about 68.7. Without it, the mean is 469 / 6, about 78.2. The median goes from 78 to 79, a small change.
What should you do with it?
Investigate before deleting. It might be a typing error, or it might be a real and interesting result. Report both versions if you remove it.
What is a common mistake?
Assuming an outlier is always wrong. A basketball player 7 feet 4 inches tall is a valid, real outlier.