Here's the headline you'll use for the rest of your maths life: the mean and range are sensitive to outliers; the median and mode are resistant to them. The toy shows it as bar lengths — but it pays to know why.
Why the Mean and Range Get Thrown
The mean adds up every actual value, so a giant number makes the total balloon and drags the average up with it. The range is even more exposed — it's literally biggest minus smallest, so one extreme value is the answer. Picture a tidy list 6, 7, 7, 8, 9: mean 7.4, range 3. Toss in a single 60 and the mean leaps to about 16.2 and the range explodes to 54. One value, two wrecked summaries.
Why the Median and Mode Shrug
The median only cares about position in the line-up, not size. Adding that 60 just makes it "the new biggest, off on the end" — the middle of the list shifts by at most one place. In our example the median nudges from 7 to 7.5, almost nothing. The mode cares only about how often a value repeats; a lonely outlier appears once, so it can't be the most common and the mode doesn't move at all.
The One Trap
Don't assume an outlier is always a mistake to delete. Sometimes it's the most important value in the dataset — a record flood level, a once-in-a-decade score. The skilled move isn't to bin it; it's to report a summary that doesn't get fooled by it. That almost always means leaning on the median (and sometimes the mode) rather than the mean — which is exactly what real problems demand on the next rung.