Course 5, lesson 45 of 100, Ages 11+
Averages and outliers
Summing up data with one number
Like I’m 5
An average is a middle number that sums up a group. If your scores are 6, 7 and 8, the average is 7. Sometimes one odd number can change the average a lot.
The big idea
There are different averages. The mean adds everything up and divides by how many there are. The median is the middle value when you line the numbers up. The mode is the most common value.
Outliers are values far from the rest. One billionaire walking into a café makes the mean income enormous, but the median barely moves. Choosing the right average stops you being misled, and AI builders check this too.
Examples
- Test scores: Scores 6, 7, 8: the mean is 7 and so is the median.
- Café incomes: One billionaire makes the mean misleading; the median stays sensible.
- Shoe shop: The mode tells the shop which size to stock most.
How it works
- Line up the values and look for outliers.
- Pick the average that fits: mean, median or mode.
- Report the average along with how spread out the data is.
Check your understanding
- What's the median of 3, 5 and 100?
- Options: 5; 36; 100.
Answer: 5. The median is the middle value when lined up: 3, 5, 100. - Why can the mean be misleading with outliers?
- Options: One extreme value can drag it far away; It ignores numbers; It's always zero.
Answer: One extreme value can drag it far away. Extreme values pull the mean, while the median resists them.
Remember
Mean, median and mode summarise data differently. Outliers can mislead the mean.
Talk about it
Is the average height in your class a mean, median or mode? Which would you use?
Go deeper
Robust statistics such as the median and trimmed mean resist outliers. In machine learning, outliers can distort training, so builders detect them and use robust loss functions when needed.