Five friends' ages: 10, 12, 13, 15, 50. The 'average' age is 20 — but nobody is anywhere near 20. The mean is powerful, and it's also easy to mislead with.
The mean (arithmetic average) is the total of all values divided by how many there are. It's the 'balance point' of the data.
Test scores, salaries, temperatures, sports stats, scientific measurements — the mean is the single most-used summary number in the world.
Σx = sum of all values. n = how many values.
A batter scores 0, 0, 50, 100, 100 across 5 innings. What's the mean? Is it a fair description?
Mean of 12, 15, 18, 21.
Sum = 66. 66 ÷ 4 = 16.5. (The mean doesn't have to be one of the data values.)
The mean is dragged by outliers. One billionaire walking into a room of 30 people makes the 'average wealth' meaningless. Use the median when data is skewed.
Mean = balance point: if the data sat on a seesaw, the mean is where it balances. Outliers far out tip the balance a lot.
- Mean = sum ÷ count.
- It's the data's balance point — sensitive to outliers.
- For skewed data (incomes, house prices), the median is usually more honest.