The arithmetic mean — what most people call the average — is the sum of a set of values divided by how many there are. It is the go-to single number for summarizing test scores, monthly spending, temperatures, commute times, or speeds, because it balances every value in the set: multiply the mean by the count and you recover the exact total. If your average monthly spending is $2,400, you spent $28,800 in the year — the mean preserves the sum, which is what makes it useful for budgeting and planning.
The mean has one famous weakness: outliers. Five salaries of $50,000 and one of $500,000 average to $125,000 — a figure nobody in the group actually earns, since the total is $750,000 across 6 people. When data is skewed like that, the median (the middle value when sorted) is usually the fairer summary of a 'typical' member. This is why house prices and incomes are almost always reported as medians in the news. Use the mean for symmetric, well-behaved data — test scores, measurements, daily step counts — and glance at the median too whenever a few extreme values might be pulling the average around. When some values should count more than others, use a weighted mean instead, as the GPA example below shows. For tracking change over time, pair the mean with the range (max minus min). Monthly spending averaging $2,400 with a range of $800 is stable; the same average with a $4,000 range means wild swings that a single emergency could break. And when averaging rates — speeds, fuel economy, investment returns — the simple mean can lie: averaging 60 mph outbound and 40 mph return over the same distance gives 48 mph (the harmonic mean), not 50, because more time is spent at the slower speed. Know which mean the situation calls for.