How to Calculate an Average

The arithmetic mean

Mean = sum of all values ÷ number of values.

The scores 72, 85, 90, 68, 95 sum to 410 across 5 tests: 410 ÷ 5 = 82.

When the mean misleads: skewed data

If five coworkers earn $45k, $48k, $50k, $52k, and $400k, the mean salary is $119k — a number that describes nobody in the room. One extreme value drags the mean toward itself.

The median — the middle value when sorted — is $50k and describes the group far better. House prices and income statistics are reported as medians for exactly this reason.

Median and mode

• Median: sort the values, take the middle one (or average the two middle ones).
• Mode: the most frequent value — useful for categories, like the most common shoe size sold.

Weighted averages

When values count differently — a final exam worth 40% of a grade versus homework worth 10% — multiply each value by its weight first, then divide by the sum of the weights.

Average speed has the same trap: driving 60 mph for an hour then 30 mph for an hour averages 45 mph, but 60 mph for a mile then 30 mph for a mile averages 40 mph, because you spend longer at the slower speed.