Three Types of Average
In everyday language "average" usually means the mean, but in statistics there are three distinct measures of central tendency, each useful in different situations.
Mean (Arithmetic Average)
Sum all values, divide by the count. Formula: Mean = Σx ÷ n
Example: Test scores: 72, 85, 91, 68, 79. Sum = 395. Count = 5. Mean = 395 ÷ 5 = 79
When to use: When data is roughly symmetrical with no extreme outliers. Best for test scores, temperatures, heights.
Weakness: One extreme value skews the result heavily. A team where 4 members earn $40,000 and one earns $400,000 has a mean salary of $112,000 — misleading.
Median (Middle Value)
Sort all values, find the middle one. With an even count, average the two middle values.
Example: Salaries: $35k, $38k, $42k, $45k, $380k. Median = $42k (the middle value). Mean = $108k — the median tells a much more honest story here.
When to use: When data has outliers or is skewed. House prices, income data, and response times are almost always better reported as median.
Mode (Most Frequent Value)
The value that appears most often. A dataset can have no mode, one mode, or multiple modes.
Example: Shoe sizes sold: 7, 8, 8, 9, 9, 9, 10, 11. Mode = 9
When to use: Categorical data or when you need the most common value — most popular product size, most frequent response in a survey.
Quick Comparison
| Measure | Best For | Affected by Outliers? |
|---|---|---|
| Mean | Symmetric data, no outliers | Yes — heavily |
| Median | Skewed data, outliers present | No |
| Mode | Categorical or frequency data | No |
Weighted Average
When some values matter more than others, use a weighted average. Formula: Σ(value × weight) ÷ Σweights.
Example: Final grade: assignments 30% (score: 85), midterm 30% (score: 72), final 40% (score: 91). Weighted average = (85×0.3 + 72×0.3 + 91×0.4) ÷ 1.0 = (25.5 + 21.6 + 36.4) = 83.5
The average calculator below computes mean, median, mode, and weighted average from any set of numbers you enter.