What Is an Average? All Types Explained

The word "average" most commonly refers to the arithmetic mean — the sum of all values divided by the count. But there are many types of averages, each useful in different situations. This calculator computes all of them.

Type	Formula	Best Used For
Mean	Sum ÷ Count	General data — most common average
Median	Middle value (sorted)	Skewed data, income, house prices
Mode	Most frequent value	Categorical data, most popular item
Range	Max − Min	Spread of data values
Geometric Mean	ⁿ√(x₁ × x₂ × … × xₙ)	Growth rates, ratios, percentages
Harmonic Mean	n ÷ Σ(1/xᵢ)	Speeds, rates, fractions
Weighted Mean	Σ(xᵢ × wᵢ) ÷ Σwᵢ	GPA, survey data, pricing
Std. Deviation	√(Σ(xᵢ−μ)² ÷ n)	How spread out data is
Variance	Σ(xᵢ−μ)² ÷ n	Variability, risk analysis

When to Use Mean vs. Median

The arithmetic mean is sensitive to outliers. If a dataset has extreme high or low values, the mean gets "pulled" in that direction and may not represent a typical value. The median is resistant to outliers, making it better for skewed data like income, home prices, or test scores with outliers.

Classic example: If 9 people earn $30,000/year and 1 person earns $1,000,000/year, the mean salary is $127,000 — which represents nobody. The median salary ($30,000) is far more representative of what a "typical" person earns.

Try These Examples

Simple Dataset

2, 4, 4, 4, 5, 5, 7, 9

Classic statistics textbook example — demonstrates mean vs. mode vs. median

Student Grades

85, 92, 78, 95, 88, 76, 91, 83, 89, 94

Class of 10 students — find the class average and median grade

Income Distribution

15k, 25k, 28k, 32k, 35k, 42k, 55k, 120k

Shows why median is better than mean for income data

1 to 10

1, 2, 3, 4, 5, 6, 7, 8, 9, 10

Perfect symmetric dataset — mean and median are the same (5.5)

Frequently Asked Questions

All three are "averages" but measure different things. Mean is the sum divided by the count — the most common type of average. Median is the exact middle value when numbers are sorted — useful when data has outliers. Mode is the most frequently occurring value — useful for categorical data. For the dataset {1, 2, 2, 3, 100}: mean = 21.6, median = 2, mode = 2. The median and mode better represent the "typical" value here.

A weighted average assigns different levels of importance (weights) to each value. It equals Σ(value × weight) ÷ Σ(weights). Common uses include GPA calculations (where credit hours are the weights), employee performance reviews (where each criteria has a different weight), investment portfolio returns (weighted by investment amount), and survey results where some responses represent more people than others.

Standard deviation measures how spread out numbers are from the mean. A low standard deviation means most numbers are close to the average; a high one means they are spread widely. For example, class A scores {78, 79, 80, 81, 82} and class B scores {50, 60, 80, 100, 110} both have a mean of 80, but class A has a very low standard deviation (≈1.4) while class B has a high one (≈22.8). This calculator uses the population standard deviation formula (÷n rather than ÷n-1).

Use geometric mean when dealing with multiplicative relationships: investment growth rates, percentage changes, ratios, and price indices. Example: if an investment grows by 10% in year 1, then loses 10% in year 2, the arithmetic mean return is 0% — suggesting no change. But you actually end up with 99% of your original investment (−1%). The geometric mean correctly shows a −0.5% average annual return. It's always ≤ arithmetic mean (with equality only when all values are identical).

A dataset has no mode when every value appears exactly once — no value is more frequent than others. A dataset is bimodal when two values appear equally often and more frequently than others (e.g., {1,2,2,3,3} has modes 2 and 3). A dataset is multimodal with three or more modes. This calculator detects and displays all modes when a dataset has multiple.

Exactly the same way — add all values (including negatives) and divide by the count. For {−5, −3, 0, 4, 8}: sum = 4, count = 5, mean = 0.8. Just enter negative numbers with a minus sign. Note: geometric mean requires all positive values and will show N/A for datasets containing negative or zero values, since you cannot take even roots of negative numbers in the real number system.