Average Calculator
Calculate mean, median, mode, range, and sum for any set of numbers.
Returns descriptive statistics for homework, data analysis, and grade averaging.
The three measures of central tendency — mean, median, and mode — each describe the “center” of a dataset differently, and each is appropriate in different situations. Knowing when to use which measure is just as important as knowing how to calculate them.
Mean (arithmetic average): Mean = Sum of all values / Count of values
Median (middle value): Arrange all values in order. If odd count: middle value. If even count: average of the two middle values.
Mode: The value that appears most frequently. A dataset can have no mode, one mode, or multiple modes.
Worked example: Dataset: 4, 7, 7, 9, 13, 15, 21
Mean = (4+7+7+9+13+15+21) / 7 = 76 / 7 = 10.86 Median = 9 (4th value in 7-item sorted list) Mode = 7 (appears twice; all others appear once)
When each measure is best:
- Mean — best for symmetric distributions without extreme outliers (test scores, temperatures)
- Median — best when outliers are present (income data, home prices). The US median household income is used instead of mean because a handful of billionaires would distort the mean dramatically.
- Mode — best for categorical data (most popular shoe size, most common eye color)
Effect of outliers: Dataset: 10, 12, 11, 13, 10, 95 (one outlier) Mean = 151 / 6 = 25.2 (distorted by 95) Median = (11+12) / 2 = 11.5 (robust to outlier)
Weighted mean: When values have different importance levels: Weighted Mean = Σ(value × weight) / Σ(weights) Used for GPA calculations, investment portfolio returns, and course final grades.