Average Calculator
Mean, median, mode
About This Calculator
The three most common measures of central tendency — mean, median, and mode — each describe the center of a data set in a different way. The mean is the arithmetic average, the median is the middle value when sorted, and the mode is the most frequently occurring value. Understanding when to use each measure helps you interpret data more accurately and avoid misleading conclusions.
Formula
Mean = (x₁ + x₂ + ... + xₙ) / n [sum divided by count]
Median = middle value after sorting (or average of two middle values)
Mode = value that appears most frequently
Example Calculation
Data set: [4, 7, 2, 9, 4, 6]
- Mean = (4+7+2+9+4+6) / 6 = 32 / 6 = 5.33
- Sorted: [2, 4, 4, 6, 7, 9] → Median = (4+6)/2 = 5.0
- Mode = 4 (appears twice, more than any other value)
Mean = 5.33, Median = 5.0, Mode = 4
Mean, Median, Mode for Sample Data Sets
| Data Set | Mean | Median | Mode |
|---|---|---|---|
| 1, 2, 3, 4, 5 | 3.0 | 3 | None |
| 2, 4, 4, 6, 8 | 4.8 | 4 | 4 |
| 10, 20, 20, 30, 100 | 36.0 | 20 | 20 |
| 5, 5, 5, 5, 5 | 5.0 | 5 | 5 |
Frequently Asked Questions
When should I use median instead of mean?
Use the median when your data has extreme outliers or is skewed. For example, median household income is preferred over mean because a few very high earners can distort the average.
Can a data set have more than one mode?
Yes. A data set with two modes is called bimodal; three or more modes is multimodal. If all values appear equally often, there is no mode.
What is a weighted average?
A weighted average assigns different importance (weight) to each value. Weighted mean = Σ(value × weight) / Σ(weights). This is used in GPA calculations, for example.
How does the mean change when an outlier is added?
The mean is highly sensitive to outliers. Adding a very large or very small value can significantly shift the mean, while the median changes minimally.