Average Calculator Guide: Mean, Median, Mode & Range
There are four key ways to summarise a set of numbers. Understanding when to use mean vs median (and why they differ) is one of the most practical math skills.
The Four Measures — Compared
Data set: [4, 7, 7, 9, 12, 15, 50]
| Measure | Formula | Result | Best for |
|---|---|---|---|
| Mean | Sum ÷ Count | 14.9 | Symmetric data without outliers |
| Median | Middle value | 9 | Skewed data or outliers present |
| Mode | Most frequent | 7 | Categorical data, most common value |
| Range | Max − Min | 46 | Understanding spread of data |
Notice how the outlier (50) pushes the mean to 14.9 while the median stays at 9 — much more representative of the "typical" value.
Frequently Asked Questions
What is the difference between mean, median, and mode?
Mean is the arithmetic average (sum ÷ count). Median is the middle value when numbers are sorted. Mode is the most frequently occurring value. For the data set [2, 3, 3, 4, 10]: Mean = 4.4, Median = 3, Mode = 3.
When should I use median instead of mean?
Use median when your data has extreme outliers that skew the mean. Income data is a classic example — a few very high earners pull the mean up dramatically. India's median household income is far lower than its mean income.
What is a weighted average?
A weighted average multiplies each value by its weight before summing, then divides by the total weight. Weighted Average = Σ(value × weight) ÷ Σ(weights). Used for GPA calculation, stock portfolio performance, and weighted exam scores.
What is the range of a data set?
Range = Maximum value − Minimum value. It measures the spread of data. For [2, 5, 7, 11, 18], Range = 18 − 2 = 16. A large range indicates high variability; a small range indicates data is tightly clustered.
Can a data set have more than one mode?
Yes. A data set with two modes is bimodal; with three or more is multimodal. For [1, 2, 2, 3, 3, 4], both 2 and 3 appear twice — this is bimodal. If no number repeats, there is no mode.
Related Calculators
Calculate Mean, Median & Mode
Enter any set of numbers to instantly get mean, median, mode, range, and more statistics.
Open Average Calculator