Mean, Median, Mode, Range Calculator
Enter Dataset
Results
| Mean (Average) | — |
|---|---|
| Median | — |
| Range | — |
| Mode | — |
| Geometric Mean | — |
| Largest | — |
| Smallest | — |
| Sum | — |
| Count | — |
| Sorted Data Set | — |
Homework problems love to ask for mean, median, mode, and range in one breath—but sorting the list, finding the middle, and counting frequencies by hand on a phone calculator is tedious. Paste your numbers once here and get all four measures plus sum, count, sorted order, geometric mean, and a full step-by-step walkthrough.
How to Use This Mean Median Mode Range Calculator
- Enter your list. Separate values with commas, spaces, tabs, or newlines. Copy-paste from a spreadsheet column works cleanly.
- Press Calculate. Results appear in the table: mean, median, range, mode, geometric mean, largest, smallest, sum, count, and the sorted dataset.
- Scroll to step-by-step. The tool shows sorting, mean arithmetic, median logic (odd vs. even N), mode frequency, range subtraction, and geometric mean when defined.
- Go deeper when needed. For variance, quartiles, and outliers together, open the Statistics Calculator. For spread-only work, use the Standard Deviation Calculator.
Mean, Median, Mode, and Range Formulas and Practical Applications
These four summaries answer different questions about the same list. Mean chases the balance point; median resists outliers; mode highlights repetition; range gives a quick full-span snapshot.
Mean (arithmetic average)
Mean = Σx / N
Add every value and divide by how many you have. For quiz scores 3, 5, 5, 6, 8, 10, 12, the sum is 49 and the mean is 49 / 7 ≈ 7.
Median (middle value)
Sort ascending first. Odd N: pick the center term. Even N: average the two middle terms. In a skewed salary list, median often describes a "typical" earner better than mean because one executive paycheck will not drag it upward as hard.
Mode (most frequent)
The tool counts how many times each value appears. A single winner is unimodal; a tie lists every value at max frequency. When all values appear once—or every value ties—there is no unique mode. Retail teams use mode for the best-selling size or SKU in a period.
Range and geometric mean
Range = Max − Min
Geometric Mean = (x₁ × x₂ × … × x_N)^(1/N)
Range is the simplest spread measure—max minus min—but it ignores everything in between. Geometric mean suits compounded growth rates; it needs strictly positive inputs, same rule as on the statistics page.
Frequently Asked Questions
What are mean, median, mode, and range?
Mean is the average, median is the sorted middle, mode is the most common value, and range is largest minus smallest. This page computes all four from one paste.
How is the median found when N is even?
With an even count, average the two central values after sorting. Example: for 4, 8, 10, 12, median = (8 + 10) / 2 = 9.
Can a dataset have more than one mode?
Yes—bimodal or multimodal lists show every value tied for top frequency. The results table states how many times each mode appeared.
When should I use median instead of mean?
Choose median when outliers would distort the average—home prices, wait times, or income surveys are classic cases. Use mean when values are fairly symmetric and every point should count equally.
Why is geometric mean undefined for some lists?
Zero or negative values break the product-and-root definition. Convert percentages to positive multipliers first if you are tracking growth. Browse math calculators for related stats tools.