This mean median mode range calculator starts from a comma-separated list of numbers and reports the arithmetic mean as the primary result. Enter values like 1,2,2,3,4,7,9 to get mean = 4. Use the same list to reason about median, mode, and range in class or reports.
Students checking homework and analysts summarizing small samples both need a clean average first. For counting selections instead of averages, see the permutation combination calculator.
How the formula works
Sum every number in the list, then divide by how many numbers you entered. That quotient is the mean. Empty lists are invalid.
Worked example
Values 1,2,2,3,4,7,9. Sum = 28. Count = 7. Mean = 28 ÷ 7 = 4. Median (middle when sorted) = 3. Mode = 2. Range = 9 – 1 = 8.
| Stat | Value |
|---|---|
| List | 1,2,2,3,4,7,9 |
| Mean (primary) | 4 |
| Median | 3 |
| Mode | 2 |
| Range | 8 |
How to use the fields
- Values should be comma-separated numbers with no extra words.
Choosing which center to report
Mean is sensitive to outliers. Median is the middle value after sorting. Mode is the most frequent value. Range is a simple spread measure. Report the one that matches the question you were asked.
Common mistakes
- Forgetting to sort before finding the median
- Calling every repeated value a mode when frequencies differ
- Mixing units inside one list
- Dividing by n-1 when the question asked for a simple mean
Classroom checklist
- Paste or type the full list once.
- Confirm the mean matches sum divided by count.
- Sort a copy for median and range checks.
- Scan frequencies for mode.
Small samples
With few numbers, one outlier can swing the mean hard. Mention the median beside the mean when you present skewed homework sets or small business samples.
Walking the default list by hand
List: 1, 2, 2, 3, 4, 7, 9. Sum the seven numbers to 28. Mean is 28 ÷ 7 = 4, which matches the primary engine result. Sort the list and pick the middle value for median 3. Count frequencies to see that 2 appears twice while others appear once, so mode is 2. Subtract the smallest from the largest for range 8.
Doing all four by hand once teaches what each word means. After that, use the calculator for longer lists where summing by hand wastes time.
When to prefer median
Income samples, home prices, and test scores with a few extreme outliers often communicate better with a median. The mean still matters for totals and for many formulas, but a single huge value can drag the mean away from what a typical person experiences.
If your teacher asks for all four statistics, report them as a set rather than arguing that one is always best.
Modes and multimodal lists
Some lists have two values tied for most frequent. Classroom rules differ on how to report multimodal sets. State the tied values clearly. The mean remains well defined even when mode talk gets messy.
Lists with all unique values are sometimes said to have no mode. Again, follow the rubric you were given and still compute mean, median, and range cleanly.
Data entry hygiene
Remove stray words, currency symbols, and extra spaces before you rely on a paste. Keep one unit system inside the list. A mix of centimeters and meters in the same comma list produces nonsense averages even if the arithmetic runs.
For grades or survey scores, confirm whether zeros are real scores or missing data codes. Missing data usually should not be averaged as zeros unless the rubric says so.
Reporting for non experts
When you share results with classmates or coworkers, state the list size and the mean first, then add median or range if skew matters. A lone average without context invites confusion. For the default list, saying “mean 4 on 7 values, range 8” already paints a clearer picture than “the average is 4” alone.
Charts help, but only after the numbers are correct. Garbage in still becomes garbage on a bar graph.
Outlier policy
Decide before analysis whether an extreme value is an error to remove or a real observation to keep. Removing inconvenient outliers after seeing the mean is bad practice. Document the rule you used.
Limitations
The primary engine result for this page is the mean. Other statistics are useful for interpretation and teaching, but keep the reported primary number aligned with the mean formula above.