Formula for Median: Mean, Median and Mode Calculator With Range
Mean, median, mode and range
Median = middle of the sorted values (average two middle values if count is even)
Values separated by commas or spaces
Read the values, keeping repeated observations.
Median = middle of the sorted values (average two middle values if count is even)
Worked example you can change
Mean = sum ÷ count; median = middle of the numeric order; modes = most frequent values.
- Sorted values: 1, 2, 2, 3, 3, 4
- Mean ≈ 2.5; median ≈ 2.5; modes = 2, 3; range ≈ 3
Calculator
Enter 1–1,000 decimal values separated by commas or ASCII whitespace, up to 32,768 characters total; each value has up to 15 significant digits and magnitude zero or 10⁻¹²–10¹².
- Count
- 6
- Mean
- 2.5
- Median
- 2.5
- Modes
- 2, 3
- Range
- 3
Formula variants
| Shape or method | Formula | Meaning |
|---|---|---|
| Mean | mean = Σx / n | The sum divided by count uses every observation. |
| Median | middle sorted value, or average of middle pair | Sort numerically before locating the center. |
| Modes | values tied for greatest frequency > 1 | All tied modes are reported; all-once lists have no mode. |
| Range | maximum − minimum | Range measures the span of the observations. |
Questions
Can a list have more than one mode?
Yes. Every value tied for the greatest frequency is reported when that frequency exceeds one.
What if every value appears once?
This calculator reports No mode. It does not label every unique observation a mode.
How is an even-length median calculated?
Sort the values numerically and average the two middle observations.
Are duplicates retained?
Yes. Duplicates contribute to the count, sum, median ordering and frequency table.
Sources and method
Find arithmetic mean, median, every tied mode and range. See numeric sorting, middle values and a worked example that updates when you change the list.
We calculate with 40 significant digits and round only the displayed result. Diagrams are labelled explanations and are not measurement drawings.
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