This mean median mode range calculator reads a comma separated list and reports mean, median, mode, and range. The primary engine result is the mean; the other three appear in the detail list.
Formulas
Mean = sum / count. Median = middle sorted value, or average of two middle values when count is even. Mode = highest frequency value(s). Range = max minus min.
Worked example
List 1,2,2,3,4,7,9. Count 7, sum 28, mean 4. Median 3. Mode 2. Range 8.
When each measure helps
Mean reacts to outliers. Median is steadier for skewed lists. Mode highlights repeats. Range only states end to end spread. If you only need the mean, the average calculator is a one-field version.
For a fuller stats panel including sample standard deviation, use the statistics calculator. For spread focused work, open the standard deviation calculator. For standardized scores, try the z-score calculator.
Definitions, as NIST states them
The NIST/SEMATECH e-Handbook of Statistical Methods defines the three measures of location:
- Mean: the sum of the data points divided by the number of data points.
- Median: the value with half the data below it and half above. For an odd count it is the middle sorted value. For an even count it is the average of the two middle values.
- Mode: the value that occurs most often. NIST notes that it is not necessarily unique.
The range is the largest value minus the smallest.
Mean median mode range calculator worked example
A tutor records ten quiz scores: 4, 8, 6, 5, 3, 8, 9, 5, 7, 45 (one student also counted bonus points).
- Sort: 3, 4, 5, 5, 6, 7, 8, 8, 9, 45.
- Mean: the sum is 100 and the count is 10, so the mean is 10.
- Median: the count is even, so average the 5th and 6th values: (6 + 7) ÷ 2 = 6.5.
- Mode: 5 and 8 each appear twice, so the list is bimodal (5 and 8). The mean median mode range calculator lists both.
- Range: 45 − 3 = 42.
Now remove the 45 and run the mean median mode range calculator again. The mean drops to 55 ÷ 9 ≈ 6.11 and the median to 6, the 5th of nine sorted values. One extreme value moved the mean by almost 4 points but the median by only 0.5. The range shrinks from 42 to 6.
Which average should the mean median mode range calculator report?
NIST explains that for skewed data the mean is pulled toward the longer tail, while the median is based on rank and is not distorted by extreme values. A practical rule:
- Roughly symmetric data with no outliers: report the mean. For normal data the mean, median and mode are about equal anyway.
- Skewed data such as incomes, house prices or response times: report the median, and say so.
- Categories or repeated values (shoe sizes, the most common rating): the mode is the useful one.
Mode edge cases
If every value appears exactly once, many textbooks say the list has no mode. This mean median mode range calculator lists every value instead, because each one is tied for the highest frequency. Read a mode result that repeats your whole list as “no mode”. With continuous measurements such as weights to two decimals, exact repeats are rare, and NIST suggests reading the mode from the tallest bar of a histogram.
Range vs a better measure of spread
The range uses only the two extreme values, so a single outlier changes it a lot, as the 45 did above. For a spread measure that uses every value, run the same list through the standard deviation calculator. To see how far one score sits from the mean, use the z-score calculator.
Last reviewed: October 2026