Mean, Median, Mode Calculator
Enter a data set to see its mean, median and mode side by side, the sorted values with the middle highlighted, and the variance and standard deviation.
Paste or type numbers separated by commas, spaces or new lines. Decimals and negatives are fine.
Sorted from smallest to largest. Highlighted = middle value (median); underlined = mode.
- Variance (sample, s²)
- 79.5714
- Standard deviation (sample, s)
- 8.9203
- Variance (population, σ²)
- 68.2041
- Standard deviation (population, σ)
- 8.2586
- Range (max − min)
- 25
- Sum
- 600
- Count
- 7
- Minimum
- 70
- Maximum
- 95
- Geometric mean
- 85.293
How the mean was calculated
- Add up all 7 numbers: 85 + 92 + 78 + 92 + 88 + 70 + 95 = 600.
- Divide the sum by how many numbers there are: 600 ÷ 7 = 85.714286.
How the median was found
- Sort the numbers from smallest to largest: 70, 78, 85, 88, 92, 92, 95.
- There are 7 numbers (odd), so the median is the middle one, the 4th value: 88.
How the mode was found
- Count how often each value appears.
- 92 appears 2 times, more than any other value, so it is the mode.
How the variance and standard deviation were calculated
- Find the mean: 85.714286.
- Subtract the mean from each value and square the result, then add those squares: Σ(x − mean)² = 477.428571.
- Population variance σ² = 477.428571 ÷ 7 = 68.204082; population standard deviation σ = √68.204082 = 8.258576.
- Sample variance s² = 477.428571 ÷ (7 − 1) = 79.571429; sample standard deviation s = √79.571429 = 8.920282.
How this mean, median, mode calculator works
Mean, median and mode are the three "measures of center" every statistics unit starts with, and they answer slightly different questions. This mean, median, mode calculator computes all three from the same list, shows the sorted data with the middle value highlighted so you can see where the median comes from, and adds the range, variance and standard deviation that usually come next in the chapter.
Mean: add everything up and divide by the count. Median: sort the numbers and take the middle one (or the average of the two middle ones). Mode: the value that shows up most often. Open the "How the…" sections under the result to see each one worked out for your data.
Worked example
Take the data set 2, 4, 4, 4, 5, 5, 7, 9. The sum is 40 and there are 8 values, so the mean is 40 ÷ 8 = 5. The list is already sorted, and with an even count the median is the average of the 4th and 5th values: (4 + 5) ÷ 2 = 4.5. The number 4 appears three times, more than any other, so the mode is 4. The range is 9 − 2 = 7.
For the variance, subtract the mean from each value and square it: (2 − 5)² = 9, (4 − 5)² = 1 three times, (5 − 5)² = 0 twice, (7 − 5)² = 4 and (9 − 5)² = 16. Those add up to 32. The population variance is 32 ÷ 8 = 4 and the population standard deviation is √4 = 2. If these eight numbers were a sample from a larger group you would divide by 7 instead: variance 4.57, standard deviation 2.14.
Median rules students forget
Always sort first. The median of 9, 2, 7 is 7, not 2, because sorted it is 2, 7, 9. With an even number of values there is no single middle, so you average the two in the middle; the result may be a number that is not in the list at all, like the 4.5 above. The calculator highlights exactly which one or two values it used.
Mode rules: none, one, or several
If every value appears exactly once, there is no mode, and writing "0" is wrong. If two values tie for the most appearances, both are modes and the data is bimodal; three or more ties make it multimodal. The calculator lists every mode and underlines them in the sorted strip. The mode is the only one of the three that works for non-numeric data, like favorite colors, and the only one that is guaranteed to be an actual value from the list.
Which one describes the data best?
When data is roughly symmetric, mean, median and mode land close together and the mean is the natural choice. When data is skewed, say most students scored 85 to 95 but two scored 20, the mean drops toward the outliers while the median stays put, so the median is the fairer summary. Comparing the mean to the median is a quick test for skew: mean below median means a tail on the low side, mean above median means a tail on the high side. For a quick average of a plain list, the average calculator focuses on just the mean; for weighted grades, use the grade calculator.
Frequently asked questions
›How do you find the median of an even number of values?
Sort the list and average the two middle values. For 1, 2, 3, 4 the middle values are 2 and 3, so the median is (2 + 3) ÷ 2 = 2.5.
›What if there is no mode?
If every value appears exactly once, the data has no mode, and this calculator says so. If two or more values tie for the most appearances, they are all modes and the data is called bimodal or multimodal.
›How do you calculate variance?
Find the mean, subtract it from each value, square each difference and add them up. Divide by n for the population variance or by n − 1 for the sample variance. For 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5, the squared differences sum to 32, and the population variance is 32 ÷ 8 = 4.
›What is the relationship between variance and standard deviation?
Standard deviation is the square root of variance. A variance of 4 means a standard deviation of 2, which is in the same units as the data and easier to interpret.
›What is the range?
The largest value minus the smallest. For test scores from 70 to 95 the range is 25. It is the simplest measure of spread but is thrown off by a single outlier.