Average Finder
Instantly calculate the mean, median, mode, and range for any set of numbers with detailed calculation steps and distribution stats.
Also covers: mean median mode and range calculator with steps · dataset summary statistics calculator · calculate average of numbers
Formula & How It Works
mean = sum ÷ count · median = middle of the sorted list · range = max − min
- The mean adds every value and divides by how many numbers you entered.
- The median sorts the values and takes the middle one, averaging the two middle values when the count is even.
- The mode is the most frequent value and is reported as a dash when every value appears once; the range is the largest value minus the smallest.
Step-by-Step Example
The sample data set 4, 8, 15, 16, 23, 42.
- 1.Sum
- 4 + 8 + 15 + 16 + 23 + 42 = 108
- 2.Mean
- 108 ÷ 6 = 18
- 3.Sorted list
- 4, 8, 15, 16, 23, 42 → middle pair 15 and 16
- 4.Median
- (15 + 16) ÷ 2 = 15.5
- 5.Mode
- every value appears once, so no mode
- 6.Range
- 42 − 4 = 38
Mean 18, median 15.5, no mode, and a range of 38.
Frequently asked questions
What is the difference between mean and median?
The mean adds every value and divides by how many there are. The median sorts the values and takes the middle one, averaging the two middle values when the count is even. For 4, 8, 15, 16, 23, 42 the mean is 18 but the median is 15.5, because the larger values pull the mean upwards.
Can a dataset have more than one mode?
Yes. The mode is whichever value appears most often, so if two or more values tie for the highest count the dataset is bimodal or multimodal and all of them are modes. If every value appears exactly once there is no mode at all, which this calculator reports as a dash.
How do outliers affect the mean versus the median?
A single extreme value moves the mean a great deal and the median very little. Adding 1,000 to 4, 8, 15, 16, 23, 42 lifts the mean from 18 to about 158 while the median only moves to 16.5. That is why median income and median house prices are usually quoted instead of averages.
About the Average Finder
Instantly calculate the mean, median, mode, and range for any set of numbers with detailed calculation steps and distribution stats.
It runs entirely in your browser — nothing you type is sent to a server — and the result updates as you edit the inputs. Estimates are for educational and informational purposes only; see ourdisclaimer.
Common searches
- mean
- median
- mode
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