Mean and statistics calculator
Mean, median, mode, range and standard deviation for a list of numbers.
Fill in the fields and the result will appear here automatically.
Works out the descriptive statistics of any list: the mean and median as different summaries of the data location, together with the mode, the range and the spread. Numbers can be pasted as a column or typed with spaces between them. Variance defaults to the sample form with n−1 in the denominator, because a list is usually a sample of something larger; the population form is an explicit choice, not a hidden one.
How it works
Formula and logic
The mean is the sum divided by the count. The median is the middle of the ordered list, or the average of the two central values when the count is even. Variance is the mean squared deviation from the mean — divided by n−1 for a sample and by n for a population — and the standard deviation is its square root. The sum, mean, median, minimum, maximum, range and standard deviation retain the data unit; variance has its square. List entries must describe the same quantity in a consistent unit. The limit is 1–10000 finite numbers and 1000000 characters. An out-of-range sum or variance is marked separately because a finite mean or standard deviation may still be recoverable. A genuine zero is distinguished from a positive value too small to represent numerically.
Example
The list 4, 8, 15, 16, 23, 42 has a mean of 18 but a median of 15.5: one large value pulls the mean up and barely moves the median.
Fields and units
- Numbers — one per line or separated by spaces — data unit
- Variance — list option
How to use
- — Paste the numbers as a column, or type them separated by spaces.
- — Choose whether the list is a sample or the whole population.
- — Read the mean and the spread measures below it.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- NIST: mean, median and possibly nonunique mode definitions NIST: sample variance, deviation, range and units of spread
- Limitation
- Variance is the mean squared deviation from the mean — divided by n−1 for a sample and by n for a population — and the standard deviation is its square root. List entries must describe the same quantity in a consistent unit.
FAQ
How does the median differ from the mean?
The mean uses the size of every value, so a single very large number shifts it noticeably. The median only uses the ordering, which makes it far more resistant to outliers.
Should I pick sample or population variance?
If the list is a sample you are using to judge something larger, use the sample form with n−1. If those numbers are every case you care about, use the population form.
Why is the mode sometimes shown as a dash?
This is a display convention: if every value occurs once, the tool shows a dash rather than listing all values tied for the greatest frequency. When values repeat, it lists every value sharing the highest frequency; a mode need not be unique.
What happens if the list has a typo in it?
Any nonnumeric or unrepresentable token stops the entire calculation. Silently skipping it would change the data set. Separators are whitespace, semicolons, newlines or commas followed by whitespace; a decimal comma without whitespace stays within the number.