๐ Statistics Calculator
Enter a comma- or line-separated list of numbers and instantly calculate basic statistics all at once: count, sum, mean, median, mode, minimum, maximum, range, and standard deviation (population and sample). Useful for analyzing test scores or doing quick data summaries.
How to use
- Enter your numbers separated by commas, spaces, or line breaks.
- Each statistic is calculated automatically and listed.
How the calculation works
The mean is the total divided by the count; the median is the middle value once sorted (the average of the middle two when the count is even); the mode is the most frequent value. The mean is pulled easily by extreme values while the median resists outliers, which is why, for something like household income where a few very large values drag the average up, the median better describes a typical value. Standard deviation measures spread: square each value's distance from the mean, average those squares, and take the square root. What you divide by gives two versions. If your data is the entire group you care about (the population), divide by n for the population standard deviation. If it is a sample drawn from a larger group, divide by n โ 1 for the sample standard deviation. Dividing by n โ 1 corrects for the fact that a sample's own mean sits closer to its data than the true population mean does, so dividing by n would underestimate the spread. This adjustment is known as Bessel's correction.
Worked example
Six test scores: 72, 85, 90, 64, 85, 78 1. Sum 474, count 6, mean 474 รท 6 = 79 2. Sorted: 64, 72, 78, 85, 85, 90 โ median (78 + 85) รท 2 = 81.5 3. Mode 85 (appears twice); range 90 โ 64 = 26 4. Sum of squared differences from the mean: 49 + 36 + 121 + 225 + 36 + 1 = 468 5. Population SD: โ(468 รท 6) โ 8.832 6. Sample SD: โ(468 รท 5) โ 9.675 If these six are the whole class, use the population figure; if they were picked from a whole year group, use the sample figure.
Things to be aware of
- Separate values with commas, line breaks or spaces. Anything that is not a number is ignored.
- With few values, the gap between population and sample SD is large. Choose based on what your data represents.
- Sample standard deviation needs at least two values.
- A standardised score of the form 50 + 10 ร (score โ mean) รท SD can be built from the mean and standard deviation shown here.
FAQ
What's the difference between population and sample standard deviation?
Use population standard deviation when your numbers represent the entire dataset, and sample standard deviation when they're a sample drawn from a larger population. Sample standard deviation is always slightly larger.
What happens if there's more than one mode?
If multiple values tie for the highest frequency, all of them are shown. If every value appears the same number of times, it shows "No mode".
Does this support decimal numbers?
Yes โ both whole numbers and decimals are supported.