NumberTally Statistics Calculator
Paste any list of numbers and get instant descriptive statistics — count, sum, mean, population and sample variance, population and sample standard deviation, minimum, and maximum. Now with a bar chart, quartiles, and a side-by-side population vs sample comparison. Free, no sign-up.
Advanced options
Population vs sample: which one do you need?
Use the population figures when your numbers are the entire group you care about (every test score in the class). Use the sample figures when your numbers are a subset drawn from a larger group — the sample formulas divide by n−1 instead of n, which corrects for the fact that a sample tends to underestimate true spread.
Reading your results
The mean is the balancing point of the data. The variance is the average squared distance from the mean, and the standard deviation is its square root — back in the original units, so it's the "typical distance from average." The range (max − min) is the quickest spread check, while the IQR (Q3 − Q1) describes the middle 50% and resists outliers.
Frequently Asked Questions
When should I use population vs sample standard deviation?
Population when you have every value in the group of interest; sample when your data is a subset of a bigger group. In practice, most real-world data (surveys, experiments) is a sample.
What is variance, in plain terms?
The average of the squared differences from the mean. Squaring keeps negative and positive deviations from canceling out. The standard deviation is simply the square root of the variance.
Can I paste numbers copied from a spreadsheet?
Yes — paste from Excel or Google Sheets; values can be separated by commas, spaces, tabs, or line breaks, and non-numeric cells are ignored.
Why is the sample standard deviation larger than the population one?
Because it divides by n−1 instead of n (Bessel's correction). A sample usually misses some extremes, so the correction inflates the estimate back toward the true population spread.
What are quartiles and the IQR?
Quartiles split sorted data into quarters: Q1 (25th percentile), the median (50th), Q3 (75th). The interquartile range, Q3−Q1, covers the middle half of the data and is robust against outliers.