How this works
Paste any list of numbers — separated by commas, spaces, or new lines — and the calculator gives you the standard descriptive statistics in one go: how many values, their sum, the average (mean), the middle value (median), the most frequent value (mode), the spread (range, standard deviation, variance) and the extremes. Useful for quickly summarising survey results, exam scores, sensor readings, or any list of measurements without firing up a spreadsheet.
The formula
n = number of values. x = each individual value. The calculator uses the population variance (divide by n) — what you want when describing the list as it stands. Sample variance (dividing by n − 1) is used when the list is a sample drawn from a larger population and you want to estimate the population's spread; rare for ad-hoc lists, common in research papers.
Example calculation
- Eight test scores: 12, 18, 22, 9, 15, 12, 27, 19.
- Sum = 134. Mean = 134 / 8 = 16.75. Sorted: 9, 12, 12, 15, 18, 19, 22, 27 → median = (15 + 18) / 2 = 16.5.
- Mode = 12 (only repeated value). Range = 27 − 9 = 18. Standard deviation ≈ 5.5.
Frequently asked questions
What's the difference between mean, median, and mode?
All three describe a "typical" value but in different ways. Mean is the arithmetic average — sensitive to outliers. Median is the middle value when sorted — robust to outliers. Mode is the most-frequent value — useful for categorical data and skewed distributions. House prices are usually reported as the median because a few mansions push the mean up; shoe-size demand is reported as the mode because it tells the shop what to stock.
Is the standard deviation here population or sample?
Population — divides by n, not n − 1. That's the right choice when you want to describe the list as it stands (e.g. "these are my eight test scores"). If your numbers are a sample drawn from a larger population and you want to estimate the population's spread, divide by n − 1; the result is roughly 7% larger for n=8 and converges quickly as the list grows.
Why does mode show 'no mode' even though my list has values?
Because every value is unique — no number appears more than once. We treat that as "no mode" rather than reporting all values as equally modal, which most stats textbooks agree with. If two or more values share the highest frequency, all of them show up (multimodal data).
Can I paste numbers from a spreadsheet?
Yes — copy a column from Google Sheets, Excel or Numbers and paste directly. The parser handles tabs, newlines, commas, and spaces interchangeably, so you don't need to clean the data first. Anything that doesn't parse as a number (column headers, blank cells, "N/A") is silently dropped.