Every everyday statistic in one dropdown: mean, median, mode and range, population and sample standard deviation, variance, z-scores, percentile ranks, normal ranges, standard error, margin of error, confidence intervals, sample size, linear regression and correlation.
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FORMULA USEDStatistics Calculator
From a raw list to a defensible number
Paste or type your numbers into the list field — commas or spaces both work — and the dropdown decides what happens next: one statistic per member, with the substituted formula shown beneath the board. The inference members (margin of error, confidence interval, sample size, regression) ask for the small extra inputs they genuinely need, such as a confidence level or a second paired list.
Population σ or sample s?
Divide by n when your list is the entire population; divide by n − 1 when it is a sample drawn from something larger. The sample version is always a little larger because one degree of freedom was spent estimating the mean. For a normal curve, roughly 68% of values sit within 1σ of the mean, 95% within 2σ, and 99.7% within 3σ — the normal-range member computes the exact percentage for any k.
Worked example
Find the sample standard deviation of 2, 4, 4, 4, 5, 5, 7.
The mean is 31 ÷ 7 ≈ 4.4286; the squared deviations sum to 13.7143.
Divide by n − 1 = 6 to get the sample variance 2.2857.
s = √2.2857 ≈ 1.512 — the population σ for the same list is 1.4.
How to use it
Pick the statistic from the dropdown.
Type or paste your numbers — comma or space separated. Paired tools ask for X and Y lists of equal length.
Read the result board, the supporting rows, and the substituted formula.
Copy, print, or share the link — it remembers the member and your values.
Frequently asked questions
Should I use population or sample standard deviation?
If your list is the whole population (every item, an entire class roster), use σ with the n divisor. If it is a sample standing in for something bigger, use s with the n − 1 divisor — the unbiased choice for inference. Both appear as rows in either member so you can compare.
What is a z-score used for?
It expresses a value in standard-deviation units: z = (x − μ) ÷ σ. A z of 1.96 marks the point beyond which only 2.5% of a normal curve lies, which is where the familiar 95% cutoffs come from.
When do I use z = 1.96 versus 2.576?
Pick the confidence level first: 95% confidence corresponds to z = 1.96 and 99% to z = 2.576. The 99% interval is wider — more confidence costs precision — so the margin-of-error member shows both via the level dropdown.
How big a survey sample do I need?
The sample-size member uses n = z²p(1−p)/e². With the safe default p = 0.5, ±5% at 95% confidence needs 385 responses; tightening to ±3% at 99% pushes it past 1,800.
How is percentile rank computed here?
As the simple percentage of values strictly below yours: count them, divide by the total, multiply by 100. Ties are handled transparently — the board also shows how many values equal yours and the rank counting ties.
What does the correlation r actually tell me?
r runs from −1 (perfect negative line) through 0 (no linear relationship) to +1 (perfect positive line), and R² is the share of Y’s variance the line explains. Remember it only measures linear association — a curved relationship can hide behind a modest r.