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Choose Sample when your data is a subset of a larger group (divides by n−1). Choose Population when your data is the entire group (divides by n).
Try an example: 2,4,4,4,5,5,7,9
Whether you are a student tackling a homework set, a teacher preparing a lesson, a researcher summarizing survey results, or a business analyst making sense of sales figures, the FistHost Statistics Calculator gives you instant, accurate descriptive statistics from any list of numbers. Paste or type your dataset — separated by commas, spaces, or new lines — and the tool immediately computes the mean, median, mode, range, variance, and standard deviation, displays your data in sorted order, and presents everything in one clean statistics table. There is no sign-up, no software to install, and no limit on the size of datasets you can analyze. A built-in population/sample toggle makes sure your variance and standard deviation always use the right formula for your data. For related math tools, try our Scientific Calculator, GPA Calculator, or CGPA to Percentage Converter.
Mean (average) — the sum of all values divided by how many there are. Formula: mean = Σx ÷ n. The mean is the most familiar "average," but it can be pulled up or down by extreme outliers.
Median — the middle value of the sorted data. Formula: median = middle value of sorted data (average of two middles if n even). The median is resistant to outliers, which is why it is often used for things like house prices and incomes.
Mode — the most frequent value(s) in the dataset. A dataset can have one mode, several modes (multimodal), or no mode at all if every value appears only once.
Range — the simplest measure of spread. Formula: range = max − min. It tells you the width of your data at a glance but says nothing about how values are distributed inside that width.
Variance — the average of the squared differences from the mean. Population formula: population variance = Σ(x−μ)² ÷ N. Sample formula: sample variance = Σ(x−x̄)² ÷ (N−1). Squaring the differences gives extra weight to values far from the mean.
Standard deviation — the square root of the variance. Formula: std dev = √variance. It brings spread back into the original units of your data, so it is the most commonly reported measure of variability.
The calculator includes a population/sample toggle because variance and standard deviation use different formulas depending on what your data represents. Use population when your numbers are the entire group you care about (for example, the test scores of every student in one class). Use sample when your data is just a subset of a larger group (for example, 50 surveyed customers standing in for thousands) — the sample formula divides by N−1 instead of N to correct for the bias of estimating from a subset. One-line rule: use sample when the data is a subset of a larger group.
Let us walk through the classic dataset 2, 4, 4, 4, 5, 5, 7, 9 exactly as the calculator does:
| Statistic | Calculation | Result |
|---|---|---|
| Count (n) | 8 values | 8 |
| Sum (Σx) | 2+4+4+4+5+5+7+9 | 40 |
| Mean | 40 ÷ 8 | 5 |
| Median | Sorted data; middle two are 4 and 5 → (4+5)/2 | 4.5 |
| Mode | 4 appears three times, more than any other value | 4 |
| Range | 9 − 2 | 7 |
| Population variance | Squared deviations 9+1+1+1+0+0+4+16 = 32 → 32 ÷ 8 | 4 |
| Population std dev | √4 | 2 |
| Sample variance | 32 ÷ 7 | 4.571 |
| Sample std dev | √4.571 | 2.138 |
Notice how the sample variance (4.571) is a little larger than the population variance (4) — that N−1 correction is the toggle at work.
Exam scores: a teacher enters 28 quiz scores to get the class mean and standard deviation, instantly seeing both the average performance and how widely scores vary.
Business sales: a shop owner pastes 12 months of revenue to find the median monthly income (resistant to one bumper holiday month) and the standard deviation to gauge how unpredictable cash flow is.
Fitness tracking: a runner logs 20 run times, checks the mean pace and standard deviation, and watches the standard deviation shrink over weeks as training makes performance more consistent.
Quality control: a small manufacturer measures 50 parts, and a rising standard deviation flags that the production process is drifting before defects pile up.
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What is the difference between population and sample standard deviation?
Population standard deviation divides the squared deviations by N (the full group); sample standard deviation divides by N−1 to correct for bias when your data is only a subset of a larger group. Use the toggle in the tool to pick the right one — one-line rule: use sample when the data is a subset of a larger group.
Can the mode have more than one value?
Yes. If two or more values tie for the highest frequency, the dataset is multimodal and the calculator reports all of them. If every value appears exactly once, there is no mode.
What separators can I use for my data?
Commas, spaces, and line breaks all work, and you can mix them. Just paste your numbers and the tool sorts out the rest.
Is there a limit on dataset size?
No practical limit — the calculations run instantly in your browser, so even thousands of values are processed in a fraction of a second.
Why is the median 4.5 for an even-sized dataset?
With an even number of values there is no single middle value, so the median is defined as the average of the two middle values. For 2, 4, 4, 4, 5, 5, 7, 9 the two middles are 4 and 5, giving 4.5.
Is my data uploaded anywhere?
No. All calculations happen locally in your browser — your numbers are never sent to any server.
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