Last updated: October 2026
How to find sample mean
Short answer: add up every value in your sample, then divide by how many values there are. Four steps: (1) list your data, (2) add them all up to get the sum, (3) count how many values you have, (4) divide the sum by the count. The calculator above runs the same steps instantly as you type.
- List your data. Example: 12, 15, 18, 22, 33.
- Add them up. 12 + 15 + 18 + 22 + 33 = 100.
- Count the values. n = 5.
- Divide. 100 ÷ 5 = 20, so x̄ = 20.
Sample mean formula
The formula never changes, only the numbers:
x̄ = Σx / n
x̄ is the sample mean, Σx (sigma-x) is the sum of all your values, and n is how many values you have. For the dataset 12, 15, 18, 22, 33: x̄ = 100 ÷ 5 = 20. The same formula works for test scores, survey responses, measurements — anything you can average. The arithmetic mean on Wikipedia covers the general math.
Sample mean vs population mean
Short answer: the calculation is identical — add and divide — but a sample mean (x̄) describes the subset you measured, while the population mean (μ) describes everyone or everything. x̄ estimates μ, and a new sample gives a slightly different x̄ every time.
Think of a pot of soup: μ is the taste of the whole pot, x̄ is the taste of one spoonful. You use the spoonful to estimate the pot — that is the entire logic of inferential statistics, and the reason the symbol matters. Mixing up x̄ and μ is the #1 notation mistake on AP Statistics exams.
Mean calculator
Searching for a plain mean calculator? You're in the right place — the sample mean of your data is the same thing as its mean. "Mean", "average" and "sample mean" all describe Σx ÷ n; the word "sample" just reminds you the data is a subset. Paste any list of numbers above and the hero result is your mean, with the full descriptive-stats breakdown (standard deviations, min, max, range) underneath. If your values carry different weights — exam scores worth different percentages — use the weighted average calculator instead.
Sample mean and standard deviation
Short answer: the mean tells you the center of your data, the standard deviation tells you how spread out it is. This calculator reports both: the sample standard deviation s (divide by n − 1) for data that is a sample, and the population standard deviation σ (divide by n) when your data is the whole population.
For 12, 15, 18, 22, 33: mean 20, squared differences 64, 25, 4, 4, 169, sum 266 — sample SD = √(266 ÷ 4) ≈ 8.15, population SD = √(266 ÷ 5) ≈ 7.29. Always pair a mean with a spread: two classes can both average 75 while one has every student at 75 and the other ranges from 40 to 100. When you report results, round sensibly — the significant figures calculator keeps your precision honest, and the scientific notation converter handles very large or small datasets.
Frequently asked questions
What is the sample mean?
The sample mean is the average of a subset of data taken from a larger population. Add up all the values in your sample and divide by how many there are: x̄ = Σx / n. Example: the sample mean of 12, 15, 18, 22 and 33 is (12 + 15 + 18 + 22 + 33) ÷ 5 = 20.
What is the sample mean symbol?
The sample mean symbol is x̄ (x-bar): the letter x with a bar over it. It is the sample's counterpart to μ (mu), the Greek letter used for the population mean. Whenever you see x̄ in a statistics textbook, it means the average of the sample you measured — not the average of everyone.
How do I find the sample mean on a calculator?
Enter each value of your dataset, then divide their sum by the count. Paste your numbers into the calculator at the top of this page — it accepts comma, space or newline separated values and shows x̄ plus the full working (sum, count, sorted data). On a physical calculator: add the values, press equals, then divide by the number of values.
What is a sample mean and standard deviation calculator?
A tool that computes both the average of your data and how spread out it is. This page's calculator is one: it returns the sample mean x̄, the sample standard deviation s = √(Σ(x − x̄)² / (n − 1)) and the population standard deviation σ = √(Σ(x − μ)² / n), plus count, sum, min, max and range — everything in one place.
What is the difference between sample standard deviation and population standard deviation?
The formulas differ by one number in the denominator. Sample standard deviation divides by n − 1 (Bessel's correction), which corrects the bias from estimating the mean from the sample itself — use it when your data is a sample of something bigger. Population standard deviation divides by n and is used when your data is the entire population.
How do you calculate sample standard deviation by hand?
Four steps: (1) find the sample mean x̄, (2) subtract x̄ from each value and square each result, (3) add those squared differences up, (4) divide by n − 1 and take the square root. Example with 12, 15, 18, 22, 33: mean 20, squared differences 64, 25, 4, 4, 169, sum 266, 266 ÷ 4 = 66.5, √66.5 ≈ 8.15.
What is the difference between sample mean and population mean?
The sample mean (x̄) is the average of a subset you actually measured; the population mean (μ) is the average of everyone or everything. The calculation is identical — add and divide — but x̄ is a statistic that changes with every new sample, while μ is a fixed (usually unknown) parameter. Samples estimate populations: that is why the distinction matters in statistics.
Is this a statistics calculator?
Yes — a focused one. The calculator at the top of this page computes the core descriptive statistics for any dataset: the sample mean, the sample and population standard deviation, count, sum, minimum, maximum and range. For related stats work, ToolVaultly's statistics cluster includes the
weighted average calculator (grades where assignments carry different weights), the
significant figures calculator (keeping your rounding precision honest) and the
scientific notation converter (very large or small datasets).
Is my data private?
Completely. Every calculation happens locally in your browser with JavaScript — your numbers are never sent to a server, stored, or tracked in any way.
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