Enter any list of numbers and get the mean, median, mode, standard deviation, and more — each result worked out step by step. The statistics solver below handles one-variable data sets in seconds.
Instant Statistics Calculator
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What the statistics solver does
The statistics solver takes a list of numbers and instantly computes the descriptive statistics you need for homework, lab reports, and data projects. Type your values into the tool above, separated by commas or spaces, and it returns each result alongside the steps that produced it.
It handles the most common one-variable measures, including:
- Measures of center — mean (average), median, and mode.
- Measures of spread — range, variance, and standard deviation (both population and sample).
- Summary values — minimum, maximum, sum, count, and quartiles.
Because our AI engine reads plain text and the built-in equation editor, you can paste a data set straight from your notes and get a clean, worked solution back — not just a final number.
Key formulas
Mean: $$\bar{x} = \frac{1}{n}\sum_{i=1}^{n} x_i$$ Sample standard deviation: $$s = \sqrt{\frac{1}{n-1}\sum_{i=1}^{n}(x_i - \bar{x})^2}$$
Worked examples
Example 1: Mean, median, and mode
Find the mean, median, and mode of \(6, 7, 7, 9, 12\).
Mean. Add the values and divide by how many there are:
$$\bar{x} = \frac{6 + 7 + 7 + 9 + 12}{5} = \frac{41}{5} = 8.2$$Median. The data is already in order with five values, so the median is the middle (third) value, \(7\).
Mode. The value \(7\) appears twice, more than any other, so the mode is \(7\).
Example 2: Population standard deviation
Find the population standard deviation of \(2, 4, 4, 4, 5, 5, 7, 9\).
First find the mean of all \(8\) values:
$$\mu = \frac{2+4+4+4+5+5+7+9}{8} = \frac{40}{8} = 5$$Next, square each deviation from the mean and add the results:
$$\sum (x_i - \mu)^2 = 9 + 1 + 1 + 1 + 0 + 0 + 4 + 16 = 32$$Divide by \(N = 8\) to get the variance, then take the square root:
$$\sigma = \sqrt{\frac{32}{8}} = \sqrt{4} = 2$$Example 3: Sample standard deviation
For the sample \(10, 12, 14, 16\), the mean is \(\bar{x} = \frac{52}{4} = 13\). The squared deviations are \(9, 1, 1, 9\), which sum to \(20\). Because this is a sample, divide by \(n - 1 = 3\):
$$s = \sqrt{\frac{20}{3}} \approx \sqrt{6.667} \approx 2.58$$Common mistake
Dividing by \(n\) instead of \(n-1\) for a sample understates the spread. Use \(N\) for a full population and \(n-1\) when your data is a sample drawn from a larger group.
How to use the statistics solver
- Enter your data. Type or paste your numbers into the box above, separating them with commas or spaces.
- Choose what you need. Ask for a full summary or a specific measure such as the median or sample standard deviation.
- Review the steps. Read each calculation, then check your own work against the highlighted answer.
Related step-by-step guides
- How to Calculate Mean, Median, and Mode — a plain-language walk through the three measures of center.
- How to Calculate Standard Deviation Step by Step — see the full population and sample formulas in action.
Keep solving
Working through a statistics problem that turns into algebra? Try our Algebra Solver or jump straight to the Equation Solver for the next step.
