Statistics CalculatorFree online math calculator — instant results, no sign-up
Summary statistics for a data set.
About the Statistics Calculator
The Statistics Calculator computes fundamental summary metrics for a numerical dataset, including sample size, total sum, central tendency measures, and data dispersion. It is designed for students, researchers, and data analysts who need quick descriptive statistics for raw numeric lists.
- Numbers
- A comma- or space-separated list of numeric values; supports negative numbers, integers, and decimals.
Formula and method
Mean = (Σ x) / n Median = Middle value if n is odd, or ((x_(n/2) + x_(n/2 + 1)) / 2) if n is even (from sorted data) SD (sample) = sqrt( Σ (x_i - Mean)^2 / (n - 1) )
- nSample size (count of numbers)
- Σ xSum of all observations in the dataset
- x_iIndividual data value in the dataset
- SD (sample)Sample standard deviation with Bessel's correction (divided by n - 1)
The calculator parses the input string into an array of numbers and sorts it in ascending order. It computes the total sum, derives the mean and sample standard deviation (both rounded to up to 6 decimal places), identifies the minimum and maximum values from the sorted list, and finds the median as either the middle value or the average of the two central values.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Numbers4, 8, 15, 16, 23, 42
Results
- Count6
- Sum108
- Mean18
- Median15.5
- Min4
- Max42
How to use the Statistics Calculator
- 1Parse the text input into a list of numbers and count the elements (n).
- 2Sum all numbers together to calculate the dataset total and divide by n to find the mean.
- 3Sort the list in ascending order to extract the minimum, maximum, and median.
- 4Compute the sum of squared differences from the mean, divide by n - 1, and take the square root to determine the sample standard deviation.
Reading your result
The Mean and Median describe the center of your data; if they are close, the distribution is roughly symmetrical, whereas a large difference indicates skewness. The SD (sample) quantifies the spread around the mean in the original measurement units, and Min and Max define the outer boundaries of the dataset.
Limitations
This calculator calculates the sample standard deviation using n - 1 degrees of freedom rather than the population standard deviation (divided by n). It also does not calculate higher-order statistics such as skewness, kurtosis, quartiles, or identify statistical outliers.
Common questions
Why does the standard deviation use n - 1 instead of n?+
It uses Bessel's correction (n - 1), which provides an unbiased estimator of the population variance when analyzing a sample dataset rather than an entire population.
How does the calculator handle an even number of values for the median?+
When the dataset size is even, the median is calculated by taking the arithmetic mean of the two middle values after sorting the list.
Can I input negative numbers and decimals?+
Yes. Values can be positive, negative, or fractional; separate each number with commas or spaces.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
Further reading
You might also like
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Sample and population standard deviation of a data set.
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Probability Calculator
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Mean, Median, Mode, Range Calculator
Central tendency and spread of a list.
Permutation and Combination Calculator
nPr and nCr.
Results are estimates for informational purposes and are not financial, medical or legal advice.