Enter your data set into the calculator above to get a full summary of descriptive statistics in seconds. This free statistics calculator computes the mean, standard deviation, median, mode, variance, sum, and more for any list of numbers.
No app install. No sign-up. Paste or type your values, pick your settings, and get results instantly.
Statistics Calculator for Basic Statistics and Descriptive Statistics
A statistics calculator takes a set of numbers and returns key summary statistics automatically. Instead of working through each formula by hand, you enter your data once and see every result on one screen.
Basic statistics cover the measures you reach for first: mean, median, mode, sum, count, and range. Descriptive statistics go a step further, adding standard deviation, variance, and distribution shape to describe how your data behaves overall.
This tool handles both. Whether you need a quick average for a homework problem or a full descriptive summary for a research report, the calculator runs every computation from the same data input.
How to Calculate: Enter Your Data Sample
Type or paste your numbers into the input field. The calculator accepts raw values separated by commas, spaces, tabs, or line breaks.
You can enter as few as two data values or a much longer data set. The tool reads each number, counts the sample size (n), and runs every calculation at once.
Paste Data from a File, Excel, or Your Browser
Already have numbers in a spreadsheet, CSV file, or web table? Copy the column and paste it directly into the input box. The calculator strips extra whitespace and blank lines automatically.
This works with Excel, Google Sheets, or any plain text file. No upload or file conversion is needed.
Comma, Table, and Value Format Options
Choose the delimiter that matches your data:
- Commas: 12, 15, 18, 22
- Spaces or tabs: 12 15 18 22
- Line breaks: one value per line
The calculator detects common formats. If your numbers use a different separator, switch the delimiter setting before you compute.
Find the Mean and Standard Deviation of a Data Sample
Mean and standard deviation are the two statistics people look up most often. The mean tells you the center of your data. The standard deviation tells you how spread out the values are around that center.
Arithmetic Mean Calculation
The arithmetic mean is the simple average. Add all values in the set, then divide by the count (n).
Formula: x̄ = Σx / n
If your data set is 4, 8, 6, 5, 9, the sum is 32 and n is 5. The mean is 6.4.
This calculator finds the mean instantly and displays it alongside the sum and count so you can verify the math.
Standard Deviation and Variance for a Sample or Population
Standard deviation measures how far individual values typically fall from the mean. Variance is the square of the standard deviation.
The formula differs slightly depending on whether your data represents an entire population or a sample drawn from a larger population:
- Population standard deviation (σ): divides by n.
- Sample standard deviation (s): divides by n − 1 to correct for estimation bias.
Select "sample" or "population" in the calculator settings. Most homework and research problems use sample standard deviation. If you measured every member of the group, choose population.
A small standard deviation means values cluster tightly around the mean. A large one means the data is more spread out.
Mode, Median, Sum, and Distribution in Descriptive Statistics
Beyond mean and standard deviation, descriptive statistics include several other measures that reveal different features of your data:
- Median: the middle value when data is sorted. Less sensitive to outliers than the mean.
- Mode: the most frequently occurring value. A data set can have no mode, one mode, or multiple modes.
- Sum (Σx): the total of all values.
- Range: the difference between the largest and smallest values.
- Count (n): the size of the data set, or how many values you entered.
- Minimum and maximum: the smallest and largest data values.
These statistics together paint a picture of your distribution. A data set where the mean and median are close is roughly symmetric. A large gap between them suggests a skewed distribution.
Sample Size and Confidence Interval Calculation
When you draw a sample from a larger population, two questions follow: Is the sample large enough? And how precise is the estimate?
Sample size (n) determines how much statistical power your analysis has. A larger sample generally narrows the margin of error.
Confidence Interval for a Sample Size and Distribution
A confidence interval gives a range around your sample statistic (like the mean) that is likely to contain the true population parameter.
For example, a 95% confidence interval means: if you repeated the sampling process many times, about 95% of those intervals would capture the true population mean.
The width of the interval depends on three things:
- The confidence level you choose (commonly 90%, 95%, or 99%).
- The standard deviation of the sample.
- The sample size (n). Larger samples produce narrower intervals.
Enter your data and select a confidence level. The calculator returns both the interval bounds and the margin of error.
Statistical Test, Hypothesis, and Regression Analysis
Descriptive statistics summarize data. Statistical tests help you draw conclusions from it.
T-Test and Hypothesis Test for a Data Set
A t-test checks whether the mean of your sample is significantly different from a known value or from another sample's mean. It is one of the most common hypothesis tests in introductory statistics.
A hypothesis test follows a standard structure:
- State a null hypothesis (for example, "the population mean equals 50").
- State an alternative hypothesis ("the population mean does not equal 50").
- Calculate the test statistic from your data.
- Compare the result to a critical value or check the p-value.
If the p-value is below your chosen significance level (often 0.05), you reject the null hypothesis.
What statistical test should you use? It depends on your data type and question. Use a one-sample t-test to compare a sample mean to a fixed value. Use a two-sample t-test to compare two groups. For proportions, use a z-test. For three or more groups, consider a one-way ANOVA.
Regression, Correlation, and P-Value
Regression analysis examines the relationship between two or more variables. Simple linear regression fits a straight line through paired data points (x, y) to predict one variable from another.
- Correlation (r): measures the strength and direction of a linear relationship. Values range from −1 to +1.
- R-squared (r²): tells you what proportion of the variation in the outcome variable is explained by the predictor.
- P-value: indicates whether the relationship is statistically significant.
Enter paired data to compute regression coefficients, the correlation coefficient, and the p-value in one step.
Probability, Normal Distribution, and Interval
Probability calculations answer "how likely?" questions. The normal distribution (the bell curve) is the most widely used probability distribution in statistics.
Key probability tools this calculator supports:
- Normal distribution probabilities: find the probability that a value falls within a given interval under a normal curve with a specified mean and standard deviation.
- Z-scores: convert a raw value into the number of standard deviations it falls from the mean. A z-score of 1.96 corresponds to the 97.5th percentile in a standard normal distribution.
- Cumulative probability: the chance that a value is less than or equal to a given number.
These calculations are essential for constructing confidence intervals and running hypothesis tests. Instead of looking up values in a z-table, enter your parameters and get an accurate result immediately.
How This Free Statistics Calculator Handles Your Data
Scientific Software vs. a Browser Statistics Calculator
Dedicated scientific software like R, SPSS, or SAS handles advanced modeling, large-scale simulation, and specialized statistical analysis. A browser-based statistics calculator is built for speed and convenience on everyday problems.
Use this online statistics calculator when you need:
- Quick descriptive statistics without installing software.
- Homework answers you can verify step by step.
- A fast check on mean, standard deviation, or a confidence interval.
Use scientific software when you need complex multivariate analysis, very large data sets, or publication-grade output with custom notation and graph types.
Calculation Size and Analysis Limits
This calculator processes most common data set sizes accurately in the browser. For extremely large data sets (tens of thousands of values or more), a desktop application or programming environment will be more practical.
All computation happens in your browser. Your data values are not uploaded to a server, so nothing is stored or shared.
Results are estimates based on the numbers you enter. For academic research, clinical decisions, or financial modeling, verify results with appropriate professional tools and qualified guidance.