Math Tools
Statistics Calculator
Calculate mean, median, mode, range, variance, standard deviation, minimum, maximum, count, and sum from a list of numbers.
Statistics Calculator
Calculate mean, median, mode, range, variance, standard deviation, count, sum, minimum, and maximum from a list of numbers.
Example: 2, 4, 4, 4, 5, 5, 7, 9
Results
Count
8
Sum
40
Mean
5
Median
4.5
Mode
4
Minimum
2
Maximum
9
Range
7
Variance
4
Standard deviation
2
Recommended Study Tool
Working with statistics often?
A statistics reference book, scientific calculator, or study-focused setup can help when learning formulas, checking datasets, and practicing data analysis.
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What this calculator does
This calculator gives a broad statistical summary of a dataset, including mean, median, mode, minimum, maximum, range, variance, and standard deviation.
What is a statistics calculator?
A statistics calculator is a tool that analyzes a list of numbers and returns important descriptive statistics such as mean, median, mode, range, variance, standard deviation, minimum, maximum, count, and sum. Instead of calculating each value by hand, you can enter your dataset and get a full statistical summary instantly.
This is useful for students, teachers, researchers, analysts, and anyone working with datasets in math, science, business, finance, education, or data analysis. It saves time, reduces manual errors, and makes it easier to understand the central tendency and spread of a dataset.
Mean, median, mode, range, variance, and standard deviation explained
Mean
The mean is the average of all numbers in the dataset.
Median
The median is the middle value after sorting the numbers.
Mode
The mode is the value or values that appear most often.
Range
The range is the difference between the maximum and minimum values.
Variance
Variance measures how far the values are spread out from the mean.
Standard deviation
Standard deviation is the square root of variance and shows the typical distance from the mean.
Statistics formula table
Use this quick reference table to understand how common statistics are calculated.
| Statistic | Formula or method | What it tells you |
|---|---|---|
| Mean | sum of values ÷ number of values | Finds the average value. |
| Median | middle value after sorting | Finds the center of an ordered dataset. |
| Mode | most frequent value | Finds the value that appears most often. |
| Range | maximum − minimum | Measures the full spread of the dataset. |
| Population variance | sum of squared deviations ÷ n | Measures spread when the dataset is the full population. |
| Sample variance | sum of squared deviations ÷ (n − 1) | Measures spread when the dataset is a sample. |
| Standard deviation | square root of variance | Shows the typical distance from the mean. |
Statistics example table
This worked example shows common statistics for a sample dataset.
| Statistic | Example value |
|---|---|
| Dataset | 2, 4, 4, 4, 5, 5, 7, 9 |
| Count | 8 |
| Sum | 40 |
| Mean | 5 |
| Median | 4.5 |
| Mode | 4 |
| Minimum | 2 |
| Maximum | 9 |
| Range | 7 |
| Population variance | 4 |
| Population standard deviation | 2 |
| Sample variance | 4.571429 |
| Sample standard deviation | 2.13809 |
How to calculate statistics step by step
First, enter your numbers separated by commas or spaces. The calculator reads the dataset, sorts the values where needed, and computes the common descriptive statistics automatically.
It calculates the sum and count, then uses those values to find the mean. The median is found from the ordered list, the mode is determined from repeated values, and the range is calculated from the minimum and maximum. Variance and standard deviation are then calculated based on whether you select population or sample mode.
Population vs sample variance and standard deviation
Population variance and population standard deviation are used when your dataset contains every value in the full group you want to study. Sample variance and sample standard deviation are used when your data is only a sample taken from a larger population.
The difference matters because sample formulas adjust for the fact that a sample is only an estimate of the whole population. In many classroom and research settings, using the correct version is important for accurate results.
Where a statistics calculator is useful
A statistics calculator is useful in math homework, exam preparation, lab reports, surveys, business reports, quality control, and data analysis. It helps you understand the center and spread of a dataset quickly without doing each calculation by hand.
It is especially helpful when you need to compare datasets, check whether values are clustered or spread out, or verify calculations during learning and research.
Statistics calculator FAQ and common questions
How do you find the mean of a dataset?
Add all values together and divide by the number of values. This gives the average.
How do you find the median of a dataset?
Sort the numbers and identify the middle value. If there are two middle values, take their average.
What is the mode in statistics?
The mode is the number that appears most often in the dataset. A dataset may have one mode, multiple modes, or no mode.
What is the difference between variance and standard deviation?
Variance measures spread in squared units, while standard deviation is the square root of variance and is easier to interpret in the original unit scale.
When should I use population instead of sample mode?
Use population mode when your dataset contains the full group you want to analyze. Use sample mode when your data is only a subset of a larger population.
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