How to use the statistics calculator
- Enter your numbers into the Dataset field, separated by commas, spaces or new lines.
- Check the Population data box if your numbers represent an entire population rather than a sample.
- Read the computed descriptive statistics below: count, sum, mean, median, mode, range, variance and standard deviation.
How each statistic is calculated
The mean is the sum of all values divided by the count. For the dataset 2, 4, 4, 5, 5, 7, 9 the sum is 40 and the count is 8, giving a mean of 5.
The median is the middle value when the data is sorted. If there is an even number of values, it is the average of the two central ones. Sorted: 2, 4, 4, 5, 5, 7, 9 has seven items, so the median is the fourth value, which is 5. For eight items like 2, 4, 4, 4, 5, 5, 7, 9 the median is the average of the fourth and fifth values: (4 + 5) / 2 = 4.5.
The mode is the most frequently occurring value. In 2, 4, 4, 4, 5, 5, 7, 9 the value 4 appears three times, making it the mode. A dataset can have more than one mode if multiple values share the highest frequency.
Variance measures how spread out the numbers are. It is the average of the squared differences from the mean. For sample variance, divide by n minus 1 instead of n. The standard deviation is simply the square root of the variance, bringing the measure back to the original units of the data.
Sample vs population variance
When you collect data from a subset of a larger group, you have a sample. Using n minus 1 in the denominator (called Bessel's correction) corrects the bias that would otherwise underestimate the true population variance. If your data includes every member of the group you care about, check the population box to divide by n instead.
For example, the values 10, 20, 30 have a mean of 20. The squared deviations are 100, 0 and 100, summing to 200. Population variance is 200 / 3 = 66.67. Sample variance is 200 / 2 = 100. The standard deviation calculator logic applies the square root to whichever variance you choose.
Common reference values
This table shows descriptive statistics for a few simple datasets so you can verify your own calculations against known results.
| Dataset | n | Mean | Median | Mode | Sample SD |
|---|---|---|---|---|---|
| 1, 2, 3 | 3 | 2 | 2 | None | 1 |
| 2, 2, 2 | 3 | 2 | 2 | 2 | 0 |
| 1, 3, 5, 7 | 4 | 4 | 4 | None | 2.582 |
| 10, 20, 30, 40, 50 | 5 | 30 | 30 | None | 15.811 |
Practical uses for descriptive statistics
A calculator statistics tool is useful whenever you need to summarize a set of measurements quickly. Teachers use it to analyze exam grades, finding the class average and whether scores cluster tightly or spread widely. Scientists apply standard deviation to quantify measurement uncertainty in experiments.
In business, analysts look at sales figures to find the typical transaction size (median) versus the average revenue per sale (mean), since outliers like one very large order can skew the mean. Quality control teams track variance to detect when a manufacturing process drifts out of specification.
Edge cases and common mistakes
Entering non-numeric characters will cause an error. Make sure your list contains only valid numbers, including negative signs and decimal points where needed. Extra commas or spaces between numbers are handled automatically.
A single-value dataset has a mean equal to that value, zero variance and zero standard deviation, but sample variance is undefined because dividing by n minus 1 means dividing by zero. This tool reports sample variance as N/A when there is only one data point.
If every value in the dataset is unique, there is no mode. Some textbooks say such a dataset has no mode, while others say every value is a mode. This tool reports "None" when no value repeats.
Worked examples
Each result below was produced by the same code the tool runs, so you can check your own numbers against them.
| Example | Input | Result |
|---|---|---|
| Test scores | Dataset: 85, 90, 78, 92, 88, 76, 95, 89; Population data (not sample): no | Count: 8; Sum: 693; Mean: 86.625; Median: 88.5; Mode: None; Min: 76; Max: 95; Range: 19; Sample Variance: 43.9821428571; Sample Std Dev: 6.6319034113; Pop Variance: 38.484375; Pop Std Dev: 6.2035775968 |
| Small dataset with repeated values | Dataset: 3, 7, 7, 2, 9, 3, 7; Population data (not sample): yes | Count: 7; Sum: 38; Mean: 5.4285714286; Median: 7; Mode: 7; Min: 2; Max: 9; Range: 7; Pop Variance: 6.2448979592; Pop Std Dev: 2.4989793835 |
| Negative and decimal numbers | Dataset: -4.5, 2.3, 0, -1.1, 5.8, 2.3; Population data (not sample): no | Count: 6; Sum: 4.8; Mean: 0.8; Median: 1.15; Mode: 2.3; Min: -4.5; Max: 5.8; Range: 10.3; Sample Variance: 12.368; Sample Std Dev: 3.5168167425; Pop Variance: 10.3066666667; Pop Std Dev: 3.2103997674 |
| Single value | Dataset: 42; Population data (not sample): no | Count: 1; Sum: 42; Mean: 42; Median: 42; Mode: None; Min: 42; Max: 42; Range: 0; Sample Variance: N/A; Sample Std Dev: N/A; Pop Variance: 0; Pop Std Dev: 0 |
FAQ
What is the difference between mean and median?
The mean is the arithmetic average of all values, while the median is the middle value when the data is sorted. The median is less affected by extreme outliers than the mean.
Why does sample variance divide by n-1?
Dividing by n-1 (Bessel's correction) produces an unbiased estimate of the true population variance when you only have a sample. Dividing by n tends to underestimate the spread.
Can a dataset have more than one mode?
Yes. If two or more values tie for the highest frequency, the dataset is multimodal. This calculator lists all modes separated by commas.
Is my data sent to a server?
No. All calculations happen locally in your browser. Nothing is uploaded or stored anywhere.
What happens if I enter only one number?
The mean, median and mode will equal that number. Variance and standard deviation will be zero for population mode, and sample variance will show N/A because it requires at least two values.
How do I format the input?
Type or paste numbers separated by commas, spaces or line breaks. Negative numbers and decimals are supported.