Worked example: Statistics Calculator
Known sample. This fixed reference example shows one complete scenario; the interactive results above use your current inputs.
View the example inputs
- Numbers
- 1, 2, 3, 4
| Calculated quantity | Example result |
|---|---|
| Count | 4 |
| Sum | 10 |
| Mean | 2.5 |
| Median | 2.5 |
| Mode | No repeated values |
| Minimum | 1 |
| Maximum | 4 |
| Range | 3 |
Understanding data summaries and statistical uncertainty
Check the data before the summary
A mean summarizes total magnitude per observation, while a median locates the middle of an ordered data set. A few extreme values can affect them differently. Standard deviation describes spread in the original units; variance uses squared units. A frequency chart helps show distribution shape that one summary cannot capture.
Keep sample and population formulas distinct. A sample-variance calculation typically uses n−1 in its denominator. Repeated observations and units must be handled consistently, and a list of numbers does not by itself establish independent random sampling.
Choose the assumptions before reading the result
Confidence intervals, sample sizes and p-values depend on a specified model, confidence or tail convention, and data assumptions. A narrow calculated interval is not evidence that the assumptions were met. A p-value is not the probability that a hypothesis is true.
Use the page’s formula and worked example to check whether the statistic, sample size and degrees of freedom match the intended analysis. Do not substitute a population standard deviation for a sample value, or a one-sided test for a two-sided one, without changing the model.
Formula and calculation method
Mean=sum/n. Range=max−min. Population variance divides squared deviations by n; sample variance divides by n−1.
Reference Sources
Frequently asked questions
How does this calculator work?
Mean=sum/n. Range=max−min. Population variance divides squared deviations by n; sample variance divides by n−1.
What assumptions should I check?
Check the units and definitions shown beside each input. Results use the values you enter.
Can I save or print this calculation?
Use Copy link with inputs to reproduce the scenario, Download results for a text record, or Print. Where a schedule is shown, its CSV download includes every row.