ARBIMETRA LAB
Descriptive Statistics
Summarises the centre, spread and size of numeric variables, keeping sample and population formulas separate.
What it does
Summarises the centre, spread and size of numeric variables, keeping sample and population formulas separate.
Use it first with any dataset, to see the scale of each variable and spot problems before modelling.
Data you need
- One or more numeric variables
Supported data: Numeric. Level: Beginner.
Formula and method
x̄ = Σx / n · s² = Σ(x − x̄)² / (n − 1) · σ² = Σ(x − x̄)² / n · SE = s / √n · CV = s / |x̄|
Each variable is summarised on its own valid values. The mean and sum of squares are computed first; sample statistics then divide by n − 1 and population statistics by n. The mode is reported only when a value repeats.
Assumptions
- Values are measured on a numeric scale
Input checks
- Each variable uses its own valid observations
- Missing values are counted and reported
How to read the result
Compare the mean with the median to judge symmetry, and the standard deviation with the mean to judge relative spread.
Worked example
Illustrative run on Simulated study data (teaching data). These figures are the actual output of this model on that example, and they say nothing about your own data.
- post_score: n = 240, mean = 73.9696, median = 74.6, sample s.d. = 12.542.
- hours: n = 240, mean = 9.8871, median = 9.7, sample s.d. = 2.8854.
- post_score: the mean is close to the median, which is consistent with a roughly symmetric centre.
- hours: the mean is close to the median, which is consistent with a roughly symmetric centre.
Limitations
- Summaries can hide subgroups and outliers
- The coefficient of variation is undefined when the mean is zero
Numerical validation
Validated 23 of 23 automated checks passed, including numerical results, invalid input, missing values, small samples, constant variables, charts and the interpretation text.
| Check | Reference | Result | Abs. error | Tolerance | Source |
|---|---|---|---|---|---|
| Michelso: mean | 299.8524 | 299.8524 | 0.0e+0 | 1e-11 | NIST StRD certified value |
| Michelso: sample s.d. | 0.07901055 | 0.07901055 | 1.1e-15 | 1e-9 | NIST StRD certified value |
| Lew: mean | -177.435 | -177.435 | 0.0e+0 | 1e-11 | NIST StRD certified value |
| Lew: sample s.d. | 277.33216804 | 277.33216804 | 1.1e-13 | 1e-9 | NIST StRD certified value |
| Mavro: mean | 2.001856 | 2.001856 | 4.4e-16 | 1e-11 | NIST StRD certified value |
| Mavro: sample s.d. | 0.00042912 | 0.00042912 | 3.2e-17 | 1e-9 | NIST StRD certified value |
| PiDigits: mean | 4.5348 | 4.5348 | 0.0e+0 | 1e-11 | NIST StRD certified value |
| PiDigits: sample s.d. | 2.86733906 | 2.86733906 | 1.8e-15 | 1e-9 | NIST StRD certified value |
Computed with python 3.13.2, numpy 2.2.5, scipy 1.14.1, pandas 2.3.3, statsmodels 0.14.4, scikit-learn 1.7.0, in your browser. A passing check confirms the listed comparison only. It does not make any result suitable for your data, and it is not a claim of equivalence with other statistical software.
Questions
What is the difference between sample and population variance?
Sample variance divides by n − 1 and estimates the variance of a wider population. Population variance divides by n and describes only the values you have.
ARBIMETRA LAB is an educational and research tool. Results should be checked by the researcher and are not professional advice.