Calculator Input
Use one value per comma, space, or new line. Optional frequencies let you analyze repeated observations without typing the same value many times.
Example Data Table
This example mirrors the default entries in the calculator and shows how values and frequencies work together.
| Label | Value | Frequency | Comment |
|---|---|---|---|
| Segment A | 12 | 3 | Lower-end observation |
| Segment B | 15 | 5 | Near central tendency |
| Segment C | 14 | 4 | Moderate value |
| Segment D | 16 | 6 | Strong frequency weight |
| Segment E | 18 | 5 | Higher-than-average value |
| Segment F | 17 | 3 | Upper-middle value |
| Segment G | 13 | 2 | Lower-middle value |
| Segment H | 19 | 4 | Upper-end observation |
Formula Used
Weighted Mean
Mean = Σ(x × f) / Σf
Here, x is the value and f is the frequency. If no frequencies are entered, each value gets a frequency of 1.
Population Variance
σ² = Σ[f × (x − μ)²] / N
This version is used when the entered data represents the full population.
Sample Variance
s² = Σ[f × (x − x̄)²] / (N − 1)
This version applies Bessel’s correction and is preferred when the entered data is a sample.
Standard Deviation and CV
Std. Dev. = √Variance
CV = (Std. Dev. / Mean) × 100
Coefficient of variation shows relative spread, making it easier to compare datasets with different scales.
How to Use This Calculator
1. Enter dataset values
Add observations using commas, spaces, or new lines. The calculator accepts decimals, negative values, and mixed numeric formats.
2. Add frequencies if needed
Enter positive whole-number frequencies only when values repeat. Leave the frequency box empty for a standard unweighted dataset.
3. Add optional labels
Labels help identify each observation inside the chart and detailed analysis table. They must match the number of values.
4. Choose the analysis basis
Select sample for sampled data and population for full datasets. This changes the primary variance and standard deviation interpretation.
5. Add benchmarks and threshold
Optional benchmark fields compare your results to target mean and variance values. The z-threshold controls outlier flagging.
6. Review and export
Submit the form to see result cards, the Plotly graph, observation contributions, and downloadable CSV and PDF reports.
Frequently Asked Questions
1. What does variance measure?
Variance measures how far values spread from the mean on average after squaring their deviations. Larger variance means greater dispersion and lower consistency within the dataset.
2. When should I use sample variance?
Use sample variance when your data represents only part of a larger population. It divides by N − 1, which reduces downward bias in estimated variability.
3. When should I use population variance?
Use population variance when every relevant observation is included in the dataset. It divides by N and describes the complete group directly.
4. Why do frequencies matter?
Frequencies let repeated values influence the mean and spread correctly without duplicating entries manually. They are useful for summarized datasets and grouped observation counts.
5. What is coefficient of variation?
Coefficient of variation expresses standard deviation as a percentage of the mean. It helps compare relative variability between datasets with different average levels.
6. How are outliers flagged here?
Each entered value receives a z-score based on the selected standard deviation basis. Any absolute z-score at or above the chosen threshold is flagged as an outlier.
7. What does skewness tell me?
Skewness describes distribution asymmetry. Positive skew suggests a longer right tail, while negative skew suggests a longer left tail.
8. Why export the results?
Exports make it easier to archive findings, share analyses, and document the summary table or observation details in reports, presentations, or audits.