Calculator Input
Enter decimal values directly or use value-frequency pairs. The form uses a responsive input grid: three columns on large screens, two on medium screens, and one on mobile.
Example Data Table
| Observation | Decimal Value |
|---|---|
| 1 | 12.5 |
| 2 | 13.1 |
| 3 | 12.8 |
| 4 | 14.2 |
| 5 | 13.6 |
| 6 | 12.9 |
| 7 | 13.4 |
| 8 | 12.7 |
This sample dataset shows how decimal values can be entered directly for standard deviation, variance, and mean analysis.
Formula Used
Mean: μ = Σx / n
Population Variance: σ² = Σ(x − μ)² / n
Population Standard Deviation: σ = √σ²
Sample Variance: s² = Σ(x − x̄)² / (n − 1)
Sample Standard Deviation: s = √s²
Mean Absolute Deviation: MAD = Σ|x − mean| / n
In frequency mode, each decimal value is multiplied by its frequency before totals, variance, and deviation measures are calculated.
How to Use This Calculator
- Select direct values or value-frequency pairs.
- Choose the decimal mark used in your dataset.
- Pick a separator if you are entering direct values.
- Choose sample or population mode.
- Set the desired output precision.
- Enter your decimal data and click the calculate button.
- Review the result block above the form.
- Use the CSV and PDF buttons to export your analysis.
FAQs
1. What does decimal standard deviation measure?
It measures how far decimal values spread from the mean. A small result shows tight clustering, while a larger result shows greater variability in the dataset.
2. When should I choose sample mode?
Choose sample mode when your decimals represent only part of a larger group. It uses n − 1, which corrects bias when estimating population variability.
3. When should I choose population mode?
Choose population mode when your dataset includes every value in the full group you want to analyze. It divides the squared deviations by n.
4. Can I use frequency pairs instead of raw decimals?
Yes. Frequency mode is useful when repeated decimal values appear many times. Enter one value and its frequency on each line to calculate the same statistics efficiently.
5. Does the calculator support comma decimals?
Yes. Switch the decimal mark to comma. When using comma decimals, separate direct values with semicolons, spaces, or new lines to avoid formatting conflicts.
6. What is the difference between variance and standard deviation?
Variance is the average squared spread around the mean. Standard deviation is the square root of variance, so it returns to the original measurement scale.
7. Why is the graph useful?
The graph helps you see distribution shape, clustering, and spread. Mean and one-standard-deviation guide lines make it easier to interpret how widely decimals vary.
8. Can I export the results?
Yes. Download CSV for spreadsheet use or PDF for sharing and reporting. Both options appear in the result section after a successful calculation.