Calculator Form
Example Data Table
| Observation | Value | Observation | Value |
|---|---|---|---|
| 1 | 12 | 6 | 22 |
| 2 | 15 | 7 | 24 |
| 3 | 18 | 8 | 25 |
| 4 | 20 | 9 | 27 |
| 5 | 22 | 10 | 30 |
Formula Used
Mean: Mean = Sum of values / Number of values.
Median: Middle value after sorting. For even counts, average the two middle values.
Mode: Value with the highest frequency. If no value repeats, there is no repeated mode.
Range: Range = Maximum − Minimum.
Quartiles: Q1 and Q3 are estimated using inclusive percentile interpolation on the sorted data.
Interquartile Range: IQR = Q3 − Q1.
Population Variance: σ² = Σ(x − μ)² / n.
Sample Variance: s² = Σ(x − x̄)² / (n − 1).
Standard Deviation: Square root of variance.
Coefficient of Variation: CV = (Standard Deviation / |Mean|) × 100.
Geometric Mean: nth root of the product of positive values, implemented with logarithms.
Harmonic Mean: Number of values divided by the sum of reciprocals.
How to Use This Calculator
- Enter your raw ungrouped values in the text area.
- Separate values using commas, spaces, semicolons, or line breaks.
- Click Calculate Statistics.
- Review the result panel shown above the form.
- Inspect the frequency table and Plotly chart.
- Download the results as CSV or PDF when needed.
FAQs
1. What is ungrouped data?
Ungrouped data is a simple list of raw observations. Values are not placed into class intervals or bins before analysis.
2. Can I paste values on separate lines?
Yes. The calculator accepts commas, spaces, semicolons, tabs, and line breaks, making pasted spreadsheet values easy to analyze.
3. What happens if all values are unique?
The tool reports no repeated mode. That means no value appears more often than the others.
4. Why are there both sample and population measures?
Population measures use all observations in the full set. Sample measures adjust for estimation when data represents only part of a larger population.
5. When is geometric mean unavailable?
Geometric mean requires all values to be positive. Zero or negative values make the measure unsuitable for this dataset.
6. When is harmonic mean unavailable?
Harmonic mean cannot be computed when any value is zero, because the reciprocal of zero is undefined.
7. Does the chart update automatically?
Yes. After calculation, the chart redraws using your submitted values and their frequency distribution.
8. Can I use decimals and negative numbers?
Yes. The calculator supports decimals and negative values for most statistics, except geometric mean and zero-based harmonic mean limits.