Calculated Results
The summary appears above the form and updates after each calculation.
Detailed Statistical Summary
| Metric | Value |
|---|
Quick Interpretation
Plotly Graph
Enter Dataset and Options
Use raw values or paired frequencies. Large screens show three columns, medium screens two, and mobile one.
Example Data Table
This sample dataset shows twelve observations you can test with the calculator. The example button loads these values automatically.
| Observation | Value | Observation | Value |
|---|---|---|---|
| 1 | 12.4 | 7 | 15.6 |
| 2 | 15.1 | 8 | 14.4 |
| 3 | 14.8 | 9 | 15.9 |
| 4 | 16.2 | 10 | 16.5 |
| 5 | 13.9 | 11 | 14.7 |
| 6 | 17.0 | 12 | 15.3 |
Formula Used
| Statistic | Formula | Meaning |
|---|---|---|
| Mean | x̄ = Σx / n | The arithmetic average of all observations. |
| Median | Middle value after sorting | The 50th percentile of the ordered dataset. |
| Mode | Most frequent value | The value or values with the highest occurrence count. |
| Range | Max − Min | The full spread from smallest to largest observation. |
| Population variance | σ² = Σ(x − μ)² / n | Measures average squared distance from the population mean. |
| Sample variance | s² = Σ(x − x̄)² / (n − 1) | Applies Bessel’s correction for sample-based estimation. |
| Standard deviation | σ or s = √variance | Shows typical deviation from the mean in original units. |
| Coefficient of variation | CV = (Std. Dev. / Mean) × 100 | Expresses variability relative to the mean as a percentage. |
| Quartiles | Q1 = P25, Q2 = P50, Q3 = P75 | Divide the sorted dataset into four equal parts. |
| Interquartile range | IQR = Q3 − Q1 | Captures the middle fifty percent spread. |
| Outlier fences | Lower = Q1 − k×IQR, Upper = Q3 + k×IQR | Flags unusually low or high values using the chosen multiplier. |
| Mean absolute deviation | MAD = Σ|x − x̄| / n | Average absolute distance from the mean. |
| Median absolute deviation | Median(|x − Median|) | A robust spread measure less sensitive to outliers. |
| Skewness | Based on the standardized third central moment | Describes asymmetry. Positive values show right skew. |
| Excess kurtosis | Based on the standardized fourth central moment minus 3 | Shows tail heaviness relative to a normal distribution. |
| Trimmed mean | Mean after removing equal tails | Reduces the impact of extreme values on the average. |
| Geometric mean | GM = exp[Σln(x) / n] | Useful for positive ratios, rates, and growth factors. |
| Harmonic mean | HM = n / Σ(1/x) | Useful for rates and ratios when values are nonzero. |
How to Use This Calculator
- Choose Raw values for direct datasets or Value and frequency pairs for grouped counts.
- Paste numbers into the values field using commas, spaces, tabs, or new lines.
- If frequency mode is selected, enter matching whole-number frequencies in the second field.
- Select whether variance and standard deviation should follow sample or population formulas.
- Adjust decimal places, trim percentage, custom percentile, histogram bins, and outlier multiplier as needed.
- Press Calculate Summary to show the result area above the form.
- Review headline metrics, the detailed summary table, interpretation notes, and the Plotly graph.
- Use Download CSV or Download PDF to export the calculated summary.
Frequently Asked Questions
1) What data formats does this calculator accept?
It accepts raw numeric values separated by commas, spaces, tabs, or line breaks. It also supports paired value-frequency input for compact grouped datasets.
2) What is the difference between sample and population mode?
Sample mode uses Bessel’s correction, dividing by n−1 for variance. Population mode divides by n and treats the dataset as the full population.
3) Why might geometric mean not be shown?
Geometric mean requires strictly positive values. If the dataset contains zero or negative numbers, the calculator marks that metric as not defined.
4) Why might harmonic mean not be shown?
Harmonic mean cannot be calculated when any value is zero. It is most useful for rates, speeds, and ratio-based measurements.
5) How are outliers detected here?
The calculator uses Tukey-style fences: Q1 − k×IQR and Q3 + k×IQR. The multiplier k is adjustable, with 1.5 as the common default.
6) What percentile method is used?
Percentiles use linear interpolation on the sorted dataset. This approach works smoothly for datasets with even or odd counts.
7) Can I export the results?
Yes. CSV export downloads a metric-value file. PDF export captures the results section, including the chart, into a document-friendly format.
8) What makes this calculator useful for data science work?
It combines descriptive statistics, shape diagnostics, outlier checks, robust spread measures, and quick visualization in one place for practical dataset review.