Density analysis results
Formula used
f̂ₕ(x) = (1 / nh) Σ K((x − xᵢ) / h)
The estimate averages a kernel around every observation. Bandwidth controls curve smoothness. The normalized area should remain close to one.
How to use
- Enter one or more numeric datasets.
- Choose a kernel and bandwidth method.
- Apply optional transformations or filters.
- Select overlays and comparison settings.
- Calculate, inspect diagnostics, and export results.
Example data
| Dataset | Example values | Expected pattern |
|---|---|---|
| Normal | 42, 46, 49, 50, 51, 54, 58 | One balanced central peak |
| Bimodal | 12, 13, 14, 25, 26, 27 | Two visible density peaks |
| Skewed | 2, 2, 3, 4, 6, 10, 18 | Long right tail |
Frequently asked questions
What is a KDE plot?
A KDE plot estimates a smooth probability density. It avoids fixed histogram boundaries. Peaks suggest common value regions.
What does bandwidth control?
Bandwidth controls curve smoothness. Small values reveal local detail. Large values create broader curves.
Which kernel should I choose?
Gaussian works well for general analysis. Compact kernels emphasize nearby observations. Kernel choice matters less than bandwidth.
Why can density exceed one?
Density is not point probability. Narrow distributions can produce tall peaks. Total area remains approximately one.
Can I compare several groups?
Yes, enter labeled dataset lines. Overlay mode compares shapes directly. Ridgeline mode separates dense curves vertically.
What indicates oversmoothing?
Oversmoothing hides meaningful peaks and shoulders. The curve becomes unusually broad. Reduce the bandwidth multiplier carefully.
What indicates undersmoothing?
Undersmoothing creates many unstable small peaks. Noise can resemble structure. Increase bandwidth or gather more data.
How are outliers detected?
The calculator uses the interquartile range rule. Values beyond standard fences are flagged. Review context before removing observations.
Can I export calculated coordinates?
Yes, download density points as CSV. Statistics have a separate CSV. Charts export as PNG or SVG.