# MagicPlot Manual

Plotting and nonlinear fitting software

histogram

# Histogram Calculation

Open Table or Figure or Fit Plot with initial data and select `Processing → Histogram` menu item to calculate histogram. ## Parameters

You can either set the bin size/count manually or specify auto binning criteria.

### Bin Bounds

MagicPlot align the the lower limit of the first bin exactly at the beginning of specified histogram range (`From` field). The upper limit of the last bin is calculated on the basis of the specified bin size and may be greater than the specified right histogram limit (`to` field) as shown on the screenshot above. Enter round value in the `From` field if you want the lower limit of the first bin to be round.

## Auto Binning Criteria

You can enter custom criteria in `Auto Binning` combo box:

• Typing `k=...` means setting the number of bins `k`
• Typing `h=...` means setting the bin size `h`.

You can use these parameters in the expression:

• `n` — the number of data points
• `s` — data standard deviation
• `m` — data mean
• `min` — data minimum
• `max` — data maximum.

The default alternatives are:

• — Default criteria in Excel, Origin and some other software
• — Scott's formula
• — Sturges' formula
• `MISE optimisation` — Shimazaki method. MagicPlot finds the minimum of Mean Integrated Squared Error (MISE) for the number of bins from 2 to `min(n/2, 20n1/2)` where `n` is the number of data points. See this paper and site for details: Shimazaki and Shinomoto, Neural Comput 19 1503-1527, 2007, http://2000.jukuin.keio.ac.jp/shimazaki/res/histogram.html.

### 'Keep on Recalculation' Option

This option is used when the histogram is recalculated. Recalculation may be cause by input data change (if `Auto Recalculate` checkbox is selected) or invoked manually (`Recalculate` menu item in histogram table column context menu). 