# Statistics

Any reference catalog must offer the statistical parameters of the three most documented values, weight, module and die axis position.

To do this, it has been necessary to develop a dynamic analysis tool able to show the statistical parameters of these three blocks of data, since it is an open catalogue, with a significant annual increase of new coins minted in different mints.

The analysis tool shows:

1. The violin and box plots of all types of each mint in a continuous sequence
2. When you click on one of the violins or boxes, all data concerning the selected type is shown below.

When browsing the catalogue, the window that describes an individual type and shows the documented copies, always includes at the end of the page the statistical summary of the type.

Of all possible statistical representations to show a data set we have chosen the violin and box plot model, with some specific summary statistics, although not much different from a box plot.

As you know, A violin plot is a combination of a box plot and a kernel density plot. Specifically, it starts with a box plot and then adds a rotated kernel density plot to each side of the box plot.

In this kind of representation, The width of the section is proportional to the number of data points in that range. A kernel density plot can be considered a refinement of a histogram or frequency plot.

The KERNEL DENSITY PLOT estimates the underlying probability density function and the cumulative distribution function (cdf), presenting a smooth approximation of the data sample used.

## How to read our diagrams plot As said, our diagram combines the representations of violin and box plots:

1. The white dot represents the median
2. The red box in the center represents the interquartile range Quartiles are the values that divide a list of numbers into quarters. The "Interquartile Range" extends from Q1 to Q3.
3. The whiskers represent the part of the distribution not covered by the box, minus 20 % of the data. The 30 % of all data of the distribution, ranging from percentiles 75 to 90 and 10 to 25, are located within the whiskers. The whiskers are still connected to the box but their length cover down to 10th percentile and up to 90 percentile. So the outermost part of the underlying distribution will not be covered by the whiskers. Of course the upper and the lower whisker may differ in length. In this representation the whiskers are drawn as solid lines.
4. Parts not covered by whiskers correspond to outliers represented by points. using a method that is a function of the interquartile range.

5. On each side of the red box is a kernel density estimation to show the distribution shape of the data, the area where there are more weights. Wider sections of the violin plot represent a higher probability that members of the population will take on the given value; the skinnier sections represent a lower probability.

The type of diagram and its shape can be chosen by displaying the control panel, which allows you to customize the representation. Two types of graphical representation have been developed; box plot overlap violin plots, but can also be viewed separately. You can see the lines that mark the weights and facilitate the reading. You can also vary the width of the boxes and violins and show / hide various components (whiskers and outliers). In the case of violins you can choose eight shapes of representation, Basis, Bump-Y...

Diagrams are also used to detect errors in the input of data, as they appear in diagrams as extremely atypical values. Sometimes it happens that the decimal point is not typed well, or that modules have been introduced in centimeters, instead of millimeters.

With this development we complete a little more the basic panorama that the digital catalogue monedaiberica.org provides on the ancient coinages of the Iberian Peninsula, since the analysis tool shows the statistical parameters of all types and variants.

https://matplotlib.org/1.4.0/users/whats_new.html#violin-plots

https://root.cern/doc/master/classTHistPainter.html#HP140b

https://www.mathsisfun.com/data/quartiles.html