This help page describes how to use Statistics commands on DataFrame objects, and other spreadsheet-type data in matrices, sometimes called Matrix data sets.

Many of the data sets you might encounter are two-dimensional in nature. They will have information about a number of items or events; for each item or event, the same properties are known. Such data sets can easily be represented in a DataFrame by having each row correspond to an item and each column to one property of all these items. This is how you would typically store such data in a spreadsheet. You can also store such data in a Matrix, as long as you keep track of labels for the rows and columns yourself.

Many commands in the Statistics package can be used with this type of data:

The following computational commands can be run on DataFrame objects (or Matrices). They are computed per column and the results are returned in a DataSeries object. The labels for the DataSeries are the column labels of the DataFrame. Alternatively, they are computed per column of a Matrix and the results are returned in a row Vector.

The following visualization commands, listed on the Statistics Visualization help page, also accept DataFrame objects. Generally, the row and column labels are used to label data points and data sets, respectively, as appropriate.

Statistics[SplitByColumn] and Statistics[Join] split Matrices into submatrices and join them back together.

DataFrame/Aggregate does similar things for DataFrame objects.

Additional examples are found in the Statistics with DataFrames example worksheet.

$\mathrm{with}\left(\mathrm{Statistics}\right)\:$

$\mathrm{bedrooms}≔⟨3\,4\,2\,4\,3\,2\,2\,3\,4\,4\,2\,4\,4\,3\,3⟩$

$\mathrm{area}≔⟨1130\,1123\,1049\,1527\,907\,580\,878\,1075\,1040\,1295\,1100\,995\,908\,853\,856⟩$

$\mathrm{price}≔⟨114700\,125200\,81600\,127400\,88500\,59500\,96500\,113300\,104400\,136600\,80100\,128000\,115700\,94700\,89400⟩$

$\mathrm{HouseSalesData}≔\mathrm{DataFrame}\left(\left[\mathrm{bedrooms}\,\mathrm{area}\,\mathrm{price}\right]\,\mathrm{columns}=\left[\mathrm{Bedrooms}\,\mathrm{Area}\,\mathrm{Price}\right]\right)$

$\mathrm{Mean}\left(\mathrm{HouseSalesData}\right)$

$\mathrm{StandardError}\left(\mathrm{Mean}\,\mathrm{HouseSalesData}\right)$

$\mathrm{Percentile}\left(\mathrm{HouseSalesData}\,30\right)$

$\mathrm{GridPlot}\left(\mathrm{HouseSalesData}\right)$

$''Tabulate''$

$\mathrm{GridPlot}\left(\mathrm{HouseSalesData}\,\mathrm{lower}=\mathrm{Correlation}\right)$

$''Tabulate0''$

$\mathrm{Aggregate}\left(\mathrm{HouseSalesData}\,\mathrm{Bedrooms}\right)$

$\mathrm{split}≔\mathrm{SplitByColumn}\left(\mathrm{HouseSalesData}\,\mathrm{Bedrooms}\right)$

$\mathrm{split}≔\left[\left[?\right]\,\left[?\right]\,\left[?\right]\right]$

$\mathrm{price\_split}≔\mathrm{map}\left(\mathrm{df}\mapsto \mathrm{convert}\left(\mathrm{df}\left[\mathrm{Price}\right]\,\mathrm{Vector}\right)\,\mathrm{split}\right)$

$\mathrm{price\_split}≔\left[\left[\right]\,\left[\right]\,\left[\right]\right]$

$\mathrm{BoxPlot}\left(\mathrm{price\_split}\,\mathrm{datasetlabels}=\left[2\,3\,4\right]\right)$

$\mathrm{HSD\_Matrix}≔\mathrm{convert}\left(\mathrm{HouseSalesData}\,\mathrm{Matrix}\right)$

$\mathrm{Mean}\left(\mathrm{HSD\_Matrix}\right)$

$\mathrm{Percentile}\left(\mathrm{HSD\_Matrix}\,30\right)$

$\mathrm{AbsoluteDeviation}\left(\mathrm{HSD\_Matrix}\,\left[3\,1000\,100000\right]\right)$

$\mathrm{StandardError}\left(\mathrm{Moment}\,\mathrm{HSD\_Matrix}\,1\,\mathrm{origin}=\left[3\,1000\,100000\right]\right)$