How to | Perform Calculations on Columns of Data

You will often need to perform calculations on the columns in a dataset, particularly when the columns represent variables. While some functions automatically operate on columns of data when a rectangular array is given, others may require some manipulation of the data in order to operate on the columns.

Create some data to work with (SeedRandom ensures a predictable result):

The Wolfram Language characterizes data by grouping lists within other lists. Every list is interpreted as a row within the matrix of data:

The Grid function displays data in the same fashion, only without the braces:

By default many functions operate on each column when a rectangular list of lists is given as the argument.

Find the mean of each column:

Find the standard deviation of the columns:

Find the median of each column:

You can also select individual columns for calculations. Here, the first column from data is selected:

For matrices with more than two columns, plot the rows as separate datasets:

Plot the columns by transposing the data:

For functions that operate on vectors, map the function onto the transposed data to operate on columns:

Transpose the result to get a matrix with normalized columns:

Transposing and mapping can also be done for functions that flatten their argument: