Mathematica HowTo
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):
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Mathematica characterizes data by grouping lists within other lists. Every list is interpreted as a row within the matrix of data:
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The Grid function displays data in the same fashion, only without the braces:
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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:
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Find the standard deviation of the columns:
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Find the median of each column:
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You can also select individual columns for calculations. Here, the first column from data is selected:
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For matrices with more than two columns, plot the rows as separate data sets:
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Plot the columns by transposing the data:
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For functions that operate on vectors, map the function onto the transposed data to operate on columns:
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Transpose the result to get a matrix with normalized columns:
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Transposing and mapping can also be done for functions that flatten their argument:
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