represents a structured dataset based on a hierarchy of lists and associations.


  • Dataset can represent not only full rectangular multidimensional arrays of data, but also arbitrary tree structures, corresponding to data with arbitrary hierarchical structure.
  • Depending on the data it contains, a Dataset object typically displays as a table or grid of elements.
  • Functions like Map, Select, etc. can be applied directly to a Dataset by writing Map[f,dataset], Select[dataset,crit], etc.
  • Subsets of the data in a Dataset object can be obtained by writing dataset[[parts]].
  • Dataset objects can also be queried using a specialized query syntax by writing dataset[query].
  • Dataset Structure
  • While arbitrary nesting of lists and associations is possible, two-dimensional (tabular) forms are most commonly used.
  • The following table shows the correspondence between the common display forms of a Dataset, the form of Wolfram Language expression it contains, and logical interpretation of its structure as a table:
  • {{,,},
    list of lists
    a table without named rows and columns

    <|"x","y",|> }
    list of associations
    a table with named columns
    association of lists
    a table with named rows
    association of associations
    a table with named columns and named rows
  • Dataset interprets nested lists and associations in a row-wise fashion, so that level 1 (the outermost level) of the data is interpreted as the rows of a table, and level 2 is interpreted as the columns.
  • Named rows and columns correspond to associations at level 1 and 2, respectively, whose keys are strings that contain the names. Unnamed rows and columns correspond to lists at those levels.
  • Rows and columns of a dataset can be exchanged by writing Transpose[dataset].
  • Part Operations
  • The syntax dataset[[parts]] or Part[dataset,parts] can be used to extract parts of a Dataset.
  • The parts that can be extracted from a Dataset include all ordinary specifications for Part.
  • Unlike the ordinary behavior of Part, if a specified subpart of a Dataset is not present, Missing["PartAbsent",] will be produced in that place in the result.
  • The following part operations are commonly used to extract rows from tabular datasets:
  • dataset[["name"]]extract a named row (if applicable)
    dataset[[{"name1",}]]extract a set of named rows
    dataset[[1]]extract the first row
    dataset[[n]]extract the n^(th) row
    dataset[[-1]]extract the last row
    dataset[[m;;n]]extract rows m through n
    dataset[[{n1,n2,}]]extract a set of numbered rows
  • The following part operations are commonly used to extract columns from tabular datasets:
  • dataset[[All,"name"]]extract a named column (if applicable)
    dataset[[All,{"name1",}]]extract a set of named columns
    dataset[[All,1]]extract the first column
    dataset[[All,n]]extract the n^(th) column
    dataset[[All,-1]]extract the last column
    dataset[[All,m;;n]]extract columns m through n
    dataset[[All,{n1,n2,}]]extract a subset of the columns
  • Like Part, row and column operations can be combined. Some examples include:
  • dataset[[n,m]]take the cell at the n^(th) row and m^(th)column
    dataset[[n,"colname"]]extract the value of the named column in the n^(th) row
    dataset[["rowname","colname"]]take the cell at the named row and column
  • The following operations can be used to remove the labels from rows and columns, effectively turning associations into lists:
  • dataset[[Values]]remove labels from rows
    dataset[[All,Values]]remove labels from columns
    dataset[[Values,Values]]remove labels from rows and columns
  • Dataset Queries
  • The query syntax dataset[op1,op2,] can be thought of as an extension of Part syntax to allow aggregations and transformations to be applied, as well as taking subsets of data.
  • Some common forms of query include:
  • dataset[f]apply f to the entire table
    dataset[All,f]apply f to every row in the table
    dataset[All,All,f]apply f to every cell in the table
    dataset[f,n]extract the n^(th) column, then apply f to it
    dataset[f,"name"]extract the named column, then apply f to it
    dataset[n,f]extract the n^(th) row, then apply f to it
    dataset["name",f]extract the named row, then apply f to it
    dataset[{nf}]selectively map f onto the n^(th) row
    dataset[All,{nf}]selectively map f onto the n^(th)column
  • Some more specialized forms of query include:
  • dataset[Counts,"name"]give counts of different values in the named column
    dataset[Count[value],"name"]give number of occurences of value in the named column
    dataset[CountDistinct,"name"]count the number of distinct values in the named column
    dataset[MinMax,"name"]give minimum and maximum values in the named column
    dataset[Mean,"name"]give the mean value of the named column
    dataset[Total,"name"]give the total value of the named column
    dataset[Select[h]]extract those rows that satisfy condition h
    dataset[Select[h]/*Length]count the number of rows that satisfy condition h
    dataset[Select[h],"name"]select rows, then extract the named column from the result
    dataset[Select[h]/*f,"name"]select rows, extract the named column, then apply f to it
    dataset[TakeLargestBy["name",n]]give the n rows for which the named column is largest
    dataset[TakeLargest[n],"name"]give the n largest values in the named column
  • Descending and Ascending Query Operators
  • In dataset[op1,op2,], the query operators opi are effectively applied at successively deeper levels of the data, but any given one may be applied either while "descending" into the data or while "ascending" out of it.
  • The operators that make up a Dataset query fall into one of the following broad categories with distinct ascending and descending behavior:
  • All,i,i;;j,"key",descendingpart operators
    Select[f],SortBy[f],descendingfiltering operators
    Counts,Total,Mean,ascendingaggregation operators
    Query[],ascendingsubquery operators
    Function[],fascendingarbitrary functions
  • A descending operator is applied to corresponding parts of the original dataset, before subsequent operators are applied at deeper levels.
  • Descending operators have the feature that they do not change the structure of deeper levels of the data when applied at a certain level. This ensures that subsequent operators will encounter subexpressions whose structure is identical to the corresponding levels of the original dataset.
  • The simplest descending operator is All, which selects all parts at a given level and therefore leaves the structure of the data at that level unchanged. All can safely be replaced with any other descending operator to yield another valid query.
  • An ascending operator is applied after all subsequent ascending and descending operators have been applied to deeper levels. Whereas descending operators correspond to the levels of the original data, ascending operators correspond to the levels of the result.
  • Unlike descending operators, ascending operators do not necessarily preserve the structure of the data they operate on. Unless an operator is specifically recognized to be descending, it is assumed to be ascending.
  • Part Operators
  • The descending part operators specify which elements to take at a level before applying any subsequent operators to deeper levels:
  • Allapply subsequent operators to each part of a list or association
    i;;jtake parts i through j and apply subsequent operators to each part
    itake only part i and apply subsequent operators to it
    "key",Key[key]take value of key in an association and apply subsequent operators to it
    Valuestake values of an association and apply subsequent operators to each value
    {part1,part2,}take given parts and apply subsequent operators to each part
  • Filtering Operators
  • The descending filtering operators specify how to rearrange or filter elements at a level before applying subsequent operators to deeper levels:
  • Select[test]take only those parts of a list or association that satisfy test
    SelectFirst[test]take the first part that satisfies test
    KeySelect[test]take those parts of an association whose keys satisfy test
    TakeLargestBy[f,n],TakeSmallestBy[f,n]take the n elements for which f[elem] is largest or smallest, in sorted order
    MaximalBy[crit],MinimalBy[crit]take the parts for which criteria crit is greater or less than all other elements
    SortBy[crit]sort parts in order of crit
    KeySortBy[crit]sort parts of an association based on their keys, in order of crit
    DeleteDuplicatesBy[crit]take parts that are unique according to crit
    DeleteMissingdrop elements with head Missing
  • The syntax op1/*op2 can be used to combine two or more filtering operators into one operator that still operates at a single level.
  • Aggregation Operators
  • The ascending aggregation operators combine or summarize the results of applying subsequent operators to deeper levels:
  • Totaltotal all quantities in the result
    Min,Maxgive minimum, maximum quantity in the result
    Mean,Median,Quantile,give statistical summary of the result
    Histogram,ListPlot,calculate a visualization on the result
    Merge[f]merge common keys of associations in the result using function f
    Catenatecatenate the elements of lists or associations together
    Countsgive association that counts occurrences of values in the result
    CountsBy[crit]give association that counts occurrences of values according to crit
    CountDistinctgive number of distinct values in the result
    CountDistinctBy[crit]give number of distinct values in the result according to crit
    TakeLargest[n],TakeSmallest[n]take the largest or smallest n elements
  • The syntax op1/*op2 can be used to combine two or more aggregation operators into one operator that still operates at a single level.
  • Subquery Operators
  • The ascending subquery operators perform a subquery after applying subsequent operators to deeper levels:
  • Query[]perform a subquery on the result
    {op1,op2,}apply multiple operators at once to the result, yielding a list
    <|key1op1,key2op2,|>apply multiple operators at once to the result, yielding an association with the given keys
    {key1op1,key2op2,}apply different operators to specific parts in the result
  • When one or more descending operators are composed with one or more ascending operators (e.g. desc/*asc), the descending part will be applied, then subsequent operators will be applied to deeper levels, and lastly, the ascending part will be applied to the result at that level.
  • Special Operators
  • The special descending operator GroupBy[spec] will introduce a new association at the level at which it appears and can be inserted or removed from an existing query without affecting subsequent operators.
  • Syntactic Sugar
  • Functions such as CountsBy, GroupBy, and TakeLargestBy normally take another function as one of their arguments. When working with associations in a Dataset, it is common to use this "by" function to look up the value of a column in a table.
  • To facilitate this, Dataset queries allow the syntax "string" to mean Key["string"] in such contexts. For example, the query operator GroupBy["string"] is automatically rewritten to GroupBy[Key["string"]] before being executed.
  • Similarly, the expression GroupBy[dataset,"string"] is rewritten as GroupBy[dataset,Key["string"]].
  • Query Behavior
  • Where possible, type inference is used to determine whether a query will succeed. Operations that are inferred to fail will result in a Failure object being returned without the query being performed.
  • By default, if any messages are generated during a query, the query will be aborted and a Failure object containing the message will be returned.
  • When a query returns structured data (e.g. a list or association, or nested combinations of these), the result will be given in the form of another Dataset object. Otherwise, the result will be given as an ordinary Wolfram Language expression.
  • For more information about special behavior of Dataset queries, see the function page for Query.
  • Exporting Datasets
  • Normal can be used to convert any Dataset object to its underlying data, which is typically a combination of lists and associations.
  • Dataset objects can be exported by writing Export["file.ext",dataset] or ExportString[dataset,"fmt"]. The following formats are supported:
  • "CSV"a comma-separated table of values
    "TSV"a tab-separated table of values
    "JSON"a JSON expression in which associations become objects
    "Package"a human-readable Wolfram Language expression
    "MX"a packed binary protocol
  • SemanticImport can be used to import files as Dataset objects.


open all close all

Basic Examples  (1)

Create a Dataset object from tabular data:

Click for copyable input

Take a set of rows:

Click for copyable input

Take a specific row:

Click for copyable input

A row is merely an association:

Click for copyable input

Take a specific element from a specific row:

Click for copyable input
Click for copyable input
Click for copyable input

Take the contents of a specific column:

Click for copyable input
Click for copyable input
Click for copyable input

Take a specific part within a column:

Click for copyable input

Take a subset of the rows and columns:

Click for copyable input

Apply a function to the contents of a specific column:

Click for copyable input
Click for copyable input
Click for copyable input

Partition the dataset based on a column, applying further operators to each group:

Click for copyable input

Apply a function to each row:

Click for copyable input

Apply a function both to each row and to the entire result:

Click for copyable input

Apply a function f to every element in every row:

Click for copyable input

Apply functions to each column independently:

Click for copyable input

Construct a new table by specifying operators that will compute each column:

Click for copyable input

Use the same technique to rename columns:

Click for copyable input

Select specific rows based on a criterion:

Click for copyable input

Take the contents of a column after selecting the rows:

Click for copyable input

Take a subset of the available columns after selecting the rows:

Click for copyable input

Take the first row satisfying a criterion:

Click for copyable input

Take a value from this row:

Click for copyable input

Sort the rows by a criterion:

Click for copyable input

Take the rows that give the maximal value of a scoring function:

Click for copyable input

Give the top 3 rows according to a scoring function:

Click for copyable input

Delete rows that duplicate a criterion:

Click for copyable input
Click for copyable input

Compose an ascending and a descending operator to aggregate values of a column after filtering the rows:

Click for copyable input

Do the same thing by applying Total after the query:

Click for copyable input

Applications  (3)

Properties & Relations  (4)

Possible Issues  (4)

Neat Examples  (2)

Introduced in 2014