--- title: "RandomSample" language: "en" type: "Symbol" summary: "RandomSample[{e1, e2, ...}, n] gives a pseudorandom sample of n of the ei. RandomSample[{w1, w2, ...} -> {e1, e2, ...}, n] gives a pseudorandom sample of n of the ei chosen using weights wi. RandomSample[{e1, e2, ...}] gives a pseudorandom permutation of the ei." keywords: - simple random sample - SRS - sampling without replacement - SRSWOR - random permutation - pseudorandom permutation - pseudo-random permutation - pseudorandom sample - random subset - shuffle - shuffling - urn problem - weighted permutation - randperm - randperm canonical_url: "https://reference.wolfram.com/language/ref/RandomSample.html" source: "Wolfram Language Documentation" related_guides: - title: "Random Number Generation" link: "https://reference.wolfram.com/language/guide/RandomNumberGeneration.en.md" - title: "Permutations" link: "https://reference.wolfram.com/language/guide/Permutations.en.md" - title: "Discrete Mathematics" link: "https://reference.wolfram.com/language/guide/DiscreteMathematics.en.md" - title: "Rearranging & Restructuring Lists" link: "https://reference.wolfram.com/language/guide/RearrangingAndRestructuringLists.en.md" - title: "Tabular Transformation" link: "https://reference.wolfram.com/language/guide/TabularTransformation.en.md" related_functions: - title: "RandomChoice" link: "https://reference.wolfram.com/language/ref/RandomChoice.en.md" - title: "RandomInteger" link: "https://reference.wolfram.com/language/ref/RandomInteger.en.md" - title: "SeedRandom" link: "https://reference.wolfram.com/language/ref/SeedRandom.en.md" - title: "BlockRandom" link: "https://reference.wolfram.com/language/ref/BlockRandom.en.md" - title: "Permutations" link: "https://reference.wolfram.com/language/ref/Permutations.en.md" - title: "Subsets" link: "https://reference.wolfram.com/language/ref/Subsets.en.md" - title: "Span" link: "https://reference.wolfram.com/language/ref/Span.en.md" - title: "Downsample" link: "https://reference.wolfram.com/language/ref/Downsample.en.md" related_tutorials: - title: "Random Number Generation" link: "https://reference.wolfram.com/language/tutorial/RandomNumberGenerationOverview.en.md" --- # RandomSample RandomSample[{e1, e2, …}, n] gives a pseudorandom sample of n of the ei. RandomSample[{w1, w2, …} -> {e1, e2, …}, n] gives a pseudorandom sample of n of the ei chosen using weights wi. RandomSample[{e1, e2, …}] gives a pseudorandom permutation of the ei. ## Details * ``RandomSample`` is also known as simple random sampling or sampling without replacement. * ``RandomSample[{e1, e2, …}, n]`` never samples any of the ``ei`` more than once. * ``RandomSample[{e1, e2, …}, n]`` samples each of the ``ei`` with equal probability. * ``RandomSample[{e1, e2, …}, UpTo[n]]`` gives a sample of ``n`` of the ``ei``, or as many as are available. * ``RandomSample[i ;; j ;; k, n]`` may be used to sample the ``Span`` from ``i`` to ``j`` in steps of ``k``. * ``RandomSample`` gives a different sequence of pseudorandom choices whenever you run the Wolfram Language. You can start with a particular seed using ``SeedRandom``. * A ``Method`` option to ``SeedRandom`` can be given to specify the pseudorandom generator used. ## Examples (12) ### Basic Examples (3) Find a sample in which no elements ever occur more than once: ```wl In[1]:= RandomSample[Range[30], 20] Out[1]= {22, 12, 24, 6, 21, 8, 25, 23, 29, 1, 2, 4, 30, 27, 14, 13, 19, 26, 10, 9} ``` --- Generate a random permutation: ```wl In[1]:= RandomSample[Range[10]] Out[1]= {3, 1, 5, 6, 8, 9, 4, 2, 10, 7} ``` --- Generate a random sample of 6 elements, or as many as there are if fewer: ```wl In[1]:= RandomSample[Range[5], UpTo[6]] Out[1]= {4, 5, 3, 2, 1} ``` ### Scope (4) The elements can be any expressions: ```wl In[1]:= RandomSample[{Exp[x], x ^ 2, 1 / x, 2}] Out[1]= {(1/x), 2, E^x, x^2} ``` --- With larger weights for later elements, later elements tend to be selected for the sample: ```wl In[1]:= RandomSample[Range[30] -> Range[30], 10] Out[1]= {24, 18, 21, 12, 25, 27, 15, 23, 30, 29} ``` --- Sample over all numbers between -10 and 10: ```wl In[1]:= RandomSample[-10 ;; 10, 10] Out[1]= {-4, -2, -7, -8, 0, -9, 1, 9, 10, -5} ``` Sample over even numbers between -10 and 10: ```wl In[2]:= RandomSample[-10 ;; 10 ;; 2, 10] Out[2]= {-8, 2, 0, 4, 8, 6, -10, 10, -6, -4} ``` --- Guarantee that a set of random integers over a big range has no repetitions: ```wl In[1]:= RandomSample[1 ;; 2 ^ 30, 10] Out[1]= {895596716, 873363267, 155594206, 1067841266, 7643595, 1039153695, 464854556, 742132254, 61477147, 429443009} ``` ### Applications (1) Successively fill in black squares down the page: ```wl In[1]:= ArrayPlot[FoldList[ReplacePart[#, #2 -> 1]&, Table[0, {30}], RandomSample[Range[30], 30]]] Out[1]= [image] ``` ### Properties & Relations (3) Use ``SeedRandom`` to get repeatable random values: ```wl In[1]:= {RandomSample[Range[10]], RandomSample[Range[10]]} Out[1]= {{10, 1, 3, 9, 6, 7, 5, 2, 4, 8}, {6, 2, 8, 9, 5, 3, 10, 4, 7, 1}} In[2]:= {SeedRandom[1234];RandomSample[Range[10]], SeedRandom[1234];RandomSample[Range[10]]} Out[2]= {{1, 7, 5, 6, 9, 3, 10, 4, 8, 2}, {1, 7, 5, 6, 9, 3, 10, 4, 8, 2}} ``` --- Use ``BlockRandom`` to block one use of ``RandomSample`` from affecting others: ```wl In[1]:= {BlockRandom[RandomSample[Range[10]]], RandomSample[Range[10]]} Out[1]= {{1, 2, 10, 3, 9, 6, 8, 4, 5, 7}, {1, 2, 10, 3, 9, 6, 8, 4, 5, 7}} ``` --- ``RandomSample`` of size 1 follows the same distribution as ``RandomChoice`` : ```wl In[1]:= Table[RandomSample[{a, b, c, d}, 1], {10 ^ 5}]//Flatten//Tally//Sort Out[1]= {{a, 25255}, {b, 24661}, {c, 25167}, {d, 24917}} In[2]:= RandomChoice[{a, b, c, d}, 10 ^ 5]//Tally//Sort Out[2]= {{a, 24978}, {b, 25145}, {c, 25070}, {d, 24807}} In[3]:= Table[RandomSample[10 ^ Range[4] -> {a, b, c, d}, 1], {10 ^ 5}]//Flatten//Tally//Sort Out[3]= {{a, 84}, {b, 933}, {c, 8890}, {d, 90093}} In[4]:= RandomChoice[10 ^ Range[4] -> {a, b, c, d}, 10 ^ 5]//Tally//Sort Out[4]= {{a, 90}, {b, 903}, {c, 9126}, {d, 89881}} ``` ### Possible Issues (1) If the sample size is larger than the population size, an error message is returned: ```wl In[1]:= RandomSample[{a, b, c, d}, 5] ``` RandomSample::smplen: RandomSample cannot generate a sample of length 5, which is greater than the length of the sample set {a,b,c,d}. If you want a choice of possibly repeated elements from the set, use RandomChoice. ```wl Out[1]= RandomSample[{a, b, c, d}, 5] ``` ## See Also * [`RandomChoice`](https://reference.wolfram.com/language/ref/RandomChoice.en.md) * [`RandomInteger`](https://reference.wolfram.com/language/ref/RandomInteger.en.md) * [`SeedRandom`](https://reference.wolfram.com/language/ref/SeedRandom.en.md) * [`BlockRandom`](https://reference.wolfram.com/language/ref/BlockRandom.en.md) * [`Permutations`](https://reference.wolfram.com/language/ref/Permutations.en.md) * [`Subsets`](https://reference.wolfram.com/language/ref/Subsets.en.md) * [`Span`](https://reference.wolfram.com/language/ref/Span.en.md) * [`Downsample`](https://reference.wolfram.com/language/ref/Downsample.en.md) ## Tech Notes * [Random Number Generation](https://reference.wolfram.com/language/tutorial/RandomNumberGenerationOverview.en.md) ## Related Guides * [Random Number Generation](https://reference.wolfram.com/language/guide/RandomNumberGeneration.en.md) * [`Permutations`](https://reference.wolfram.com/language/guide/Permutations.en.md) * [Discrete Mathematics](https://reference.wolfram.com/language/guide/DiscreteMathematics.en.md) * [Rearranging & Restructuring Lists](https://reference.wolfram.com/language/guide/RearrangingAndRestructuringLists.en.md) * [Tabular Transformation](https://reference.wolfram.com/language/guide/TabularTransformation.en.md) ## Related Links * [An Elementary Introduction to the Wolfram Language: Rearranging Lists](https://www.wolfram.com/language/elementary-introduction/30-rearranging-lists.html) ## History * [Introduced in 2007 (6.0)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn60.en.md) \| [Updated in 2014 (10.0)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn100.en.md) ▪ [2015 (10.3)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn103.en.md)