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In mathematics 
A sample is any sequence of numbers.
In Statistics 
A sample is a sequence of numbers taken semi-randomly from a source set to represent either the source set in its entirety, individual constituents of the source set or trends within it.
In electronic music (pre 1980) 
A sample is any sequence of numbers as in general mathematics.
In electronic music (post 1980) 
A sample is an external sound usually of a short duration that has been digitised to use as the basis of a musical sound played back by an electronic instrument, if the instrument can sample sounds it is referred to as a "Sampler".

The odd use of the word sample in the modern electronic music has its origins in the incorrect use of the term by the designers of the Australian QUASAR digital synthesiser in the late 1970's. When they added a ADC and software updates to the instrument that allowed it to make digital recordings, the function that had such a short duration due to memory constraints that rather than refer to the function as a recorder they named it "sampling function" with the idea being that you could take a "sample" of a sound and use that portion of the sound to create new sounds with using the digital synthesis and processing facilities on offer.

When an updated version of the instrument was released as the Fairlight Computer Music Instrument (CMI) around 1980 with a larger memory set that actually had enough memory to record and store whole sounds the documentation was read by its users in such a way that any digitised sound was a "sample".

The change means that papers on electronic music published up to ca. 1985 are frequently misread, where "sequences of numbers" are read to be "recordings of sounds", this is especially problematic in papers relating to granular synthesis where rather than using simple modulators people use a complex recorded waveform or forms to modulate another complex waveform, but this has a tendency to make one sound similar to the next.