A Simple Random Sample (SRS) is the type of sample used almost exclusively in statistics. It involves identifying a population (the entire group of individuals you wish to report data on) giving each a number, and then picking numbers randomly to create a sample. Nowadays, picking random numbers is generally done by computers, but thats only pseudorandom; if you want to be hardcore, RAND Corporation publishes a book entitled One Million Random Digits containing (you guessed it) one million random digits.

One important thing to note about an SRS is that while many people will define it as being a sample in which each individual from the population has an equal chance of being picked, this is only half of the definition; the more accurate definition is that every possible sample has an equal chance of being the sample.

To understand the difference, consider the following situation. Let's say you want to find out the mean weight of bowling balls. Bowling balls, in our imaginary world come in blue and red. 70% of all bowling balls in this world are red. The other 30% are blue. Picking 7 red balls and 3 blue balls does not make a simple random sample, even though each ball will get representation in the sample equal to its proportion of the population (this is a stratified random sample, actually). In a simple random sample, it would be possible (though unlikely) that you would get ten blue balls. This is the essence of a simple random sample - every possible sample has an equal chance of being the sample you pick.

A simple random sample is more or less the only type of sample permissible in most statistical calculations. This is also why you shouldn't trust statistics from call-in polls, standing-around-in-the-mall-asking-people-to-fill-out-a-survey polls, etc. - they're going to be very biased and unrepresentative of the population.

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