simple random sample

A sample S of size n from a population U of size N is called a simple random sample if

  1. 1.

    it is a sample without replacement, and

  2. 2.

    the probability of picking this sample is equal to the probability of picking any other sample of size n from the same population U.

From the first part of the definition, there are (Nn) samples of n items from a population of N items. From the second part of the definition, the probability of any sample of size n in U is a constant. Therefore, the probability of picking a particular simple random sample of size n from a population of size N is (Nn)-1.

Remarks Suppose x1,x2,,xn are values representing the items sampled in a simple random sample of size n.

  • The sample meanMathworldPlanetmath x¯=1ni=1nxi is an unbiased estimatorMathworldPlanetmath of the true population mean μ.

  • The sample variance s2=1n-1i=1n(xi-x¯)2 is an unbiased estimator of S2, where (N-1N)S2=σ2 is the true varianceMathworldPlanetmath of the population given by

  • The variance of the sample mean x¯ from the true mean μ is


    The larger the sample size, the smaller the deviation from the true population mean. When n=1, the variance is the same as the true population variance.

Title simple random sample
Canonical name SimpleRandomSample
Date of creation 2013-03-22 15:13:01
Last modified on 2013-03-22 15:13:01
Owner CWoo (3771)
Last modified by CWoo (3771)
Numerical id 5
Author CWoo (3771)
Entry type Definition
Classification msc 62D05