Central limit theorem

If sample size is large (e.g. n≧30), 3 important characteristics for sampling distribution by using random draws, regardless of the population’s distribution,

• The sample mean will be approximately normally distributed.
• Mean of sample means = Mean of the population.
• Variance of sample means = Variance of population / Sample size, i.e. σ²/n
  

Notes:

• For large sample size, if population variance is unkown, use sample sampling error of the sample mean as the variance.
• Increase in sample size leads to decrease in variance of sample means