Central Limit Theorem

  • Consider that a market survey is done with Sample Size of 150 customers to arrive at annual income of the Population.
  • Suppose, the Sample Mean(X-bar) is derived as 8 lakhs per annum and given Sample Size(n) is 150 customers. 
  • If Population Mean is found to 8.7 lakhs per annum, then Sampling Error is difference between Population Mean and Sample Mean which is 0.7 lakhs
  • Similar exercise is repeated for multiple samples of 150 customers and corresponding Sample Mean is calculated. 
  • Distribution(Plotting) of these sample means is called the Sampling Distribution of the Sample Mean.
  • ASSUMPTION: Sample Estimate will be reflective of reality meaning using sample means, we can infer the behavior of the population.
  • Smaller value for Standard Error means the calculation is more accurate
  • If n number of samples are taken from population N with Mean = Mu and Standard Deviation = sigma, X-bar calculated for each sample will have Mean = Mu and Standard Deviation = Sigma/Sqrt(n) also known as Standard Error. 

CENTRAL LIMIT THEOREM

  • Irrespective of the shape of the distribution of the original Population, the Sampling Distribution of the Sample Mean will approach a Normal Distribution as the size of the sample increases and becomes large.
  • NOTES: Sample size should be >= 30 for Central Limit Theorem to work


 REFERENCES

Comments

Post a Comment