A statified population has five strata. Given their stratum sizes,means,and sample variance how can I estimate the population mean, population variance and population total
To estimate the population mean, population variance, and population total in a stratified population, you can use the following formulas:
1. Estimating the Population Mean:
- Calculate the mean within each stratum by using the given stratum sizes and means.
- Multiply each stratum mean by its corresponding stratum size.
- Sum up the products from all strata.
- Divide the total sum by the overall population size, which is the sum of all stratum sizes.
Formula: Population Mean = (Sum of (Stratum Mean × Stratum Size)) / (Sum of Stratum Sizes)
2. Estimating the Population Variance:
- Calculate the variance within each stratum using the given sample variance.
- Multiply each stratum variance by its corresponding stratum size.
- Sum up the products from all strata.
- Divide the total sum by the overall population size minus one, which corrects for the degrees of freedom.
Formula: Population Variance = (Sum of (Stratum Variance × Stratum Size)) / (Sum of Stratum Sizes - 1)
3. Estimating the Population Total:
- Multiply the population mean (calculated in step 1) by the overall population size.
Formula: Population Total = Population Mean × (Sum of Stratum Sizes)
By following these steps and applying the appropriate formulas, you can estimate the population mean, population variance, and population total of a stratified population.