n média (margem E)

The 'n mean (margin E)' calculator determines the sample size required to estimate a population mean with a specific margin of error and a predetermined confidence level. The formula used is (z·σ/E)², where 'z' is the z-score corresponding to the confidence level, 'σ' is the population standard deviation, and 'E' is the desired margin of error. This calculation is crucial in statistical studies to ensure results are representative of the population.

The z-score varies depending on the chosen confidence level (e.g., 1.96 for 95% confidence). The standard deviation (σ) must be known or estimated from prior data. The margin of error (E) is the maximum precision limit accepted by the researcher. This tool helps properly size the sample, avoiding excessive data or undersized samples.

This calculator is ideal for market research, scientific experiments, and social studies when the population is large and variability is known. If the standard deviation is unknown, a pilot study is recommended to estimate it. The defined margin of error directly impacts the sample size: smaller margins require more observations.

Note: The formula assumes an infinite or much larger population than the sample. For small populations, adjust the final result using a finite population correction formula. Additionally, the calculated margin of error refers only to the precision of the mean; other factors, such as sampling biases, can affect data reliability.