Six Sigma Green Belt Certification Practice Exam

What does the central limit theorem indicate about control charts?

1. A process where the data points are randomly situated around the average

2. Data can be validated within a certain range

3. As a sample size increases, the distribution of averages approaches a normal distribution

4. A process where the data points approach upper and lower control limits

The correct answer is: As a sample size increases, the distribution of averages approaches a normal distribution

The correct answer highlights a fundamental aspect of the central limit theorem, which states that as the sample size increases, the distribution of the sample means will approach a normal distribution, regardless of the shape of the population distribution from which the samples are drawn. This concept is crucial for control charts in process management and quality control as it enables practitioners to make inferences about the process’s behavior over time. In the context of control charts, this means that even if the original data points themselves do not follow a normal distribution, the means of larger samples taken from that data will tend to be normally distributed. This characteristic allows for the establishment of control limits based on the assumption of normality, facilitating the detection of variations in the process. Hence, the ability to apply statistical analysis becomes much more robust with larger sample sizes. Understanding this allows organizations to better monitor processes for stability and quality, utilizing these principles to achieve improvements and maintain standards effectively.