The Central Limit Theorem is important for statistics because it allows us to safely assume that the sampling distribution of the mean will be normal in most cases. This means that we can take advantage of statistical techniques that assume a normal distribution, as we will see in the next section.
What is the main result from the central limit theorem?
The Central Limit Theorem states that the sampling distribution of the sample means approaches a normal distribution as the sample size gets larger — no matter what the shape of the population distribution. This fact holds especially true for sample sizes over 30.
What condition is necessary to apply the central limit theorem?
The central limit theorem (CLT) states that the distribution of sample means approximates a normal distribution as the sample size gets larger, regardless of the populations distribution. Sample sizes equal to or greater than 30 are often considered sufficient for the CLT to hold.
Where can we apply central limit theorem?
Central limit theorem helps us to make inferences about the sample and population parameters and construct better machine learning models using them. Moreover, the theorem can tell us whether a sample possibly belongs to a population by looking at the sampling distribution.