The central limit theorem (CLT) says that as sample sizes grow higher, the distribution of sample means approaches a normal distribution, independent of the population's distribution. For the CLT to hold, sample sizes of 30 or more are frequently regarded sufficient.
The central limit theorem gives a formula for the sample mean and the sample standard deviation when the population mean and standard deviation are known. This is given as follows: Sample mean = Population mean = μ μ Sample standard deviation = (Population standard deviation) / √n = σ / √n.
To summarise, the central limit theorem has three different components:
A population is sampled repeatedly.
Increasing the size of the sample
The distribution of the population.
The Central Limit Theorem underpins what a data scientist does on a daily basis: making statistical judgments about data. Without having to take a fresh sample to compare it against, the theorem allows us to calculate the likelihood that our sample will diverge from the population.