Central Limit Theorem: population drawn from a simple random sample capacity of n, when the sample size is large, the sampling distribution of the sample mean of the normal distribution approximation.
(Note: the overall data to be independent and identically distributed)
When it reaches the sample size should be big, central limit theorem to apply it? A: For most applications, when the sample size is greater than or equal to 30 can.
As can be seen from the figure, no matter what kind of overall distribution, when the sample size of 30, when the distribution of the sample mean is a bell-shaped distribution:
The role of the Central Limit Theorem:
(1) In general there is no way to get all the data, the sample can be used to estimate the population.
(2) The overall mean and standard deviation, it is determined whether a sample as a whole.
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Most of the early 20th century scientists call the probability theorem Limit Theorem (Limit Theorem), due to the central theorems in such an important position in probability theory, the probability of so many cherished for its school of martial arts master, so mathematician Polya (G.Polya) in 1920 in front of the theorem known as the word "center", which follow people called the central limit theorem.