0
Describe the central limit theorem and give an example of how it can be used in statistics?
Wiki User
∙ 14y ago
The Central Limit Theorem (CLT) is a theorem that describes the fact that if a number of samples are taken from a population, the distribution of the means of the samples will be normal. This is true for all different distributions, whether or not the population is normal or something else. The main exception to this is that the theorem does not work particularly well if the samples are small (<30) and the original population is not distributed normally.
The sample means will be distributed with a mean equal to the population mean, and with variance equal to the variance of the population divided by the size of each sample.
This can sound confusing when first working it out, but once it makes sense it is very useful in statistics. It is the basis for confidence intervals and hypothesis testing, as well as other statistical tests.
Wiki User
∙ 14y ago
Add your answer:
Earn +20 pts
What is the definition of central limit theorem?
The central limit theorem basically states that as the sample size gets large enough, the sampling distribution becomes more normal regardless of the population distribution.
Why you prefer Normal Distribution over the other distributions in Statistics?
For theoretical reasons (such as the central limit theorem), any variable that is the sum of a large number of independent factors is likely to be normally distributed. For this reason, the normal distribution is used throughout statistics, natural science, and social science as a simple model for complex phenomena.
What kind of triangle it used to describe for pythagorean inequality theorem?
Obtuse
Why is the central limit theorem an important idea for dealing with a population not normally distributed?
According to the Central Limit Theorem, even if a variable has an underlying distribution which is not Normal, the means of random samples from the population will be normally distributed with the population mean as its mean.
How do you know x bar and R charts follow normal distribution?
Central Limit Theorem
What is the Test for normal distribution?
Normal Distribution is a key to Statistics. It is a limiting case of Binomial and Poisson distribution also. Central limit theorem converts random variable to normal random variable. Also central limit theorem tells us whether data items from a sample space lies in an interval at 1%, 5%, 10% siginificane level.
What is an example of a corner point theorem?
what is corner point theorem
What does the central limit theorem say about the shape of the sampling distribution of?
The central limit theorem can be used to determine the shape of a sampling distribution in which of the following scenarios?
What does the Central Limit Theorem state?
The Central Limit Theorem (abbreviated as CLT) states that random variables that are independent of each other will have a normally distributed mean.
The Central Limit Theorem is important in statistics because?
According to the central limit theorem, as the sample size gets larger, the sampling distribution becomes closer to the Gaussian (Normal) regardless of the distribution of the original population. Equivalently, the sampling distribution of the means of a number of samples also becomes closer to the Gaussian distribution. This is the justification for using the Gaussian distribution for statistical procedures such as estimation and hypothesis testing.
In statistics what is the fundamental assumption?
You may be referring to the Central Limit Theorem.The Central Limit Theorem states that if you draw a large enough random sample from any population with a finite variance, the distribution of that sample will be approximately Normal (i.e. it will follow a Gaussian, or classic "Bell Shaped" pattern).
Example of theorem?
A theorem in math is defined as a result that has been proved to be true using facts that were known. An example of this is the Pythagorean Theorem for right triangles a^2 + b^2 = c^2.
What is the definition of central limit theorem?
The central limit theorem basically states that as the sample size gets large enough, the sampling distribution becomes more normal regardless of the population distribution.
Definition of kleene's theorem plus example?
kleene's theorem state that those who defined fa
What kind of triangle it used to describe for pythagorean inequality theorem?
Obtuse
Why you prefer Normal Distribution over the other distributions in Statistics?
For theoretical reasons (such as the central limit theorem), any variable that is the sum of a large number of independent factors is likely to be normally distributed. For this reason, the normal distribution is used throughout statistics, natural science, and social science as a simple model for complex phenomena.
When do you use the central limit theorem?
You use the central limit theorem when you are performing statistical calculations and are assuming the data is normally distributed. In many cases, this assumption can be made provided the sample size is large enough.
