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Why is the central limit theorem an important idea for dealing with a population not normally distributed?
Wiki User
∙ 7y ago
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.
Wiki User
∙ 7y ago
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When is the sample mean over repeated samples from the same population or process not normally distributed?
Provided the samples are independent, the Central Limit Theorem will ensure that the sample means will be distributed approximately normally with mean equal to the population mean.
Will the sampling distribution of the mean always be approximatelly normally distributed?
Yes, and more so for larger samples. (It follows from the Central Limit Theorem.)
Will sample means be nearly normally distributed if the distribution of the measurement among the individuals are not from a normal distribution?
Yes, as you keep drawing more and more samples and the number of samples become sufficiently large. This is known as the Central Limit Theorem.
When do you use a normal distribution?
When studying the sum (or average) of a large number of independent variables. A large number is necessary for the Central Limit Theorem to kick in - unless the variables themselves were normally distributed. Independence is critical. If they are not, normality may not be assumed.
Describe the central limit theorem and give an example of how it can be used in statistics?
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 (
When is the sample mean over repeated samples from the same population or process not normally distributed?
Provided the samples are independent, the Central Limit Theorem will ensure that the sample means will be distributed approximately normally with mean equal to the population mean.
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.
Will the sampling distribution of the mean always be approximatelly normally distributed?
Yes, and more so for larger samples. (It follows from the Central Limit Theorem.)
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.
Why scalability is an important feature in design of distributed OS?
Advantages of distributed operating system include: sharing of resources, reliability, communication and computation speedup. Distributed systems are potentially more reliable than a central system because if a system has only one instance of some critical component like CPU.
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