JP Morgan Interview Questions | CLT
Question
What is the Central Limit Theorem? Explain it. Why is it important?
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. The central limit theorem states that if you have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement , then the distribution of the sample means will be approximately normally distributed
In the study of probability theory, the central limit theorem (CLT) states that the distribution of sample means approximates a normal distribution (also known as a “bell curve”), as the sample size becomes larger, assuming that all samples are identical in size, and regardless of the population distribution shape.
The central limit theorem states that when you take n no of samples of equal size from a
population and you find out the mean of every sample, you will find that the
distribution of all the means takes the form of a normal distribution, irrespective
of the form of the distribution the population has.
Many practices in statistics, such as those involving hypothesis testing or confidence intervals,
make some assumptions concerning the population that the data was obtained from.
One of the assumption is that the populations that we are working with is normally distributed.
The use of an appropriate sample size and the central limit theorem help us to get around the problem
of data from populations that are not normal.
If we have large enough population size and good number of samples than mean of all samples will follow the normal distribution and will be same as the population mean.
CLT states that if we have sample distribution of means of different samples where each sample is of size >30(ideal value , can be less as well) then the distribution would be normal.