In this world, there are many people of small, average & tall height. In general we find average heighted people to be more in number than a smaller number of very tall and very short people. So it’s obvious, the more extreme the height, the rarer the people with that height. If we imagine a situation in which there was a certain average height and with every inch added there was a drop in the probability by a constant amount.
The answer to this is a mathematical fact called the central limit theorem which can be defined as output/result from probability theory and used extensively in the fields of statistics. This approximation will yield better results as the size of the random samples is increased.
The field of statistics is based upon the fact that it is not always feasible or practical to collect all of the data from an entire population. Instead, we can gather a subset of data from a population and then use statistics for that sample to draw conclusions about the population.
For example, we can collect random samples from an industrial process and then use the means of our samples to make conclusions about the stability of the overall process.
So it is understood how important the results of central limit theorem is, in analytics. A wrong sample can end up in complete failure of analytics. Since the theorem makes assumptions about the distribution of population, so we can conclude that central limit theorem concerns mainly on the sampling distribution of the sample means.
The central limit theorem is a very important tool
for thinking about sampling distributions. It tells us the shape (normal) of the sampling distribution, along with its centre (mean) and spread (standard error). Even if we don’t know the shape of the distribution where our data comes from, the central limit theorem states that we can treat the sampling distribution as if it were normal. It provides the basis on which we can infer population mean when the population distribution is not known.
Since usually we cannot gather data from the entire population. So even in relatively small population, the data may be needed urgently and including everyone in the population in our data collection, may take too long. A sample when taken from a population, the sample information can be used to infer some specific things about the population. So the need for sampling can be described as:
• Checking all items in the population is physically impossible.
• Studying all the items in a population and the cost related to it.
• The sample results are usually adequate.
• Contacting the whole population would often be time-consuming.
• Destructive nature of certain tests.
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