In your own words, explain the Central Limit Theorem (CLT). Why it is important in the context of decision-making for business?

Brief Explanation is given below

Explanation:

According to the central limit theorem, the average of a sample of data will be closer to the average of the general population in question, as the sample size increases, despite the actual distribution of the data. In other words, the data is accurate if the distribution is normal or aberrant.

As a general rule, sample sizes equal to or greater than 30 are considered sufficient for the CLT to be maintained, which means that the distribution of the sample means is distributed quite normally. Therefore, the more samples taken, the more plotted results take the form of a normal distribution.

The Central Limit Theorem exhibits a phenomenon in which the average of the sample means and the standard deviations are equal to the population mean and the standard deviation, which is extremely useful for accurately predicting the characteristics of the populations.

In Finance or decision Making with example

The CLT is useful when examining the returns of an individual share or broader indices, because the analysis is simple, due to the relative ease of generating the necessary financial data. Consequently, investors of all kinds rely on the CLT to analyze the profitability of the shares, build portfolios and manage risk.

Say, for example, that an investor wishes to analyze the overall performance of a stock index that comprises 1,000 shares. In this scenario, that investor can simply study a random sample of shares, to cultivate the estimated returns of the total index. At least 30 randomly selected actions must be sampled, in various sectors, to maintain the central limit theorem. In addition, previously selected actions should be exchanged with different names, to help eliminate bias.

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