If you were asked to provide constructive feedback. What statistical explanation would you provide?

Person 1

These are two mathematical concepts that help us better understand statistics and the frequency (probability) of an event happening. faces we know that each face has a 1/6 chance of success, rolling the die 6 times but we don't get all 6 numbers. The theorem says that if an experiment is repeated identically a large number of times the probabilities will tend to equal the expectation of the result, in simpler words if we roll the die 6 million times it is very likely that on average each number will be about 1 million times. In this way, if the probability of an event is not known, then repeating the experiment or action a very high number of times we could obtain a value very close to the theoretical probability.

The central limit theorem is another important theorem in the study of data in statistics, in statistics the data in question can have different distributions in space (uniforms, exponents, normals, etc.) but we will not go into detail, sometimes we do not know how a data is distributed consequently we do not know how to best evaluate the data in our possession. Let's take a practical example to better explain, we want to know on average how much a US individual spends weekly on food shopping. If we had the data of each individual citizen it would be enough for us to divide it by the total number of citizens but it is unthinkable to ask everyone how much they spend, so we must base our research on samples. By analyzing many samples of large quantities we obtain for each sample an average of expenditure, the theorem states that given a large number of samples from which we obtain an average with a normal distribution, the average of our averages will be approximately equal to the average of the entire population from which samples were taken. Not having taken a cue from other sources, I have not included citations.

Person 2

The Law of Large Numbers

Any sample of the population can be collected and can be as the sampling distribution and approximately can get to the mean by the sampling of numbers represented as statistics in a collected sample data and as the numbers get bigger and larger in numbers the more approximated and closely concentrated the mean using in the form by normal distribution (Yakir, B. 2011 pg. 115).

Central Limit Theorem

"A mathematical result regarding the sampling distribution of the sample average. States that the distribution of the average is approximately Normal when the sample size is large" (Yakir, B. 2011 Glossary p.123). In which is that for any population size that is large can closely approximate the accuracy of the mean and expectations to be normal.

Person 3

In probability and statistics, the law of large numbers states the following according to James (2020), "as a sample size grows, its mean gets closer to the average of the whole population." In simpler words, when observing a sample average from a large size sample, it will be close to the true population average, and the larger the sample, the closer it will get to the true average. Of importance to notice is that the law of large numbers will not necessarily reflect the true population characteristics if the sample size is small.

The Central Limit Theorem on the other hand deals with approximating any shape of population distribution with normal distribution as the sample gets larger. Specifically, this applies to the sampling distribution of the sample mean and it is true for sample-sized larger than 30, according to Central Limit Theorem (n.d.). In simpler words, the more samples taken from the population, especially large ones, the graph of the sample means will resemble that of a normal distribution.