# Law of large numbers

The law of large numbers is a statistical principle that states that as a sample size grows, the mean of the sample converges towards the mean of the population. In other words, as more data is collected, the average of the data will more closely approximate the average of the population. The law of large numbers is an important tool in statistics and helps to ensure that results are accurate.

##### Why is law of large numbers important?

The law of large numbers is a statistical principle that states that as the sample size increases, the sample mean will converge towards the population mean. In other words, the larger the sample size, the more accurate the estimate of the population mean.

The law of large numbers is important because it allows us to make valid inferences about a population based on a sample. Without the law of large numbers, we would not be able to accurately estimate the population mean and confidence intervals would be much wider.

#### What is the law of large numbers in data science?

The law of large numbers is a statistical principle that states that as a sample size grows, the mean of the sample will tend to become closer to the true population mean. In other words, the larger the sample size, the more representative it will be of the population as a whole.

This principle can be applied to data science in a number of ways. For example, when building predictive models, it is important to use a large enough training dataset so that the model can learn the true underlying relationships in the data. If the training dataset is too small, the model may overfit the data and perform poorly on new data.

Similarly, when evaluating the performance of a model, it is important to use a large enough test dataset so that the results are representative of the model's true performance. If the test dataset is too small, the results may be misleading.

In general, the law of large numbers is an important consideration in data science whenever we are working with samples of data. Using a large enough sample will help ensure that the results we obtain are representative of the population as a whole.

#### Who discovered law of large numbers?

The law of large numbers is a statistical law that states that, as a sample size grows, the mean of the sample will tend to become closer and closer to the mean of the population. The law is also known as the "law of averages" or the "law of large proportions."

The law of large numbers was first discovered by Jacob Bernoulli, a Swiss mathematician, in his book Ars Conjectandi, published in 1713.

##### What is weak and strong law of large numbers?

The weak law of large numbers is a statement in probability theory that says that, as the number of independent trials n gets larger, the average of the trial results gets closer and closer to the expected value.

The strong law of large numbers is a statement in probability theory that says that, as the number of independent trials n gets larger, the probability that the average of the trial results is close to the expected value approaches 1.

##### What is law of large numbers in psychology?

The law of large numbers is a statistical principle that states that the more data points you have, the more reliable your results will be. In other words, the larger your sample size, the more accurate your estimates will be.

This principle is important in psychology because it helps researchers to understand how best to design their studies. For example, if a researcher wants to study the effects of a new drug, they need to be sure that their sample size is large enough to accurately reflect the population. Otherwise, their results could be skewed by chance.

The law of large numbers is also important in machine learning, as it helps to ensure that algorithms are trained on enough data to produce accurate results. Without enough data, a machine learning algorithm could produce inaccurate or even biased results.