law of large numbers

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Explanation of "Law of Large Numbers"

Definition: The "law of large numbers" is a principle in statistics that states that when you take a large number of random samples from a population, the average of those samples will get closer to the average of the entire population. In simpler terms, if you do something many times, the results will start to show the true average.

Usage Instructions:

• The term is commonly used in discussions about statistics, probability, and data analysis.
• You can use it to explain why larger samples give more reliable results in experiments or surveys.

Example:

Imagine you want to know the average height of students in your school. If you measure just a few students, your result might be very different from the true average height of all the students. However, if you measure the heights of 100 students instead of just 5, the average you calculate will be much closer to the actual average height of everyone in the school. This is an example of the law of large numbers in action.

Advanced Usage:

In more advanced statistics, the law of large numbers helps in making predictions and decisions based on data. It is foundational for fields like economics, psychology, and any area that relies on statistical analysis.

Word Variants:

• There are no direct word variants, but related terms include:
  • Sample size: The number of observations or data points collected.
  • Population: The entire group from which a sample is taken.

Different Meanings:

The "law of large numbers" specifically refers to statistics and does not have different meanings outside this context.

Synonyms:

• There are no direct synonyms for this term, but it can be explained as a statistical principle or theorem.

Idioms and Phrasal Verbs:

• There are no specific idioms or phrasal verbs associated with the term "law of large numbers." However, you might come across phrases like "the more the merrier," which conveys a similar idea: that having more participants can lead to better outcomes.

Summary:

In short, the law of large numbers tells us that larger samples provide more reliable estimates of population characteristics.

Academic

Noun

1. (statistics) law stating that a large number of items taken at random from a population will (on the average) have the population statistics

Synonyms

• bernoulli's law