Difference between revisions of "SOCR EduMaterials Activities LawOfLargeNumbers"
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==== Example ==== | ==== Example ==== | ||
The average weight of 10 students from a class of 100 students is most likely closer to the ''real average'' weight of all 100 students, compared to the average weight of 3 randomly chosen students from that same class. This is because the sample of 10 is a ''larger number'' than the sample of only 3 and better represents the entire class. At the extreme, a sample of 99 of the 100 students will produce a sample average almost exactly the same as the average for all 100 students. On the other extreme, sampling a single students will be an extremely variant estimate of the overall class average weight. | The average weight of 10 students from a class of 100 students is most likely closer to the ''real average'' weight of all 100 students, compared to the average weight of 3 randomly chosen students from that same class. This is because the sample of 10 is a ''larger number'' than the sample of only 3 and better represents the entire class. At the extreme, a sample of 99 of the 100 students will produce a sample average almost exactly the same as the average for all 100 students. On the other extreme, sampling a single students will be an extremely variant estimate of the overall class average weight. | ||
| − | ==== | + | ==== Statement of the Law of Large Numbers ==== |
If an event of probability p is observed repeatedly during '''independent repetitions''', the ratio of the observed frequency of that event to the total number of repetitions converges towards p as the number of repetitions becomes arbitrarily large. | If an event of probability p is observed repeatedly during '''independent repetitions''', the ratio of the observed frequency of that event to the total number of repetitions converges towards p as the number of repetitions becomes arbitrarily large. | ||
| − | ==== Complete details about the LLN can be found [http://en.wikipedia.org/wiki/Law_of_large_numbers here] === | + | ==== Complete details about the LLN can be found [http://en.wikipedia.org/wiki/Law_of_large_numbers here] ==== |
== SOCR Demonstrations of the LLN == | == SOCR Demonstrations of the LLN == | ||
| − | * '''Exercise 1''': Go to the [http://socr.ucla.edu/htmls/SOCR_Experiments.html SOCR Experiments] and select the [About_pages_for_SOCR_Experiments Coint Sample Experiment] | + | * '''Exercise 1''': Go to the [http://socr.ucla.edu/htmls/SOCR_Experiments.html SOCR Experiments] and select the [[About_pages_for_SOCR_Experiments | Coint Sample Experiment]] |
<center>[[Image:SOCR_Activities_CardCoinSampling_Dinov_092206_Fig1.jpg|300px]]</center> | <center>[[Image:SOCR_Activities_CardCoinSampling_Dinov_092206_Fig1.jpg|300px]]</center> | ||
Revision as of 12:53, 14 December 2006
Contents
SOCR Educational Materials - Activities - SOCR Law of Large Numbers Activity
This is a heterogeneous Activity that demonstrates the Law of large Numbers (LNN)
The Law of Large Numbers (LLN)
Example
The average weight of 10 students from a class of 100 students is most likely closer to the real average weight of all 100 students, compared to the average weight of 3 randomly chosen students from that same class. This is because the sample of 10 is a larger number than the sample of only 3 and better represents the entire class. At the extreme, a sample of 99 of the 100 students will produce a sample average almost exactly the same as the average for all 100 students. On the other extreme, sampling a single students will be an extremely variant estimate of the overall class average weight.
Statement of the Law of Large Numbers
If an event of probability p is observed repeatedly during independent repetitions, the ratio of the observed frequency of that event to the total number of repetitions converges towards p as the number of repetitions becomes arbitrarily large.
Complete details about the LLN can be found here
SOCR Demonstrations of the LLN
- Exercise 1: Go to the SOCR Experiments and select the Coint Sample Experiment
- SOCR Home page: http://www.socr.ucla.edu
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