Statistics Dictionary

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Law of Large Numbers

One can think about the probability of an event in terms of its long-run relative frequency. The relative frequency of an event is the number of times an event occurs, divided by the total number of trials.

P(A) = ( Frequency of Event A ) / ( Number of Trials )

For example, a merchant notices one day that 5 out of 50 visitors to her store make a purchase. The next day, 20 out of 50 visitors make a purchase. The two relative frequencies (5/50 or 0.10 and 20/50 or 0.40) differ. However, summing results over many visitors, she might find that the probability that a visitor makes a purchase gets closer and closer 0.20.

The scatterplot above shows the relative frequency as the number of trials (in this case, the number of visitors) increases. Over many trials, the the relative frequency converges toward a stable value (0.20), which can be interpreted as the probability that a visitor to the store will make a purchase.

The idea that the relative frequency of an event will converge on the probability of the event, as the number of trials increases, is called the law of large numbers.

See also:   Probability