Statistics Dictionary

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Randomization Randomized Block Design Randomized Block Experiment Range Ratio Scale Reduced Row Echelon Form Region of Acceptance Region of Rejection Regression Relative Frequency Relative Frequency Table Repeated Measures Design Replication Representative Residual Residual Plot Response Bias Row Echelon Form Row Vector Sample Sample Design Sample Point Sample Space Sample Survey Sampling Sampling Distribution Sampling Error Sampling Fraction Sampling Method Sampling With Replacement Sampling Without Replacement Scalar Matrix Scalar Multiple Scatterplot Scheffe Test Selection Bias Set Significance Level Simple Random Sampling Simple Regression Singular Matrix Skewness Slope Sphericity Standard Deviation Standard Error Standard Normal Distribution Standard Score Statistic Statistical Experiment Statistical Hypothesis Statistics Stemplot Strata Stratified Sampling Subset Subtraction Rule Sum Vector Sums of Squares Symmetric Matrix Symmetry Systematic Sampling T Distribution T Score T Statistic Test Statistic Transpose Treatment t-Test Two-Sample t-Test Two-stage Sampling Two-Tailed Test Two-Way Table Type I Error Type II Error Unbiased Estimate Undercoverage Uniform Distribution Unimodal Distribution Union Univariate Data Variable Variance Variance Inflation Factor Vector Inner Product Vector Outer Product Vectors Venn Diagram Voluntary Response Bias Voluntary Sample Y Intercept z-score

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