Central Limit Theorem Example
Formula:Mean = populationMean, Standard Error = populationSD / sqrt(sampleSize)
Introduction to Central Limit Theorem
The Central Limit Theorem (CLT) is a fundamental theorem in statistics that describes the characteristics of the distribution of sample means. It states that when an infinite number of successive random samples are taken from a population, the sample means will approximate a normal distribution (a bell-shaped curve), regardless of the shape of the population distribution, provided the sample size is sufficiently large (usually n > 30).
Parameter usage:
sampleSize
= number of observations in each samplepopulationMean
= mean of the populationpopulationSD
= standard deviation of the populationnumberOfSamples
= number of samples taken from the population
Example valid values:
sampleSize
= 36populationMean
= 100populationSD
= 20numberOfSamples
= 100
Output:
mean
= mean of the sampling distribution of the sample meanstandardError
= standard error of the sample means
Data validation
Sample size must be greater than 30 for the theorem to hold true.
Summary
This calculator approximates the mean and standard error of the sampling distribution of the sample mean, based on the Central Limit Theorem.
Tags: Statistics, Central Limit Theorem, Normal Distribution, Sampling