Central Limit Theorem Example

 Sample Size: Population Mean: Population SD: Number Of Samples:

Output: `Press calculate`

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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 sample
• `populationMean` = mean of the population
• `populationSD` = standard deviation of the population
• `numberOfSamples` = number of samples taken from the population

Example valid values:

• `sampleSize` = 36
• `populationMean` = 100
• `populationSD` = 20
• `numberOfSamples` = 100

Output:

• `mean` = mean of the sampling distribution of the sample mean
• `standardError` = 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.