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Central Limit Theorem Calculator
To use central limit theorem calculator, input population mean, population standard deviation, & sample size and hit calculate button
Central Limit Theorem Calculator
Central limit theorem calculator is used to find the mean and standard deviation of the given sample data. It takes population mean, population standard deviation, and sample size to measure the sample mean & standard deviation.
What is the central limit theorem?
A theorem that states the sampling distribution of the sample mean approaches the normal distribution as the sample size gets larger is said to be the central limit theorem.
Central limit theorem formula
For sample mean
Sample mean = population mean
x̄ = µ
For sample standard deviation
Sample standard deviation = population standard deviation /√n
s = σ / √n
How to calculate the central limit theorem?
The central limit theorem is used to find the sample mean & standard deviation. Follow the below example to understand it.
Example
Find the sample mean & standard deviation if the population mean is 14, the population standard deviation is 28, and the sample size is 25.
Solution
Step 1: Write the given information.
Population mean = µ = 14
Population standard deviation = σ = 28
Sample size = n = 25
Population mean =?
Population standard deviation =?
Step 2: Determine the sample mean.
Sample mean = population mean
Sample mean = x̄ = 14
Step 3: Now find the sample standard deviation.
Sample standard deviation = population standard deviation /√n
s = 28/√25
s = 28/5
s = 5.6