Central Limit Theorem Calculator

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

1. For sample mean

Sample mean = population mean

x̄ = µ

2. 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