# Central Limit Theorem Calculator (CLT)

Online statistics central limit theorem calculator to calculate sample mean and standard deviation using Central Limit Theorem (CLT). Calculate sample mean and standard deviation by the known values of population mean, population standard deviation and sample size.

## Calculate Sample Mean and Standard Deviation using CLT

Online statistics central limit theorem calculator to calculate sample mean and standard deviation using Central Limit Theorem (CLT). Calculate sample mean and standard deviation by the known values of population mean, population standard deviation and sample size.

Code to add this calci to your website

#### Formula:

Sample mean ( μ_{x} ) = μ Sample standard deviation ( σ_{x} ) = σ / √ n
**Where,**
μ = Population mean
σ = Population standard deviation
n = Sample size
Use our online central limit theorem Calculator to know the sample mean and standard deviation for the given data. Generally CLT prefers for the random variables to be identically distributed.

**Central Limit Theorem:**
It is one of the important probability theorems which states that given a sufficiently large sample size from a population with a finite level of variance, the mean of all samples from the same population will be approximately equal to the mean of the population.

It implies that probabilistic and statistical methods for normal distribution can be applicable to other types of distributions. The central limit theorem (CLT) states that, when independent random variables are added, their properly normalized sum tends toward a normal distribution ('bell curve') even if the original variables themselves are not normally distributed.

**Calculate Sample Mean and Standard Deviation using CLT Formula:**
Calculating the sample mean and standard deviation using CLT (Central Limit Theorem) depends upon the population mean, population standard deviation and the sample size of the data. Given above is the formula to calculate the sample mean and the standard deviation using CLT. Using CLT all of the samples will follow an approximate normal distribution pattern, with all variances being approximately equal to the variance of the population divided by each sample's size.