Sampling Distribution Calculator

Sampling Distribution Calculator

Use this calculator to find the probability distribution of a sample statistic. This mean of sampling distribution calculator also calculates the characteristics of sample distribution such as expected value and standard error of a mean along with the graphical representation. 

What is Sampling Distribution?

“A sample distribution refers to the probability distribution of a statistic derived from many samples from a specific population”

Variability of a Sampling Distribution

The variability of a sampling distribution depends on the following factors:

• n - Number of observations from the sample
• N - Number of observations in the population
• σ - Standard deviation by which the sample is drawn

Suppose you need to find the age of adults from the country's overall population. So, take multiple random samples from this population, find the statistics (age) for every sample, and plot a distribution graph of these sample averages. Sampling distribution is based on many random samples from a single population. This distribution is known as the sampling distribution of a mean. 

How do you Calculate Sample Distribution?

In case when the standard deviation is unknown then the sampling distribution is calculated with the help of sample data. To calculate it, follow the step-by-step guidance below:

• Draw random samples: Select multiple samples from a population and repeat this process to get a new sample. Each time find their mean
• Determine the difference: Find the difference between the sample means 
• Standard error: Calculate the standard error from the given population
• Plot the distribution: Construct the difference in samples in the form of a graph to know their distributions 

Standard error evaluates how much the values of different samples from the same population can differ. This is calculated as:

Standard error = σx = σ √n

If a sample size is smaller as compared to the population size, (σ) standard deviation of the sampling distribution is equal to the standard error. The normal probability calculator for sampling distributions helps to approximate the sampling distribution when the sample size is small relative to the population mean. 

Z-score of Sampling Distribution:

This shows how many standard errors are away from the population mean. The formula to calculate it is as follows:

z = (x̄ - μ) (σ / √n)

Mean of Sampling Distribution:

The mean of the sampling distribution corresponds to the population mean, as they are both the same values. 

μX̄ = μ

It is also shown by μM.