Choose a population shape, sample size, and statistic to see how the sampling distribution forms
The distribution we sample from (n=10,000)
One sample of size n=30
Distribution of 0 sample means
A sampling distribution is the probability distribution of a statistic (like the mean) computed from many random samples of the same size drawn from a population. It describes how a sample statistic varies from sample to sample due to random chance alone.
"If you could take every possible sample of size n from a population and compute the statistic for each, the resulting distribution of those statistics is the sampling distribution."
For the sample mean, the expected value of the sampling distribution equals the population mean:
This means the sample mean is an unbiased estimator of the population mean.
The standard deviation of the sampling distribution is called the standard error. For the sample mean:
As the sample size increases, the standard error decreases — larger samples give more precise estimates.
By the Central Limit Theorem, the sampling distribution of the mean approaches a normal distribution as sample size increases, regardless of the population shape. Try selecting a skewed or bimodal population in the simulation above and increase the sample size to see this in action.
Choose a population shape, sample size, and statistic to see how the sampling distribution forms
The distribution we sample from (n=10,000)
One sample of size n=30
Distribution of 0 sample means
A sampling distribution is the probability distribution of a statistic (like the mean) computed from many random samples of the same size drawn from a population. It describes how a sample statistic varies from sample to sample due to random chance alone.
"If you could take every possible sample of size n from a population and compute the statistic for each, the resulting distribution of those statistics is the sampling distribution."
For the sample mean, the expected value of the sampling distribution equals the population mean:
This means the sample mean is an unbiased estimator of the population mean.
The standard deviation of the sampling distribution is called the standard error. For the sample mean:
As the sample size increases, the standard error decreases — larger samples give more precise estimates.
By the Central Limit Theorem, the sampling distribution of the mean approaches a normal distribution as sample size increases, regardless of the population shape. Try selecting a skewed or bimodal population in the simulation above and increase the sample size to see this in action.
