The Distribution of Sample Means

Distribution of Sample Means is the distribution form by

all possible sample means of size n

Distribution of Sample Means shows how sample mean

cluster around the population mean

Distribution of Sample Means is approximately

normal in shape

the larger the sample size, the closer the

sample means will be to the population mean

the larger the sample size, the smaller

the sample error (standard error)

The mean of the distribution of sample mean (μM) is

equal to the mean of the population mean (μ)

The name of the mean of the distribution of sample mean (μM) is

Expected value of M

Standard Error is

SD distribution of sample mean [ σM ]

SD is the

variability of a distribution

you want the SD to get

as close to 0 as possible

less variability (as close to 0) means

your sample mean is closer to the true population mean

Central Limit Theorem is when

as sample size (n) approaches infinity, the sample mean distribution will form a normal distribution even if the original population isn’t normal

finding z-score using sample mean

use M instead of X in the equation and use standard error instead of SD