Download Chapter 9 - Lone Star College

Sampling Distribution of the Mean
Sampling Distribution
 The sampling distribution of the mean refers to the
probability distribution of means for all possible
random samples of a given size from some population.
 Viewing the variability of all the samples identifies
whether one occurrence of the mean is unusual
(significant).
Mean of all sample means
 The mean of the sampling distribution of the mean
always equals the mean of the population.
 µx
Symbols
Type of Distribution
Mean
Standard Deviation
Sample
X
s
Population
µ
σ
Sampling distribution of the mean
µx
σx
Sampling distribution
demonstration
Central Limit Theorem
 Regardless of the population shape, the
shape of the sampling distribution of the
mean approximates a normal curve if the
sample size is sufficiently large.
Three key characteristics of the
sampling distribution of the mean
The mean of the sampling distribution equals the
population mean
2. The standard error equals the population standard
deviation divided by the square root of the sample
size
3. The shape of the curve approximates a normal curve
1.
Bottom Line
 Sampling distribution is the most important concept
in inferential statistics.
 The sampling distribution of the mean is defined as
the probability distribution of means for all possible
random samples of a given size from some population.