Sampling Distribution of the Sample Mean /
Central Limit Theorem

Click onand wait for the applet to open.

The graph at the top of the window (Graph 1) shows the distribution of the population from which the samples are going to be taken.

In this case, the population has a Normal distribution.

Graph 1

  1. Write down the mean and standard deviation of this Normally distributed population.

Mean = SD =

Graph 2shows the sample data selected from the population.

Graph 2

  1. Randomly select a sample of 5 data from the population by clickingonce.
  2. From Graph 2, write down the values of the 5 data that have been sampled.

Data sampled:

  1. From the left of Graph 2, write down the sample mean for these 5 data.

Sample Mean =

Graph 3now shows the first sample mean.

Graph 3

  1. Why is sd = 0.00 when there is one value for a sample mean showing on Graph 3?
  2. Click once again on to select your second random sample. You can see this sample on Graph 2. The sample mean for this second sample will have been added to Graph 3. Complete the following:

2nd Sample Mean = (Left of Graph 2)

Mean of the 2 sample means = (Left of Graph 3)

SD of the 2 sample means = (Left of Graph 3)

  1. Click on 8more times. Ten sample means should now be showing in Graph 3.

Using the information to the left of Graph 3, complete the following:

Mean of the 10 sample means = SD of the 10 sample means =

  1. Now speed up the process:

In Graph 2: Click on for 5 more samples; then click on .

Then keep clicking on until you have taken about 100, 000 samples.

Using the information to the left of Graph 3, complete the following:

Mean of the sample means = SD of the sample means =

  1. Using your answers in Question 6, complete the second row (n = 5) of the table below.

Sample Size n / Mean / Standard Deviation / Variance / Shape
Parent Population
(Graph 1) / 16.00 / 5.00 / 25.00 / Normal
Distribution
of
the Sample Mean,

(Graph 3) / 5
10
16
20
  1. Repeat the process: take about 100,000 of samples of size 10 by setting. in Graph 3.

Repeat for n = 16 and n = 20. Complete the table above.

Conclusion:

Sample Size n / Mean / Standard Deviation / Variance / Shape
Parent Population
(Graph 1) /  /  / 2 / Normal
Distribution of Sample Mean

(Graph 3) / n

Department of Statistics / AMA