Standard Deviation of the Sample Mean

Table of Contents

1. Introduction.
2. Overview of applet.
3. Exploring the standard deviation of the mean with an applet.
4. Experiment with different sample sizes.
5. Summarize the results.
6. Put it to use.

Exploring the standard deviation of the mean with an applet.

If we take different samples we get different sample means. How spread out are these sample means? We can experiment with this using the applet you examined earlier. If you closed the applet open it again by clicking "begin".

Assume our population is normally distributed. We would like to take a sample of 5 items from this population. To do this"

1. Set the choice of distribution to "Normal."
2. Next set the statistic to "Mean" and the sample size to N=16.
3. Click "Animated" to see the first sample appear on the section marked Sample Data.

Look at the left side of the applet. Notice that the standard deviation of the population is given in red.

Click the 1000 button 5 times to produce a total of 5000 samples.

1

Standard Deviation for n=16. Look at the left side of the blue histogram. Notice that it gives the standard deviation of the sample means (given in red). What is this standard deviation? a) 10 b) 16 c) about 50 d) about 7.0 e) about 2.5 f) about 1.0 Please select an answerIncorrect, look at the spread of the sample means (blue histogram) not the population (black histogram).Incorrect, look at the spread of the sample means (blue histogram) not sample size.Incorrect, look at the spread of the sample means (blue histogram).Incorrect, the standard deviation is not 7.0 look at the spread of the sample means (blue histogram).Correct. The spread of the sample means is around 2.5 which is 1/4 the spread of the population.Incorrect, the standard deviation is not 1.0. Look at the spread of the sample means (blue histogram).