1. Notes: Sample Means
2-7-12

2. Standards
MM2D1. Using sample data, students will make informal inferences about
population means and standard deviations.
a. Pose a question and collect sample data from at least two different populations.
d. Compare the means and standard deviations of random samples with the corresponding population parameters, including those population parameters for normal distributions. Observe that the different sample means vary from one sample to the next. Observe that the distribution of the sample means has less variability than the population distribution.

3. Variability The more spread out your data, the higher the variability.
The less spread out your data, the lower the variability

4. Type of distribution The distribution of the samples means will be more compact then the distribution of the population.

5. How does the mean of the sample means relate to the mean of the population? This is easy! The mean of the sample means will be approximately the same as the mean for the whole population!

6. How does the standard deviation of the sample mean relate to the standard deviation of the population?
The standard deviation will be lower for the sample means (thus, the variability will also be lower for the sample means).

7. Approximating the Standard deviation of the population:
Formula:
Where Sx is the standard deviation of your sample means, and n is the sample size

8. Example 1:
Sample sizes of 10 cards are pulled from a deck of cards. The standard deviation of the sample sizes are Estimate the standard deviation of the original population.

9. Example 1 Answer

10. Example 2: You want to know the height of the average person at JHS
Example 2: You want to know the height of the average person at JHS. You take 7 samples of sample size 9 from the student population. The mean of the samples is 68.5 inches and the standard deviation is 2.74 inches.
Estimate the standard deviation of the original population.
Estimate the mean of the original population.

11. Example 2 Answers SD of Population:
Mean of Population: It is the same! inches

12. Going backwards
What if you wanted to estimate the standard deviation of the sample means?

13. Example 3
The heights of all the people in Atlanta have a standard deviation of 1.89 inches.
What should be the standard deviation of sample means of sample size 12 people?

14. Answer to example 3

15. Questions?