1. Introduction - Standard Deviation

2. Journal Topic  A recent article says that teenagers send an average of 100 text messages per day. If I collected data from 6 teenagers, what could the possible data set look like to get this average?

3. Definitions  Standard Deviation – A measure of how spread out numbers are.  Introduce Symbol  The formula is easy: It is the square root of the Variance.

4. Definitions … one more  Variance – The average of the squared differences from the mean.

5. Example

6. Step 1. Calculate the Mean  Go ahead….Calculate the Mean

8. Step 2. We got the mean, now Calculate the difference from the mean.

9. Variance Time!

10. Now we have our Standard Deviation

12. Why do we take the square root??

13. Properties of Standard Deviation  S measures the spread about the mean and should be used only when the mean is chosen as the measure of center  S = 0 only when there is no spread/variability. This happens only when all observations have the same value. Otherwise s > 0. As the observations become more spread out about their mean, s gets larger.  S, like the mean, is not resistant to outliers. A few outliers can make s very large

14. Choosing a summary  The five number summary is usually the better than the mean and standard deviation for describing a skewed distribution with strong outliers.  Use the mean and standard deviation for reasonably symmetric distributions that are free of outliers.

15. Individual Practice – Get into partners!  Each partner should be either an A or B, decide!

16. For each graph  1. Create Data sets  Display data using a box plot  Calculate 5 number summary and mean  Check for outliers  Calculate variance and standard deviation  Decide on a measure of center  Which measure of center and spread should be used for the following data? For each case, write a sentence or two to explain your reasoning.