Introduction - Standard Deviation

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?

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.

Definitions … one more

Variance – The average of the squared differences from the mean.

Example

Step 1. Calculate the Mean

Go ahead….Calculate the Mean

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

Variance Time!

Now we have our Standard Deviation

Why do we take the square root??

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

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.

Individual Practice – Get into partners!

Each partner should be either an A or B, decide!

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.