introduction - standard deviation. journal topic a recent article says that teenagers send an...
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Introduction - Standard Deviation
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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?
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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.
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Definitions … one more
Variance – The average of the squared differences from the mean.
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Example
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Step 1. Calculate the Mean
Go ahead….Calculate the Mean
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Step 2. We got the mean, now Calculate the difference from the mean.
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Variance Time!
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Now we have our Standard Deviation
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Why do we take the square root??
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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
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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.
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Individual Practice – Get into partners!
Each partner should be either an A or B, decide!
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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.