Today, we reviewed the first quarter test.  The answer for question #1 was incorrectly specified, so I will go back and change people's grades to reflect that.  Sorry for the error. 

Today, we talked about ways to think about the entire distribution of a variable.  We created frequency tables -- both on data that students found on the internet, and on income data as a class.  The PivotTable feature in Excel makes it easy to group cases together into intervals.  After creating the PivotTable, one just right-clicks on the numbers,  selects the "Group" option and then decides the size of the intervals with which to group the data. 

We created histograms, which are simply bar charts based on frequency distributions. 

A histogram can tell you the shape of the distribution.  Distributions can be symmetrical or skewed.  When the tail on the right side tail of the distribution is longer than the left side tail, then we say the distribution is skewed to the right.  When the left-hand tail is longer than the right-hand tail, then we say that the distribution is skewed to the left. 

An example of a distribution skewed to the right is income in the US (and just about everywhere.)  There are a small group of people making a lot of money, which pulls the tail of the income distribution out to the right.  This rightward skew causes mean (average) income to be higher than median income.  Recall that extreme values (called outliers) affect the mean but do not affect the median.

The homework for Tuesday is posted on the homework part of the website.


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