Section 2.4 Working with Summary Statistics

 What were the main concepts of Section 2.4  When removing an outlier from a data set, which measure of center does it have the largest effect on?  In general, what does a percentile tell you?

 Measures of Center  Mean, Median, and sometimes Mode  Measures of Spread  Standard Deviation, and Quartiles (Q1 and Q3)  Remember SD gives an “average” deviation from the mean.  The quartiles divide the data into 25% portions.

 Lets say we know the mean value of the homes in a community along with the total number of homes: $213,500; 412 homes  We also know the tax rate: 1.5%  How can we use the mean to determine the total tax dollars received by the community?  The mean is used to represent the value of every home.

 When we describe the center of the annual income of a group of people, it is typical to use the median instead of mean…Why?  There are typically a large group of people clustered around the low end of the scale with a few having very large incomes. This creates a distribution that is…..  Skewed right and therefore the mean gives a measure that is higher than expected. The median filters out these extreme values.

 Create a dot plot of the following data:  Now create a dot plot of the distance the temperature is from freezing (32 o ). Positive if above freezing, negative if below.

 Recentering a set of data is when we add or subtract a constant from each data value.  This shifts the data on the number scale, but does nothing to change the shape or spread.  The mean will be shifted by the constant added or subtracted.

 Now use the same data and convert it to celsius.  Simply multiply the degrees above or below freezing by 1/1.8.  What happened to your data set?  Shape  Mean?  Standard deviation?  Notice that the mean and SD are multiplied by 1/1.8, but the shape stays the same.  This simply shrinks or if by a number greater than 1, stretches the distribution.

 A summary statistic is resistant to outliers if it is not changed very much when the outlier is removed from the data.  A summary statistic is sensitive to outliers if it is changed significantly when the outlier is removed from the data.  Remember our discussion of Mean vs Median  Refer to page 77: example of television viewers

 Percentile: If a value is at the k th percentile, then k% of the data is at or lower than this value.  Example: You got a 32 on math portion of the ACT. You are told this is the 86 th percentile.  That means 86% of the test takers scored at a 32 or lower.  It also means that 14% scored above a 32.  This is a measure of where a data value lies within the data set.

 Frequency plot where the plotted points show you the accumulated percent of data up to that point.  Example: page 78

 Page 80 E47, 49,

 Re-Centering happens when you…..??  What happens to the shape?  What happens to the center?  What happens to the spread?  Re-Scaling happens when you….??  What happens to the shape?  What happens to the center?  What happens to the spread?