Boxplots (Box and Whisker Plots)

Boxplot and Modified Boxplot 25% of data in each section

How to make a Boxplot Find the 5 number Summary of the dataFind the 5 number Summary of the data –Minimum –Q1 (Quartile 1 – 25 th percentile) –Median (50 th percentile) –Q3 (Quartile 3 – 75 th percentile) –Maximum Scale the axis so all numbers fit appropriatelyScale the axis so all numbers fit appropriately Make the box span the quartilesMake the box span the quartiles Draw a line down in the box marking the medianDraw a line down in the box marking the median Extend lines “whiskers” to the minimum and maximumExtend lines “whiskers” to the minimum and maximum –Modified Boxplot: If there are outliers, extend whiskers to the smallest and largest values that aren’t outliers and put dots where the outliers lie

Finding the Median & Quartiles To find the median of a set of data:To find the median of a set of data: –Order the data from least to greatest –The median is the middle number –If there is an even number of numbers and there is no one middle number, then average the two middle numbers To find the Quartiles:To find the Quartiles: –Q1 is the median of the lower half of the data –Q3 is the median of the top half of the data

Finding Outliers IQR(Interquartile Range) = Q3 – Q1 An outlier on the low end is any point lower than Q (IQR) Q (IQR) An outlier on the high end is any point higher than Q (IQR)

Make and compare Boxplots: Poverty Rates in the Eastern US Southern Poverty (%) Northern Maryland6.1 New Hampshire 4.3 Delaware6.5Wisconsin5.6 Florida9.0Connecticut6.2 North Carolina 9.0 New Jersey 6.3 Georgia9.9Vermont6.3 Tennessee10.3Indiana6.7 South Carolina 10.7Massachusetts6.7 Alabama12.5Michigan7.4 Kentucky12.7Maine7.8 Virginia13.9Ohio7.8 West Virginia 13.9Pennsylvania7.8 Mississippi16.0Illinois7.8 Rhode Island 8.9 New York 11.5

5 Number Summary & Outliers Southern States Min: 6.1 Q1: 9.0 Median: 10.5 Q3: 13.3 Max: 16 Outliers: < 9.0 – 1.5( ) < 2.55 so none on low end OR > ( ) >19.75 so none on high end Northern States Min: 4.3 Q1: 6.3 Median: 7.05 Q3: 7.8 Max: 11.5 Outliers: < 6.3 – 1.5( ) < 4.05 so none on low end OR > ( ) >10.05 so NY on high end since it is 11.5

Boxplots in Calculator Enter data into List (Stat Edit)Enter data into List (Stat Edit) Choose 1 st boxplot option in StatPlotChoose 1 st boxplot option in StatPlot Choose the list you used for XlistChoose the list you used for Xlist Choose 1 for Freq or a 2 nd list if data is stored in two lists (values in one, frequency in another)Choose 1 for Freq or a 2 nd list if data is stored in two lists (values in one, frequency in another) Zoom 9 will scale it for you to see the graphZoom 9 will scale it for you to see the graph Press Trace and the arrow keys to see the five number summary and any outliersPress Trace and the arrow keys to see the five number summary and any outliers

Measures of Center Mean( , ) —add up data values and divide by number of data values Median (M)—list data values in order, locate middle data value; average middle 2 if necessary Data Set: 19, 20, 20, 21, 22 Mean = 20.04; Median = 20 Data Set: 19, 20, 20, 21, 38 Mean = 23.6; Median = 20

Robust (Resistant) Statistic Robust or resistant: value doesn’t change dramatically when extreme values (including outliers) are added to (or taken out of) the data set.Robust or resistant: value doesn’t change dramatically when extreme values (including outliers) are added to (or taken out of) the data set. –Median is resistant. –Mean is NOT resistant against extreme values. Mean is pulled away from the center of the distribution toward the extreme value (“tails of graph”).

Mean or Median?

Measures of Center on Different Distribution Shapes Skewed to the left Symmetric Skewed to the right In each of the graphs, decide where the mean, median, and mode are relative to one another. Remember the mean is pulled toward extreme values.