5 Interpretation of Box Plots The five number summary divides a data distribution into 4 parts. About what percent of the data values in each of the following intervals? • before the median • after the median • in the box (between the 1st and 3rd quartiles) • before the upper quartile • after the upper quartile • before the lower quartile • after the lower quartile • between median and upper quartile • between the median and the lower quartile
6 Definition of outliers Steps to determine if there are outliers:Find the Interquartile range (IQR)IQR = Q3 – Q1Multiply: 1.5 * IQRAdd: Q *IQRAny value greater than Q3+ 1.5*IQR is an outlierSubtract Q1 – 1.5*IQRAny value less than Q1-1.5*IQR is an outlier
7 Definition of OutlierAny value more than 1.5 IQRs above Q3 or below Q1.OrAny value more than 1.5 “boxes” above Q3 or below Q1Example: Natural Peanut Butter Quality Ratings:Find the 5 number summaryMake a box plotDetermine if there are any outliers
8 Comparing two or more Groups Side by side box plotsCalories for all beef hot dogs:Calories for all poultry hot dogs:
9 Comparing two groups Each each type of hot dog Find the 5 number summaryConstruct a box plot of each using the same scale for both. Place the beef hot dog box plot above the poultry hot dog box plot.What type of hot dog has the fewer number of calories? Use the box plots and the percent to explain your answer.