13.8 Box and Whisker Plots

We previously learned how to calculate Median. This is our “center”. We can now use our strategy to create a “box and whisker plot”, which looks at 5 specific numbers. Minimum: (Lowest Number) Lower Quartile: (25% of data is smaller) Median: (Middle Number) Upper Quartile: (25% of data is bigger) Maximum: (Highest Number)

Minimum Lower Quartile Median Upper Quartile Maximum 25% of data 25% of the data

So how do we calculate these numbers? We already know how to do 3 of them…. Suppose we have this number set (already in order) {10, 20, 30, 40, 50, 60, 70, 80, 90} That is our median…..Now let’s find the smallest and biggest numbers….. To find our quartiles, find the medians between the green and red numbers….

10, 20, 30, 40 60, 70, 80, 90 Minimum: 10 Lower Quartile: 25 Median: 50 Upper Quartile: 75 Maximum: 90

Graphing it Minimum: 10 Lower Quartile: 25 Median: 50 Upper Quartile: 75 Maximum: 90 This box is known as the IQR (Interquartile range). 75– 25= 50 IQR = UQ – LQ

Outliers Sometimes we have data that is very different from the rest. We can calculate outliers by doing the following rule 1.5 * IQR If it is lower than LQ – 1.5IQR OR Higher than UP + 1.5IQR It is considered an outlier

Graphing it IQR = IQR = 1.5*50 = 75 Go 75 to the left of LQ Go 75 to the right of UQ ARE ANY POINTS OUTSIDE OF THE BARRIERs?? NO OUTLIERS!!!

Mr. Martin is one of the best cow tippers in all of Germany. He can really moooove it! Mr. Martin joined a German league to practice. Here is the distribution of number of cows tipped in the past mooooonth (okay that one was bad) by all the members Find me the 5 Number Summary: Min: 39 LQ: 46 Med : 55 UQ: 62.5 Max: 78

Mr. Martin joined a German league to practice. Here is the distribution of number of cows tipped in the past mooooonth (okay that one was bad) by all the members Min: 39 Q1: 46 Med : 55 Q3: 62.5 Max: 78 We now want to see if there are outliers. We do “1.5 * IQR”. Remember that IQR is UQ-LW = 16.5 Now multiply by 1.5

We now want to “extend” our LQ and UQ to make “outlier barriers.” If any point is OUTside of these barriers, they are an OUTlier. First, subtract our 1.5IQR from LQ to extend our left barrier. LQ – (1.5 * IQR) = = Next, add our 1.5IQR to our UQ to extend our right barrier. UQ + (1.5 * IQR) = = Notice how none of the points (more notably the min and max) are INSIDE the barriers? There are NO OUTLIERS!!!!!

Classwork 13.7g pg.886 #1-2 (EC) 13.8 pg #2-24 even 13.8g pg.893 #1-2 (EC)