Chapter 5 Stories Quantitative Data Tell

How far out is too far? >1.5 times IQR Outliers - Adding Fences to Box & Whisker Plots How far out is too far? >1.5 times IQR Consider the following data set: 1, 5, 6, 7, 8, 9, 10, 11, 12, 13, 24 Find Q1= 6 Q2 = 9 Q3= 12 IQR = 6 1.5 * IQR = 9

Construct the Box and Whisker Plot for: 1, 5, 6, 7, 8, 9, 10, 11, 12, 13, 24 Q1= 6 Q2 = 9 Q3= 12 IQR = 6 1.5IQR = 9 That outlier sort of makes the plot look weird

Create Fences Lower Fence at Q1 - 1.5IQR Upper Fence at Q3 + 1.5IQR Note: Fences are not typically drawn on the Box & Whisker Plot. Simply connect the whisker from the box to the furthest dot within the fence. The outliers are shown as dots, but not connected.

Q1 - 1.5IQR = 6 - 9 = -3 (not on our plot) and Create fences at (we will use a light dotted line for 
illustration) 1, 5, 6, 7, 8, 9, 10, 11, 12, 13, 24 Q1 - 1.5IQR = 6 - 9 = -3 (not on our plot) and Q3 + 1.5IQR = 12 + 9 = 21 (is on our plot) Q1= 6 Q2 = 9 Q3= 12 IQR = 6 1.5IQR = 9 Draw a whisker to the furthest point that 
falls within the fence. Then use dots at outliers

So the final Box and Whisker plot for 1, 5, 6, 7, 8, 9, 10, 11, 12, 13, 24 would look like Q1= 6 Q2 = 9 Q3= 12 IQR = 6 1.5IQR = 9

Consider the following data set: 21, 23, 24, 25, 29, 33, 49 Find Outliers - Adding Fences to Box & Whisker Plots Consider the following data set: 21,  23,  24,  25,   29,  33,  49 Find Q1= 23 Q3= 33 IQR = 10 1.5 * IQR = 15

Construct the Box and Whisker Plot for: 21,  23,  24,  25,   29,  33,  49 Q1= 23 Q3= 33 IQR = 10 1.5 * IQR = 15 That outlier sort of makes the plot look weird

Q1 - 1.5IQR = 23 - 15 = 8 (not on our plot) and Create fences at (we will use a light dotted line for illustration) 21,  23,  24,  25,   29,  33,  49 Q1 - 1.5IQR = 23 - 15 = 8 (not on our plot) and Q3 + 1.5IQR = 33 +15 = 48 (is on our plot) Draw a whisker to the furthest point that falls within the fence. In this case, the point is 33. Then use dots at outliers

So the final Box and Whisker Plot for 21,  23,  24,  25,   29,  33,  49 would be:

Note: Can you find the mistake in this video? Comparing Histograms Note: Can you find the mistake in this video? Video http://tinyurl.com/otap-wando-compare-histograms

Would you want sandwich A or sandwich B? Why? 40 students were asked to taste two different chicken sandwiches. The students were asked to score the sandwiches, with 1 being awful and 6 being great. The charts show the scores for each sandwich. A B Would you want sandwich A or sandwich B? Why?

Sandwich A has a symmetric graph. The mean and median are 3.5 B Sandwich A has a symmetric graph. The mean and median are 3.5 Sandwich B requires some work Count in 20 and 21 the median is 4 Calculate the mean: (7*1) + (7*2)+(5*3)+(9*4)+(4*5)+(8*6) = 3.5 40

Now Consider the Boxplot for each Sandwich Did you know Boxplots could be Vertical?

Practice Matching Histograms and Boxplots Online Activity http://higheredbcs.wiley.com/legacy/college/mann/0470444665/applets/applet_01_v4.html

Back-to-Back Stem and Leaf Plots Double the Fun

Parallel Box Plots (y-axis must be the same) Video