Statistics Boxplots https://www.123rf.com/photo_6622261_statistics-and-analysis-of-data-as-background.html.

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Presentation transcript:

Statistics Boxplots https://www.123rf.com/photo_6622261_statistics-and-analysis-of-data-as-background.html

Exploring Data We are using the descriptive statistics to summarize our sample (and, hopefully, our population) in just a few numbers

Exploring Data The “five-number summary” is: the min Q1 the median Q3 the max

Boxplots There is a graph statisticians use to show this summary: the box plot (or boxplot)

Boxplots The boxplot (a.k.a. box and whisker diagram) is a standardized way of displaying the distribution of data based on the five number summary: minimum, first quartile, median, third quartile, and maximum

Boxplots

BOXPLOTS IN-CLASS PROBLEM Daily high temperatures Feb 2008 for Fairbanks, Alaska: 14, 12, 17, 25, 10, -1, -8, -15, -7, 0, 5, 14, 18, 14, 16, 8, -15, -13, -17, -12, 0, 1, 9, 12, 14, 7, 6, 8 Create a Boxplot

What do we need for a Boxplot? BOXPLOTS IN-CLASS PROBLEM What do we need for a Boxplot?

BOXPLOTS IN-CLASS PROBLEM Daily high temperatures Feb 2008 for Fairbanks, Alaska: 14, 12, 17, 25, 10, -1, -8, -15, -7, 0, 5, 14, 18, 14, 16, 8, -15, -13, -17, -12, 0, 1, 9, 12, 14, 7, 6, 8 Find the 5-number summary

BOXPLOTS IN-CLASS PROBLEM Min = Q1 = Median = Q3 = Max =

BOXPLOTS IN-CLASS PROBLEM Min = -17 Q1 = -4 Median = 7.5 Q3 = 14 Max = 25 Notice they’re all in order at the bottom of your list! YAY!

Min = -17 Now for the box! Q1 = -4 Median = 7.5 Q3 = 14 Max = 25 BOXPLOTS IN-CLASS PROBLEM Min = -17 Now for the box! Q1 = -4 Median = 7.5 Q3 = 14 Max = 25 -24 -20 -16 -12 -8 -4 0 4 8 12 16 20 24

Min = -17 Q1 = -4 Median = 7.5 Q3 = 14 Max = 25 Min! BOXPLOTS IN-CLASS PROBLEM Min = -17 Q1 = -4 Median = 7.5 Q3 = 14 Max = 25 Min! -24 -20 -16 -12 -8 -4 0 4 8 12 16 20 24

Min = -17 Q1 = -4 Median = 7.5 Q3 = 14 Max = 25 Q1! BOXPLOTS IN-CLASS PROBLEM Min = -17 Q1 = -4 Median = 7.5 Q3 = 14 Max = 25 Q1! -24 -20 -16 -12 -8 -4 0 4 8 12 16 20 24

Min = -17 Q1 = -4 Median = 7.5 Q3 = 14 Max = 25 Median! BOXPLOTS IN-CLASS PROBLEM Min = -17 Q1 = -4 Median = 7.5 Q3 = 14 Max = 25 Median! -24 -20 -16 -12 -8 -4 0 4 8 12 16 20 24

Min = -17 Q1 = -4 Median = 7.5 Q3 = 14 Max = 25 Q3! BOXPLOTS IN-CLASS PROBLEM Min = -17 Q1 = -4 Median = 7.5 Q3 = 14 Max = 25 Q3! -24 -20 -16 -12 -8 -4 0 4 8 12 16 20 24

Min = -17 Q1 = -4 Median = 7.5 Q3 = 14 Max = 25 Max! BOXPLOTS IN-CLASS PROBLEM Min = -17 Q1 = -4 Median = 7.5 Q3 = 14 Max = 25 Max! -24 -20 -16 -12 -8 -4 0 4 8 12 16 20 24

Min = -17 Q1 = -4 Median = 7.5 Q3 = 14 Max = 25 Box! BOXPLOTS IN-CLASS PROBLEM Min = -17 Q1 = -4 Median = 7.5 Q3 = 14 Max = 25 Box! -24 -20 -16 -12 -8 -4 0 4 8 12 16 20 24

Min = -17 Q1 = -4 Median = 7.5 Q3 = 14 Max = 25 Whiskers! BOXPLOTS IN-CLASS PROBLEM Min = -17 Q1 = -4 Median = 7.5 Q3 = 14 Max = 25 Whiskers! -24 -20 -16 -12 -8 -4 0 4 8 12 16 20 24

Questions?

Outliers Because the min and max may be outliers, a variation on the boxplot includes “fences” to show where most of the data occurs

Outliers Lower fence: Q1 - 1.5 * IQR Upper fence: Q3 + 1.5 * IQR

Min = -17 What is the IQR? Q1 = -4 Median = 7.5 Q3 = 14 Max = 25 OUTLIERS IN-CLASS PROBLEM Min = -17 What is the IQR? Q1 = -4 Median = 7.5 Q3 = 14 Max = 25 -24 -20 -16 -12 -8 -4 0 4 8 12 16 20 24

OUTLIERS IN-CLASS PROBLEM Min = -17 IQR=14-(-4)=18 Q1 = -4 What is the Median = 7.5 lower fence? Q3 = 14 Max = 25 -24 -20 -16 -12 -8 -4 0 4 8 12 16 20 24

OUTLIERS IN-CLASS PROBLEM Min = -17 IQR=14-(-4)=18 Q1 = -4 Lower fence = Median = 7.5 Q1-1.5*IQR Q3 = 14 -4-1.5(18) Max = 25 = -31 -24 -20 -16 -12 -8 -4 0 4 8 12 16 20 24

OUTLIERS IN-CLASS PROBLEM Min = -17 IQR=14-(-4)=18 Q1 = -4 Lower fence=-31 Median = 7.5 What is the Q3 = 14 upper fence? Max = 25 -24 -20 -16 -12 -8 -4 0 4 8 12 16 20 24

OUTLIERS IN-CLASS PROBLEM Min = -17 IQR=14-(-4)=18 Q1 = -4 Lower fence=-31 Median = 7.5 Upper fence= Q3 = 14 Q3+1.5*IQR Max = 25 14+1.5(18)=41 -24 -20 -16 -12 -8 -4 0 4 8 12 16 20 24

OUTLIERS IN-CLASS PROBLEM Min = -17 IQR=14-(-4)=18 Q1 = -4 Lower fence=-31 Median = 7.5 Upper fence=41 Q3 = 14 So, do we have Max = 25 any outliers? -24 -20 -16 -12 -8 -4 0 4 8 12 16 20 24

OUTLIERS IN-CLASS PROBLEM Min = -17 IQR=14-(-4)=18 Q1 = -4 Lower fence=-31 Median = 7.5 Upper fence=41 Q3 = 14 Max and Min are Max = 25 inside the fence! -24 -20 -16 -12 -8 -4 0 4 8 12 16 20 24

Outliers How outliers are shown in a boxplot

Types of Boxplots

Questions?

Boxplots Boxplots are typically used to compare different groups

Data Summary Table from a Ball-bouncing Experiment Boxplots Data Summary Table from a Ball-bouncing Experiment Super Ball Wiffle Golf Splash SpongyBall Minimum 66 38 70 7 44 Q1 71 45 75 14 58 Median 76 48 78 16.5 60 Q3 50 80 23 62 Maximum 91 90 28 67

Boxplots

Boxplots

BOXPLOTS IN-CLASS PROBLEM What differences?

Boxplots Unfortunately it is almost impossible to get a true boxplot using Excel

Boxplots Unfortunately it is almost impossible to get a true boxplot using Excel (there are several YouTube videos showing how to get one…

Boxplots Unfortunately it is almost impossible to get a true boxplot using Excel (there are several YouTube videos showing how to get one… but they are all wrong…)

Questions?