Box Plots and Outliers
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Transcript of Box Plots and Outliers
![Page 1: Box Plots and Outliers](https://reader035.fdocuments.net/reader035/viewer/2022062720/5681351d550346895d9c79f7/html5/thumbnails/1.jpg)
Box Plots and Outliers
![Page 2: Box Plots and Outliers](https://reader035.fdocuments.net/reader035/viewer/2022062720/5681351d550346895d9c79f7/html5/thumbnails/2.jpg)
Box Plot
We need 5 numbers, called the 5 number summary:
1. minimum value
2. Q1
3. median
4. Q3
5. maximum value
![Page 3: Box Plots and Outliers](https://reader035.fdocuments.net/reader035/viewer/2022062720/5681351d550346895d9c79f7/html5/thumbnails/3.jpg)
Harry Potter Data
The 5 number summary is:
Minimum 70.9
Q1 78.9
Median 81.35
Q3 84.45
Maximum 86.2
![Page 4: Box Plots and Outliers](https://reader035.fdocuments.net/reader035/viewer/2022062720/5681351d550346895d9c79f7/html5/thumbnails/4.jpg)
Drawing the plot free hand
• Use a scaled line to draw the box plot• Approximate locations of the values.
• We say this is SKEWED LEFT since the longer tail is on the left side.
![Page 5: Box Plots and Outliers](https://reader035.fdocuments.net/reader035/viewer/2022062720/5681351d550346895d9c79f7/html5/thumbnails/5.jpg)
Using the TI
• Put the data into the list
• Press y = ; make sure that there is nothing in the 10 equations
![Page 6: Box Plots and Outliers](https://reader035.fdocuments.net/reader035/viewer/2022062720/5681351d550346895d9c79f7/html5/thumbnails/6.jpg)
• Press 2nd key, y =
• There are 3 statistical plots.
• Press #1
![Page 7: Box Plots and Outliers](https://reader035.fdocuments.net/reader035/viewer/2022062720/5681351d550346895d9c79f7/html5/thumbnails/7.jpg)
• Turn the plot ON
• Select the 2nd box plot
• Make the x list L1
![Page 8: Box Plots and Outliers](https://reader035.fdocuments.net/reader035/viewer/2022062720/5681351d550346895d9c79f7/html5/thumbnails/8.jpg)
• Press Zoom
• Press Enter on #9
![Page 9: Box Plots and Outliers](https://reader035.fdocuments.net/reader035/viewer/2022062720/5681351d550346895d9c79f7/html5/thumbnails/9.jpg)
• The Box plot will appear
![Page 10: Box Plots and Outliers](https://reader035.fdocuments.net/reader035/viewer/2022062720/5681351d550346895d9c79f7/html5/thumbnails/10.jpg)
• Press TRACE to see values; use right or left arrow keys to move around.
![Page 11: Box Plots and Outliers](https://reader035.fdocuments.net/reader035/viewer/2022062720/5681351d550346895d9c79f7/html5/thumbnails/11.jpg)
Inter-quartile Range
• The inter-quartile range (IQR) is the value of Q3 – Q1
![Page 12: Box Plots and Outliers](https://reader035.fdocuments.net/reader035/viewer/2022062720/5681351d550346895d9c79f7/html5/thumbnails/12.jpg)
Outliers
• An outlier is an unusual score, relative to the data set. It will influence the mean and the standard deviation.
• A data set might have no outliers, one outlier, or several outliers.
• Two types: Mild and Extreme
![Page 13: Box Plots and Outliers](https://reader035.fdocuments.net/reader035/viewer/2022062720/5681351d550346895d9c79f7/html5/thumbnails/13.jpg)
Mild Outliers
Look for data values (x) that are either:
1.
2.
Q1 - 3 IQR x <Q1-1.5 IQR
Q3 + 1.5 IQR < x Q3 + 3 IQR
![Page 14: Box Plots and Outliers](https://reader035.fdocuments.net/reader035/viewer/2022062720/5681351d550346895d9c79f7/html5/thumbnails/14.jpg)
Extreme Outliers
Look for values that are either:
1.
2.
x < Q1 - 3 IQR
x > Q3 + 3 IQR
![Page 15: Box Plots and Outliers](https://reader035.fdocuments.net/reader035/viewer/2022062720/5681351d550346895d9c79f7/html5/thumbnails/15.jpg)
Harry Potter data - checking
![Page 16: Box Plots and Outliers](https://reader035.fdocuments.net/reader035/viewer/2022062720/5681351d550346895d9c79f7/html5/thumbnails/16.jpg)
Example: Ages of actresses at the time they first won the Oscar
50 44 35 80 26 28 41
21 61 38 49 33 74 30
33 41 31 35 41 42 37
26 34 34 35 26 61 60
34 24 30 37 31 27 39
34 26 25 33
![Page 17: Box Plots and Outliers](https://reader035.fdocuments.net/reader035/viewer/2022062720/5681351d550346895d9c79f7/html5/thumbnails/17.jpg)
5 number summary for actresses
• Min = 21
• Q1 = 30
• Med = 34
• Q3 = 41
• Max = 80
![Page 18: Box Plots and Outliers](https://reader035.fdocuments.net/reader035/viewer/2022062720/5681351d550346895d9c79f7/html5/thumbnails/18.jpg)
Actresses
• Check for outliers. Identify type.
![Page 19: Box Plots and Outliers](https://reader035.fdocuments.net/reader035/viewer/2022062720/5681351d550346895d9c79f7/html5/thumbnails/19.jpg)
Box plot with outliers
• When we select the 1st box plot on the TI, it allows us to see outliers. Select the mark that is visible for you.
![Page 20: Box Plots and Outliers](https://reader035.fdocuments.net/reader035/viewer/2022062720/5681351d550346895d9c79f7/html5/thumbnails/20.jpg)
• Zoom #9 results in:
![Page 21: Box Plots and Outliers](https://reader035.fdocuments.net/reader035/viewer/2022062720/5681351d550346895d9c79f7/html5/thumbnails/21.jpg)
• Trace and go to the right twice.
• The 50 is the last data value that is not an outlier.
![Page 22: Box Plots and Outliers](https://reader035.fdocuments.net/reader035/viewer/2022062720/5681351d550346895d9c79f7/html5/thumbnails/22.jpg)
Comparison of Boxplots and histograms