Boxplots. Lecture 17 Section Robb T. Koether. Hampden-Sydney College. Wed, Feb 10, 2010
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1 Boxplots Lecture 17 Section Robb T. Koether Hampden-Sydney College Wed, Feb 10, 2010 Robb T. Koether (Hampden-Sydney College) Boxplots Wed, Feb 10, / 34
2 Outline 1 Boxplots TI-83 Boxplots 2 Modified Boxplots TI-83 Modified Boxplots 3 Assignment 4 Answers to Even-numbered Exercises Robb T. Koether (Hampden-Sydney College) Boxplots Wed, Feb 10, / 34
3 Outline 1 Boxplots TI-83 Boxplots 2 Modified Boxplots TI-83 Modified Boxplots 3 Assignment 4 Answers to Even-numbered Exercises Robb T. Koether (Hampden-Sydney College) Boxplots Wed, Feb 10, / 34
4 Boxplots Definition (Boxplot) A boxplot is a graphical display of a five-number summary. The interquartile range is represented by a rectangle over a vertical scale. The median is represented by a vertical line through the rectangle. The maximum and minimum are represented by tails or whiskers attached to the ends of the rectangle. Robb T. Koether (Hampden-Sydney College) Boxplots Wed, Feb 10, / 34
5 Example Example (Boxplot) Draw a boxplot of the sample 5, 20, 30, 45, 60, 80, 100, 140, 150, 200, 240. Robb T. Koether (Hampden-Sydney College) Boxplots Wed, Feb 10, / 34
6 Example Example (Boxplot) Robb T. Koether (Hampden-Sydney College) Boxplots Wed, Feb 10, / 34
7 Example Example (Boxplot) Min Q1 Med Q3 Max Robb T. Koether (Hampden-Sydney College) Boxplots Wed, Feb 10, / 34
8 Example Example (Boxplot) Min Max Robb T. Koether (Hampden-Sydney College) Boxplots Wed, Feb 10, / 34
9 Example Example (Boxplot) Min Max Robb T. Koether (Hampden-Sydney College) Boxplots Wed, Feb 10, / 34
10 Example Example (Boxplot) Robb T. Koether (Hampden-Sydney College) Boxplots Wed, Feb 10, / 34
11 Example Example (Boxplot) Robb T. Koether (Hampden-Sydney College) Boxplots Wed, Feb 10, / 34
12 Boxplots and Shape What would a boxplot for a uniform distribution look like? What would a boxplot for a symmetric distribution look like? What would a boxplot for a right-skewed distribution look like? Robb T. Koether (Hampden-Sydney College) Boxplots Wed, Feb 10, / 34
13 Outline 1 Boxplots TI-83 Boxplots 2 Modified Boxplots TI-83 Modified Boxplots 3 Assignment 4 Answers to Even-numbered Exercises Robb T. Koether (Hampden-Sydney College) Boxplots Wed, Feb 10, / 34
14 TI-83 - Boxplots TI-83 Boxplots Press STAT PLOT. Select Plot1 Turn Plot1 On. Under Type, select the boxplot icon (2nd row, 2nd icon). Specify list L 1. Press ZOOM. Select ZoomStat (#9) and press ENTER (or press 9). Robb T. Koether (Hampden-Sydney College) Boxplots Wed, Feb 10, / 34
15 TI-83 - Boxplots TI-83 Boxplots To get the five-number summary from the boxplot, Press TRACE. Use the arrow keys to see the values of the minimum, Q 1, the median, Q 3, and the maximum. Robb T. Koether (Hampden-Sydney College) Boxplots Wed, Feb 10, / 34
16 TI-83 - Boxplots Example (TI-83 Boxplots) Use the TI-83 to draw a boxplot of the rainfall data Robb T. Koether (Hampden-Sydney College) Boxplots Wed, Feb 10, / 34
17 Outline 1 Boxplots TI-83 Boxplots 2 Modified Boxplots TI-83 Modified Boxplots 3 Assignment 4 Answers to Even-numbered Exercises Robb T. Koether (Hampden-Sydney College) Boxplots Wed, Feb 10, / 34
18 Modified Boxplots Definition (Outlier) An outlier is any value that is more than 1.5 IQR below Q 1 or more than 1.5 IQR above Q 3. Definition (Extreme outlier) An extreme outlier is any value that is more than 3 IQR below Q 1 or more than 3 IQR above Q 3. Definition (Modified boxplot) A modified boxplot is a boxplot in which the outliers (and extreme outliers) are indicated by separate dots. Robb T. Koether (Hampden-Sydney College) Boxplots Wed, Feb 10, / 34
19 Modified Boxplots To draw a modified boxplot, Draw the box part of the boxplot as usual. Compute STEP = 1.5 IQR. The inner fences are at Q 1 STEP and Q 3 + STEP. Robb T. Koether (Hampden-Sydney College) Boxplots Wed, Feb 10, / 34
20 Modified Boxplots To draw a modified boxplot, Draw the box part of the boxplot as usual. Compute STEP = 1.5 IQR. The inner fences are at Q 1 STEP and Q 3 + STEP. IQR Robb T. Koether (Hampden-Sydney College) Boxplots Wed, Feb 10, / 34
21 Modified Boxplots To draw a modified boxplot, Draw the box part of the boxplot as usual. Compute STEP = 1.5 IQR. The inner fences are at Q 1 STEP and Q 3 + STEP. 1.5 x IQR IQR 1.5 x IQR Robb T. Koether (Hampden-Sydney College) Boxplots Wed, Feb 10, / 34
22 Modified Boxplots To draw a modified boxplot, Draw the box part of the boxplot as usual. Compute STEP = 1.5 IQR. The inner fences are at Q 1 STEP and Q 3 + STEP. 1.5 x IQR IQR 1.5 x IQR Lower (inner) fence Upper (inner) fence Robb T. Koether (Hampden-Sydney College) Boxplots Wed, Feb 10, / 34
23 Modified Boxplots Extend the whiskers from the box to the smallest and largest values that are within the inner fences. Any values that are outside the inner fences should be drawn as individual dots. These dots represent outliers. Robb T. Koether (Hampden-Sydney College) Boxplots Wed, Feb 10, / 34
24 Modified Boxplots Practice Draw a modified boxplot of the sample 9, 13, 38, 40, 42, 43, 46, 47, 49, 53, 55, 60, 84. Robb T. Koether (Hampden-Sydney College) Boxplots Wed, Feb 10, / 34
25 Outline 1 Boxplots TI-83 Boxplots 2 Modified Boxplots TI-83 Modified Boxplots 3 Assignment 4 Answers to Even-numbered Exercises Robb T. Koether (Hampden-Sydney College) Boxplots Wed, Feb 10, / 34
26 TI-83 - Modified Boxplots TI-83 Modified Boxplots Follow the same steps as for a regular boxplot, but for the Type, select the modified-boxplot icon, the first icon in the second row. It looks like a boxplot with a couple of extra dots. Robb T. Koether (Hampden-Sydney College) Boxplots Wed, Feb 10, / 34
27 TI-83 - Modified Boxplots Example TI-83 Modified Boxplots Use the TI-83 to draw a modified boxplot of the rainfall data Robb T. Koether (Hampden-Sydney College) Boxplots Wed, Feb 10, / 34
28 TI-83 - Modified Boxplots Practice Use the TI-83 to draw a modified boxplot of the sample data. 9, 13, 38, 40, 42, 43, 46, 47, 49, 53, 55, 60, 84. Robb T. Koether (Hampden-Sydney College) Boxplots Wed, Feb 10, / 34
29 Box Plots For an example of modified boxplots, see DePaul University s web page on retention. Robb T. Koether (Hampden-Sydney College) Boxplots Wed, Feb 10, / 34
30 Box Plots Robb T. Koether (Hampden-Sydney College) Boxplots Wed, Feb 10, / 34
31 Outline 1 Boxplots TI-83 Boxplots 2 Modified Boxplots TI-83 Modified Boxplots 3 Assignment 4 Answers to Even-numbered Exercises Robb T. Koether (Hampden-Sydney College) Boxplots Wed, Feb 10, / 34
32 Assignment Homework Read Section 5.3.3, pages Let s Do It! 5.8, 5.9, 5.10, Page 333, exercises 12, 13, 15, 19. Robb T. Koether (Hampden-Sydney College) Boxplots Wed, Feb 10, / 34
33 Outline 1 Boxplots TI-83 Boxplots 2 Modified Boxplots TI-83 Modified Boxplots 3 Assignment 4 Answers to Even-numbered Exercises Robb T. Koether (Hampden-Sydney College) Boxplots Wed, Feb 10, / 34
34 Answers to Even-numbered Exercises Page 333, Exercise (a) (b) It is more than 50%, but not more than 75%. (c) $37, 000 Robb T. Koether (Hampden-Sydney College) Boxplots Wed, Feb 10, / 34
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