Boxplots Lecture 17 Sec 5 3 3 Wed

Boxplots Lecture 17 Sec. 5. 3. 3 Wed, Feb 13, 2008

Boxplots n Boxplot – A graphical display of a five-number summary. ¨ Draw and label a scale representing the variable. ¨ Draw a box over the scale with its left and right ends at Q 1 and Q 3. ¨ Draw a vertical line through the box at the median. ¨ Draw a left tail (whisker) from the box to the minimum. ¨ Draw a right tail from the box to the maximum.

Example n Draw a boxplot of the sample 5, 20, 30, 45, 60, 80, 100, 140, 150, 200, 240.

Example 0 20 40 60 80 100 120 140 160 180 200 220 240

Example Min 0 Q 1 20 Med 40 60 80 Q 3 100 120 140 160 Max 180 200 220 240

Example Min 0 Max 20 40 60 80 100 120 140 160 180 200 220 240

Example Min 0 Max 20 40 60 80 100 120 140 160 180 200 220 240

Example Max 0 20 40 60 80 100 120 140 160 180 200 220 240

Example 0 20 40 60 80 100 120 140 160 180 200 220 240

Example 0 20 40 60 80 100 120 140 160 180 200 220 240

Boxplots and Shape What would a boxplot for a uniform distribution look like? n What would a boxplot for a symmetric distribution look like? n What would a boxplot for a right-skewed distribution look like? n

TI-83 – Boxplots n Press STAT PLOT. ¨ Select Plot 1 Turn Plot 1 On. n Select the Boxplot Type. n Specify list L 1. n n Press ZOOM. ¨ Select Zoom. Stat (#9) and press ENTER.

TI-83 – Boxplots n Press TRACE. ¨ Use the arrow keys to see the values of the minimum, Q 1, the median, Q 3, and the maximum.

Modified Boxplots n Modified boxplot – A boxplot in which the outliers are indicated.

Modified Boxplots n n n 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. Q 1 Q 3

Modified Boxplots n n n 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 Q 1 Q 3

Modified Boxplots n n n 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 IQR IQR Q 1 Q 3

Modified Boxplots n n n 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 IQR IQR Upper fence Lower fence Q 1 Q 3

Modified Boxplots Extend the whiskers from the box to the smallest and largest values that are within the inner fences. n Any values that are outside the inner fences should be drawn as individual dots. These dots represent outliers. n

Case Study 8 n 2007 Small Arms Study (p. 47) ¨ Find the five-number summary of the data. ¨ Draw a modified boxplot.

Box Plots n For an example of modified boxplots, see De. Paul University’s web page on retention.