Boxplots Boxplots n Boxplot A graphical display of

Boxplots

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

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

Modified Boxplots STEP 1 Draw the box part of the boxplot as usual. n STEP 2 Compute IQR. (Q 3 -Q 1) n Q 1 Q 3

Modified Boxplots Compute 1. 5 IQR. n The inner fences are Q 1 – THE ANSWER FROM STEP ABOVE AND and Q 3 + ANSWER TO STEP ABOVE. n 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