Measuring Variation Boxplots Lecture 17 Sec 5 3

Measuring Variation – Boxplots Lecture 17 Sec. 5. 3. 3 Tue, Oct 3, 2006

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

Example n Draw a boxplot of the sample 5, 20, 30, 45, 60, 80, 100, 140, 175, 200, 240.

Example Draw a boxplot of the sample 5, 20, 30, 45, 60, 80, 100, 140, 175, 200, 240. n Recall that n Min = 5 n Q 1 = 37. 5 n Med = 80 n Q 3 = 157. 5 n Max = 240 n

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

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

Example Min 0 Med 20 40 60 80 Max 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. n Select Plot 1 n n Press WINDOW. n n Set min. X and max. X appropriately. Or press ZOOM. n n Turn Plot 1 On. Select the Boxplot Type. Specify list L 1. Select Zoom. Stat (#9) and press ENTER. Press GRAPH.

TI-83 – Boxplots n Press TRACE. n 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 Draw the box part of the boxplot as usual. n Compute STEP = 1. 5 IQR. n The inner fences are at Q 1 – STEP and Q 3 + STEP. n Q 1 Q 3

Modified Boxplots Draw the box part of the boxplot as usual. n Compute STEP = 1. 5 IQR. n The inner fences are at Q 1 – STEP and Q 3 + STEP. n IQR Q 1 Q 3

Modified Boxplots Draw the box part of the boxplot as usual. n Compute STEP = 1. 5 IQR. n The inner fences are at Q 1 – STEP and Q 3 + STEP. n 1. 5 IQR IQR Q 1 Q 3

Modified Boxplots Draw the box part of the boxplot as usual. n Compute STEP = 1. 5 IQR. n The inner fences are at Q 1 – STEP and Q 3 + STEP. n 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 Draw as individual dots any values that are outside the inner fences. These dots represent outliers. n

Example n Draw a modified boxplot of the sample 10, 15, 40, 42, 46, 49, 54, 58, 75, 84.

TI-83 – Modified Boxplots n 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. n n It looks like a boxplot with a couple of extra dots. Use the TI-83 to find a modified boxplot of the sample data 10, 15, 40, 42, 46, 49, 54, 58, 75, 84.

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