Lecture 19Sec. 5.3.3Tue, Feb 20, 2007

Measuring Variation – Boxplots

Boxplots

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 Q1 and Q3. 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

Draw a boxplot of the sample

5, 20, 30, 45, 60, 80, 100, 140, 175, 200, 240.

Example

0 20 60 80 100 120 140 160 180 200 220 24040

Example

0 20 60 80 100 120 140 160 180 200 220 24040

Min Q1 Med Q3 Max

Example

0 20 60 80 100 120 140 160 180 200 220 24040

Min Med Max

Example

0 20 60 80 100 120 140 160 180 200 220 24040

Min Max

Example

0 20 60 80 100 120 140 160 180 200 220 24040

Max

Example

0 20 60 80 100 120 140 160 180 200 220 24040

Example

0 20 60 80 100 120 140 160 180 200 220 24040

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?

TI-83 – Boxplots

Press STAT PLOT. Select Plot1

Turn Plot 1 On. Select the Boxplot Type. Specify list L1.

Press WINDOW. Set minX and maxX appropriately.

Or press ZOOM. Select ZoomStat (#9) and press ENTER.

Press GRAPH.

TI-83 – Boxplots

Press TRACE.Use the arrow keys to see the values of the

minimum, Q1, the median, Q3, and the maximum.

Modified Boxplots

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

Modified Boxplots

Q1 Q3

Draw the box part of the boxplot as usual. Compute STEP = 1.5 IQR. The inner fences are at Q1 – STEP and Q3 +

STEP.

Modified Boxplots

Q1 Q3

IQR

Draw the box part of the boxplot as usual. Compute STEP = 1.5 IQR. The inner fences are at Q1 – STEP and Q3 +

STEP.

Modified Boxplots

Q1 Q3

IQR 1.5 IQR1.5 IQR

Draw the box part of the boxplot as usual. Compute STEP = 1.5 IQR. The inner fences are at Q1 – STEP and Q3 +

STEP.

Modified Boxplots

Q1 Q3

IQR 1.5 IQR1.5 IQR

Lowerfence

Upperfence

Draw the box part of the boxplot as usual. Compute STEP = 1.5 IQR. The inner fences are at Q1 – STEP and Q3 +

STEP.

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.

Example

Draw a modified boxplot of the sample

9, 12, 39, 40, 42, 46, 49, 54, 58, 60, 84.

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.

Use the TI-83 to find a modified boxplot of the sample data

9, 12, 39, 40, 42, 46, 49, 54, 58, 75, 84.

Example: DePaul University

For an example of modified boxplots, see DePaul University’s web page on retention.