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Measuring Variation – Boxplots. Lecture 19 Sec. 5.3.3 Tue, Feb 20, 2007. 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. - PowerPoint PPT Presentation
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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.