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Modified Boxplots

Brief Instructions

Press STAT and ENTER. Enter the list of numbers under L1. Press Y= and clear the right-hand sides of all equations. Press 2ND, Y= and ENTER. Select On and next to Type, choose the icon in the lower left corner. Next to Xlist, L1 should be entered, and next to Freq, 1 should be entered. If you have a frequency distribution with the midpoints in L1 and the frequencies in L2, then you would put L2 next to Freq. Any symbol may be selected next to Mark. This will be the symbol used to identify outliers.

Press ZOOM, choose ZoomStat and press ENTER. A modified boxplot should appear. To find the locations of whisker tips, box ends, the median and possible outliers, press TRACE. Using the left and right arrow keys, you can move the cursor anywhere in the boxplot and out to the outliers. The values of cursor locations are shown below the plot. Use these values to setup a numeric scale and recreate the modified boxplot on paper.

Detailed Instructions

To demonstrate this procedure, we will use the following list of numbers:

70, 71, 74, 75, 76, 79, 92, 77, 78, 72

Press STAT and ENTER, and enter the numbers in the column under L1. For information on how to do this, see the webpage entitled Entering Data.

If you have not created a statistics plot with the calculator recently, press Y= and clear everything to the right of Y1 =, Y2 =, Y3 = , etc. If you do not clear the right hand sides of these equations, your box plot may not appear at all or you may have spurious lines and curves cutting through your box plot. To clear the right side of an equation, just put the cursor on the right side and press the CLEAR button. You should use the down arrow button to make sure that Y8 =, Y9 = and Y0 = are also clear.

Next press the 2ND, Y= and ENTER buttons. This will bring up the plots screen with Plot1 highlighted. To make a selection on this screen, highlight the option you want and press the ENTER button.

Make sure the plot is On as opposed to Off. Next to Type, choose the icon in the lower left corner which looks like a box plot without a middle bar and has two dots off to the right; DO NOT choose the icon that looks like an unmodified box plot.

Next to Xlist, L1 should be entered, and next to Freq, 1 should be entered. If you had entered a frequency distribution with the numbers in L1 and the frequencies in L2, then you would put L2 next to Freq.

Mark is the symbol used to identify outliers. The default setting is fine, though any of the symbols could be used.

When your settings on the plot screen are correct, press the ZOOM button and choose the ZoomStat option. You will have to use the down-arrow button to find this option. Then press ENTER. A modified boxplot should appear on the screen. To see where the whisker tips, the box ends, the median and possible outliers are located, press the TRACE button. By using the left and right arrow buttons, you can move the cursor from the left whisker tip through the box to the right whisker tip and out to the possible outliers, and the values of these points will be shown at the bottom of the screen.

Moving the cursor from left to right through the modified box plot for the list of numbers given above, the calculator gives the values as minX = 70, Q1 =72, Med = 75.5, Q3 = 78, X = 79, maxX = 92. The plain X in this case is the new maximum, since it is at the right whisker tip. The other numbers are the five number summary of the original data set.

To create the modified box plot on your own paper, you just need to set up a uniform number scale which extends from 70 at the minimum to 92 at the maximum, but not much farther. You would place vertical lines of the same length above each of the quartiles and the minimum and new maximum. Connect the middle three lines across the top and bottom to make the box. Draw a horizontal line connecting the minimum to the first quartile, and another horizontal line connecting the new maximum to the third quartile. Finally, put an asterisk at 92 to mark the outlier.

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