**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 *Y**1**
=*, *Y**2**
=*, *Y**3**
= ,* 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 *Y**8** =*, *Y**9** =* and *Y**0** =* 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*, *L**1* 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 *L**2* 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.