To demonstrate these steps we need to start with some data. We will use the GNRND4 program on the calcualtor to generate this data.

Figure 1	Before we do anything we will make sure that the calculator is cleared of any old data that happened to be on it already. By using the keys we open the window shown in Figure 1. From this list we select the fourth item by pressing the key.
Figure 2	This pastes the ClrAllLists command onto the main screen. We press teh key to perform the function. This will empty any list that is on the calculator.
Figure 3	Next we press to open the STAT menu shown in FIgure 3. From this list we choose the fifth item, SetUpEditor by pressing the key.
Figure 4	This pastes the command SetUpEditor onto the main screen. We press the key to perform that command. This will make sure that the editor is set to display the six built-in lists starting with L1.
Figure 5	Once the calculator is cleared and set up we start the GNRND4 program. (Note that this page was created using version 1.1 of that program.) We provide the key values to the program. Note that the second key in this case is quite long. It is so long that it extends to a second line. You will not get the correct results if you omit the finl two 0's in 500515300200. Then we press to have the program continue. The program will give a few intermediate screens before it finally displays the list that it generated, as shown in Figure 6.
Figure 6	Here we see the start of the list of values. We can use the key to scroll over to see the rest of the values in the list.
Figure 7	After reviewing all the numbers, we press to end the program.

We will generate the same list of values here. As noted in Figure 5, we generated the list of data on the calculator using GNRND4 with Key 1=1125735009 and Key 2=500515300200. That list, shown in Figures 6 and 7, has the same numbers that appear in the following table:

Figure 8	Continuing with the calculator, we press to open the STAT menu, then use the key to move to the CALC sub-menu shown in Figure 8. The command that we want is the first one, 1-Var Stats. We press to select that command and paste it to the main screen.
Figure 9	The 1-Var Stats command, when given by itself, will do an analysis of the values in L1. That is exactly where the GNRND4 program put our numbers. Thus, we are ready to perform the command. To do that we press the key.
Figure 10	The calculator does the analysis and then provides 11 lines of output, the first six of which are immediately available on the screen. Here we see that the mean of the data is 37.21372549 to 10 significant digits. (There is little chance that we really need so many digits, but the calculator is happy to provide them anyway.) The next line, , provides us with the sum of all the values. We follow that with the line . This gives us the sum of the squares of all the values. The line displays the calculated sample standard deviation of the values in our list, while displays the population standard deviation of those values. Finally, this page indicates that the size of the sample or population is 51 items. THe down arrow to the left of the n=51 merely indicates that there are more values to display. We use the key to scroll down to see those values.
Figure 11	The remaining values are the five quartile points: Q0 the lowest value Minimum Value Q1 25% point First quartile point Q2 the middle value, 50%       Median Value Q3 75% point Third quartile point Q4 the hiighest value Maximum Value
Figure 12	A Box-and-whisker plot gives a graphic representation of the five quartile values noted above. To get that Box-and-whisker plot we return to the STAT PLOT menu via the keys. Here we see that Plot1 is On and that it is set for a histogram based on L1 with no list of the frequency of the individual items in the list. Clearly, to obtain a Box-and-whisker plot we need to make some changes to Plot1. Since that plot is already highlighted, press the to move to the Plot1 settings screen shown in Figure 13.
Figure 13	Figure 13 shows the Plot1 settings before we have made any changes to them. We want to change the Type: setting from histogram, shown selected as , to the Box-and-whisker icon, shown unselected as .
Figure 14	To make this selection we move the cursor to the desired spot, shown in Figure 14, and then press to actually make the selection. Once the selection is made the Box-and-whisker choice will appear as . [Note that the image shown here was captured before the ENTER key was pressed. We can see that because the histogram icon is still selected. After the ENTER key is pressed the histogram icon will change to .]
Figure 15	After we set the Type: to the , we can move directly to the ZOOM menu, and then move down the menu to the 9th option, ZoomStat. We then select that option. This will cause the calculator to examine the data associated with the Plots that are turned ON, to adjust, based on those values, the WINDOW settings, and then display the image, as shown in Figure 16.
Figure 16	The Box-and-whisker plot for our data is shown here. We recall the values that we saw above.   25.2   Q0 the lowest value Minimum Value   35.0   Q1 25% point First quartile point   36.5   Q2 the middle value, 50%       Median Value   41.0   Q3 75% point Third quartile point   50.0   Q4 the hiighest value Maximum Value The Box-and-whisker plot shows us the relationship between these values. It is easier to see, in the plot, that the middle two quartiles are in the middle of the range, that the second quartile is quite narrow, and that the first and fourth quartiles are wider than are the middle two.
Figure 17	As a small demonstration of another calculator capability, we can move into TRACE mode by pressing the key. The plot changes to highlight the median value on the chart and to display the actual value of the median and the bottom of the screen. We can use the cursor keys to move the highlight to other quartile points.
Figure 18	One of the concerns that we always face is that of identifying any outliers in the data. Our "rule" for doing this is to first compute an intra-quartile range (IQR) as the value of Q3–Q1, or in this case, 41–35=6. Then we take 1.5 times that value, (1.5)*6=9 and we use that value to set limits, one below Q1 and one above Q3. In this particular case that puts us at Q1–9=35–9=26 and Q3+9=41+9=50. These are the lower and upper limits, respectively. Any data values outside of those limits are considered outliers. For our data set we immediately know tat we have at least one such outlier because the minimum data value is 25.2 which is below the lower limit that we found, namely, 26. There is a modified Box-and-whisker plot that depicts the lower and upper limits. We return to the STATS PLOT menu, via , choose the Plot in which we will change our settings to that style. Once there we can press to select Plot1.
Figure 19	In the Plot1 screen we have moved the highlight to the icon and pressed . (Unfortunately, we cannot see directly that the modified Box-and-whisker icon has been selected because the screen was captured as the blinking cursor covered the icon. However, since no other Type: is selected we are sure that we have selected this one.)
Figure 20	Having made the selection we return, via . to the ZOOM menu. We could scroll down to our desired ZoomStat. However, at this point we have done this so often that we know it it the 9th option. Therefore, we will just press the key to select that option.
Figure 21	The display is now that of the modified Box-and-whiskerr plot. Note that the "whiskers" only extend to the ends of the lower limit (Q1–1.5*IQR) and the upper limit (Q3+1.5*IQR). Furthermore, the one outlier in our data set is identified by a mark beyond the "whisker".
Figure 22	It might be interesting to now view the same data with a historgram. To change our plot to such a histogram we first return to the STAT PLOT menu via . Then we move to the Plot1/B> settings via the key.
Figure 23	This capture of the Plot1 settings is after we have moved to the icon and pressed to select it and change it to the icon.
Figure 24	Use to return to the ZOOM menu. Use to select the ZoomStat action.
Figure 25	Here is the graph of the data.
Figure 26	Here we have pressed the column is highlighted and the range of that key to move to TRACE mode. The first column is highlighted and the range of that column along with the count of items in that range is given at the bottom of the screen.
Figure 27	We use the cursor keys to change the column selection. In Figure 27 we have moved the selection to the rightmost column. THe calculator chose the breakpoints for the columns. We may want to set up different breakpoints. To do this we press to open the WINDOW settings.
Figure 28	These were the values that the ZoomStat action derived from the data in L1. We can change any of these.
Figure 29	We will reorganize the chart by having the first column start at 25 and setting the column width to 5. That means, if we want the maximum value, 50, to be in a column, then we will need to have a final column tha tgoes from 50 to 55. Therefore, we want to set the Xmax value to 55.
Figure 30	Press to display the new histogram. There is an obvious problem with this histogram. the third column is off the screen. We cannot see the top of that column. We can move into TRACE mode to gather more information.
Figure 31	Figure 31 shows the calculator in TRACE mode and after we have used to move the highlight to the second column.
Figure 32	We use again to look at the third column. Here we note, at the bottom of the screen, that there we 24 items in the range for this column. If we glance back to Figure 29 we see that the Ymax value was left at 18.72, well below the 24 items in this column. We will need to change that Ymax setting.
Figure 33	We have made three changes here. We changed the column width to 4. THis will give us 7 columns. We have changed the max value to 53, corresponding to the 7 columns. And, we have changed the Ymax value to 25. This will accomodate the 24 items that we found earlier, but we should remember that by changing the column width we will probably change the number of items in each column.
Figure 34	Returning to the histogram by pressing we see the effect of the new settings. It would seem that we made a bigger adjustment to the Ymax value than we needed to do once we changed the column width.
Figure 35	Moving back into TRACE mode, via the key, we can see that there are 7 items in that first class (the first column). We could continue to move across the classes to get the count of items in each class. Alternatively, we could run the COLLATE3 program and do that and more.
Figure 36	Here we have started the COLLATE3 program. It asks for the location of the data. We respond with L1. Then press to have the program continue.
Figure 37	The program reads all the data and reports that the lowest value found was 25.2 and the highest was 50. Using its own "strange" algorithm, the program suggests a starting value for our first class should be 23.65. We, however, want our first class to start at 25. We enter that value and press to continue.
Figure 38	The program responds by suggesting a class (column) width of 3.1, but we want to use a class width of 4. We enter that value and press .
Figure 39	The output from the program gives us the same values that we got from 1-VAR STATS back in Figure 10 but this time those values have been rounded to 2 decimal places. The COLLATE3 program is still running at this point, but it is in a paused condition, waiting for us to press before it continues with its output.
Figure 40	Figure 40 has the rest of the output from the program. So far it does not look like there is much advantage to running COLLATE3. However, that program does much more than just produce the out we have seen. In particular, that program creates six lists of values and it sets the StatEditor to display those lists when the user chooses the Edit... option in the STAT nebu.
Figure 41	We press to open that menu and then to select the highlighted optin, Edit...
Figure 42	The StatEditor opens showing the values in three lists, along with the name of each list. The highlight is on the first item in the first list. The name and index of that item is shown at the bottom of the page along with the value that is in that indexed position of that list. Each row of data, i.e., each of the list items with a the same index number, represents attributes of the class associated with the given index. Thus, reading across the first data line in Figure 43, we see that the first class starts at 25, that 7 of the values in L1 fall into the first class, and that 0.13725 (i.e., 13.725%) of the values are in this first class. Because the second class has a LOW value of 29 we know that the first class is really values 25≤x<100. Remembering that each "row" across the various lists holds the attributes of a single "class" (i.e., grouping) of values in the original user specified list, the following table gives the names and intended use of the lists produced by COLLATE3. List name Intended use for this List LOW Class Lower Limit: the lowest allowed value in this class. Note that there is an extra entry in this list. That final entry gives the lower limit of what would be the next class if there were one. ICNT Class Frequency: the number of values found in the user specified list that are in this class RFREQ Class Relative Frequency: the relative frequency of the values that fall into this class. This is just the number of items in the class divided by the total number of items in the original user specified list. CMCNT Class Cumulative Frequency: the sum of the class frequencies up to and including this class. CRFRQ Class Cumulative Relative Frequency: the sum of the class relative frequencies up to and including this class DPIE Degrees in a Pie Chart: the number of degrees that should be allocated in a pie chart to this class. This is just 360*ICNT/(total number of items).
Figure 43	For FIgure 43 we have moved down the fist list to see that there is indeed an 8th entry representing the lower limit of an 8th class if there were an 8th class. Of course, this is also the upper limit of the 7th class. Again, note that the index of the class is displayed in the last line of the display.
Figure 44	For Figure 43 we have moved back to the top of the lists and moved to the right to see the values in the other three lists. Note here that the last item in the CMCNT list is 51, the number of items in the original list. Also, the last item in the CRFRQ list is 1 which should always be the case since the sum of all relative frequencies must be 1 representing 100% of the values.