The first data set is the following list:

We will use the GNRND4 program on the calcualtor to generate this same data.

Figure 1	We start the GNRND4 program and give it the two key values shown in Figure 1. Then we press to continue.
Figure 2	The same data that we have in the table above now appears in the the list shown by the program After looking at the list we press to have the program continue to its normal end.
Figure 3	We want to do a one variable analysis on this data. The command to do that is in the STAT menu. We press to move to that menu and to move to the CALC sub-menu shown in Figure 3. The command that we want is 1-Var Stats. It is the highlighted command so we can just press to select it.
Figure 4	This pastes the command onto the main screen. We press to have the calculator perform the command.
Figure 5	Here is the first set of computed results. We see that The mean of the values is approximately 26.24137931 The sum of the items is 761 The sum of the squares of the items is 20011 If the list holds the values in a sample that we have taken, then the standard deviation of that list is approximatly 1.214647874 If the list holds the values of a population, then the standard deviation of that list is approximately 1.193521952 There were 29 values in the original list. THe down arrow on the last line of information indicates that there are more values to display. We use the key to reveal those additional values.
Figure 6	In Figure 6 we still see the n=29 line, but now we see an additional 5 lines of information, namely, The minimum value found was 24 If we calculate quartile points, then the first quartile point, Q1, has the value 25.5. We note that this quartile point is not a value in the list. Rather, it is a value chosen so that 25% of the values in the list are less than this Q1 value. The median of the list is 26. In this case the median value, also known as Q2, is a value in our list. the third quartile point, Q3, has the value 27. Again this value happens to be a value in our list. We choose the third quartile value so that 75% of the original items in the list are less than this value. The maximum value found in the list was 28.
Figure 7	Although we just found all of these interesting values related to our original list of values, we would like to get a picture or two of the values, a picture that helps us see how these values are spread out and how thaey may be clustered. To do this we press to open the STAT PLOT menu shown in Figure 7. We note here that Plot1 is On and it is set to produce a histogram (since is shown), to use L1 as the source of values, and to assume that each value in L1 represents itself, i.e., it has a frequency of 1. This is what we want. If we had to make changes to match these settings then we could open the Plot1 widown and change settings there to match these. We just happen to be lucky to find that the calculator already has the settings that we want.
Figure 8	We can leave Figure 7 and move to this menu by pressing the key. We have seen this list many times before. We know that we want the 9th option, ZoomStat. Ratehr than moving down to highlight the action and then select it, we can just press the key to select that option. This will cause the calculator to examine the values in L1 and then to determine some appropriate values for the WINDOW settings, and finally to produce the histograam of the data based upon those settings.
Figure 9	Figure 9 shows this histogram.
Figure 10	Press to put the calcualtor into TRACE mode. From the display we can see that the first "class" of values has a lower limit of 24 and an upper limit of 24.666667. One immediate consequence of this is that we now know the class width is 2/3. Furthermore, thre were 3 values in the original list that fell into this class. Knowing, as we do, that all of the values in the original list were integers we can conclude that the values 26 appears three times in the list.
Figure 11	We use the to move the highlight to the next class. Here the class lower limit is that 24.666667 and the upper class limit is 25.333333. There are 4 values in this class. Again, for the values we know to be in our list that means that tehre were 4 entries of the value 25.
Figure 12	We use the to move the highlight to the next class. Here the class lower limit is that 25.333333 and the upper class limit is 26. The display shows that there are 0 values in this class. This seems strange in that we know, by examination, that the value 26 actually appears 10 times in the original list. The key to understanding why the calculator reports 0 entries in this column is to recall that we have agreed to have the lower limit be part of the class but to require any value in the class to be strictly less than the upper limit. The 10 entries of the value 26 are all equal to the upper limit (i.e., 26) but they are not strictly less than that upper limit. Therefore, the calculator reports 0 entries in this class. Looking ahead, the next class will have a lower limit of 26 and an upper limit of 26.666667. Our 10 instances of 26 will all fall into that class.
Figure 13	It would seem that a change in the WINDOW settings would improve the usefulness of the historgrm. We press to open the WINDOW settings screen. THe settings shown in Figure 13 correspond to the values determined by the calculator when we used the ZoomStat command between FIgures 8 and 9.
Figure 14	The values that we have enterd to change the display to that shown in Figure 14 will give us columns that are 1 unit wide with the column center being the integer values that appear in the original list. That way each column will correspond to a single integer value from our original list. Once we have made these changes we press to redraw the Histogram, this time using the new settings.
Figure 15	Here is the redrawn histogram. Note that tehre are five classes. These correspond to the five different values that appear in our list, 24, 25, 26, 27, and 28. (Remember that we knew the range of values from the output of the 1-Var Stats command shown in Figure 6.
Figure 16	Againm, we can move to TRACE mode by pressing teh key. We have done that and then used to move the highlight to the second class in Figure 16. Observe the lower and upper clas limits as well as the number of items in the class.
Figure 17	We move to the next class, the one that contains the value 26, and we are pleased to see that the calcultor reports that there were 10 such values in the original list.
Figure 18	An alternative to this kind of analysis is to use the COLLATE2 program. That program is designed to process even a long list of values, as long as there are just a small number of different values in the list. For Figure 18 we have started the COLLATE2 program and we have given it the location of our list of values. We will press to have the program continue.
Figure 19	The initial output of the program tells us that there were 29 values in the list but that there were only 5 different values. The approximate mean of the original values is 26.2414. The approximate standard deviation of the values, treated as a sample, is 1.2146, whereas, the approximate mean of the values, treated as a popultion, is 1.1935. We press to have the program continue.
Figure 20	The program goes on to display the five quartile points. In addition, COLLATE2 displays the mode value of the original data, in this case it is 26. The display output of COLLATE2 is not much different from that of the built-in 1-Var Stats command that we saw in Figures 5 and 6. One difference is that the 1-Var Stats command displays many more significant digits for the computed values. A second is that COLLATE2 provides the number of distinct values found as well as the mode of the data. A third difference is that COLLATE2 creates six other useful lists that we can inspect, as well as setting the StatEditor to display those lists.
Figure 21	We use to open the STAT menu. Then we use to select the highlighted Edit...
Figure 22	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, is associated with the value shown in the ITEM list. Thus, reading across the first data line in Figure 43, we see that the first ITEM is 24, that 3 of the values in L1 are 24's, and that those 3 values represent 0.10345 (i.e., 10.345%) of the combined 29 values. The following table gives the names and intended use of the lists produced by COLLATE2. List name Intended use for this List ITEM A distict value: a list, in ascending order, of the different values found in the original list ICNT Item Frequency: the number of times that the corresponding number in ITEM is found in the user specified list RFREQ Item Relative Frequency: the relative frequency of appearance of the corresponding number in ITEM within the original list. This is the value in ICNT divided by the number of values in the original list. CMCNT Item Cumulative Frequency: the sum of the item frequencies up to and including this item. CRFRQ Item Cumulative Relative Frequency: the sum of the item relative frequencies up to and including this item DPIE Degrees in a Pie Chart: the number of degrees that should be allocated in a pie chart to this item. This is just 360*ICNT/(total number of values).
Figure 23	We use to scroll over to see the other three lists produced by COLLATE2.

Thus far we have taken a list of values that we produced by GNRND4 in L₁ and we have looked at that list of values in a number of different ways. Using COLLATE2, as demonstrated above, gives us not only the displayed values of Figures 19 and 20, but also the six computed lists shown in Figures 21 and 22. Of those lists, the first two, ITEM and ICNT provide us with all the information that we need to reconstruct the original list, although not in the origianl order of values. Thus, from looking at ITEM and ICNT that we need three 24's, four 25's, ten 26's, seven 27's, and five 28's. This view of the values in a list, where we specify both each distinct value and its corresponding frequency, is a grouped data view. Our next task is to see how the calculator can deal with such grouped data. Fortunately, we already have an example of this in ITEM and ICNT.

Figure 24	First, we will return to the 1-Var Stats command. When we give that command by itself it automatically assumes that we want it to use the values in L1. However, we can actually specify not only the location of the data to use, but also the location of a corresponding list of frequencies for that list of values. In this case, we want to form the command 1-Var Stats LITEM, LICNT To start doing this we safely left Figure 24 via . Then we returned to the STAT menu via , moved to the CALC sub-menu via and selected the 1-Var Stats command by pressing . This pastes the command onto our main page.
Figure 25	We use to open the LIST menu and then we use to scroll down to the desired ITEM name. Now we press to select that name.
Figure 26	We have pasted the desired list name, LITEM, onto the command, and followed that by pressing the key to append the comma.
Figure 27	We use to return to the LIST menu, where we scroll down to the desired ICNT. Press to select that name.
Figure 28	This completes the command. We will ask the calculator to perform a 1-Var Stats command on data specified by the distinct values in LITEM and their corresponding frequency of appearance as given in LICNT. Now we press to get the calculator to actually do the task.
Figure 29	This first page of output is identical to that produced above, in Figure 5, as well it should be.
Figure 30	When we scroll down to see the values in Figure 30 we see that they are the same as those in Figure 6.

Figures 24 through 30 demonstrate the expanded use of the 1-Var Stats command. Let us do this again, but this time with some new data. We have been given the assignment of finding and displaying various attributes of the following data:

Figure 31	First, let us clear and set up the calculator. We use to open the memory meny, from which we choose the 4th option, ClearAllLists by pressing the key. Press to perform that action. The calculator responds with Done to indicate that it has removed all data from any lists that exist on the calcualtor. Then we move to the STAT menu via the key, and select the 5th option, SetUpEditor by pressing the key. Again, this pastes the command to the main screen where we press to perform the action. This will set the editor to display L1 through L6. Press to perform the action.
Figure 32	Open the editor via . We see that the desired lists are present and empty.
Figure 33	We start entering the data for our task. We will do this moving down the first column, pressing the after each value is entered.
Figure 34	Then, press to move to the L2 column and enter the appropriate values there. At this point our display looks just like the problem statement given in the table above.
Figure 35	We return to the STAT menu via the key. Then press to move to the CALC sub-menu and press to select 1-Var Stats.
Figure 36	This places the command on the main screen. Now, in our haste, we press to get our results.
Figure 37	The results are shown in Figure 37. Something is terribly wrong! For one thing, we know that we have many more that 6 values. In fact, we know that we have exactly six distinct values, one of which, 27, appears 9 times. What have we done wrong? The mistake is that we jsut issued the 1-Var Stats command. We never told the calculator to sue the frequencies that we carefully placed into L2. Before we correct this error, we will page down to see the rest of the output.
Figure 38	The 1-Var Stats command that we had the calculator perform produces all of this output. It is important to note that the calculator merely follwos our commands. It is up to us to verify that the results at least seem correct. In this case we know that we have made an error.
Figure 39	To produce the desired command, 1-Var Stats L1, L2 we press to recall our last command (this was 1-Var Stats) followed by . Finally, press to perform the command.
Figure 40	This is much better. We see results that are much more reasonable.
Figure 40a	Here we scroll down to see the rest of the sults produced by 1-Var Stats.
Figure 41	Now we would like to get a picture of this data. We will start with a histogram. To do this we check the STAT PLOTS menu by pressing . The result, on this calculator, is shown in Figure 41. We want to use Plot1 to generate our histogram, but the settings for that plot are not correct. Therefore, we open the Plot1 settings by pressing .
Figure 42	Here we have already used the cursor keys to move to the Type: selections and we have moved to the histogram choice, , and pressed to change that to . This gives us the correct Type: setting, but we still have a problem in that the Xlist: setting is not pointed to our data in L1.
Figure 43	We move to that setting, press and to get to the correct image in Figure 43. From that we press to do a ZoomStat which takes us immediately to the histogram in Figure 44.
Figure 44	This is an interesting histogram, but it might help us to see a bit more detail. Therefore, we move to TRACE mode via the key.
Figure 45	In TRACE mode we see that the first column represents all of the values that are 14 or more and less than 21.833333. In our data that is just the 2 instances of the value 14.
Figure 45a	Moving one column to the right, we see that there are 16 instances of values greater than or equal to 21.833333 and less than 29.666667. Looking back at the rel data we see that this class (column) represents the combined seven 22's and nine 27's.
Figure 46	Moving even further to the right we do see that there are no values in the class greater than or equal to 37.5 and less than 45.333333.
Figure 46a	The historgram that the calculator created using the WINDOW values that were set by the ZoomStatcommand is not particularly convenient. In particular, that histogram has 7 "classes" but only 5 of them show any data. This seems to be a little misleading in that we know that we have 6 distinct values in our data set. With a little planning and even a bit of experimentation, we expect that the values that we have placed into the WINDOW settings shown in Figure 46a will produce a slightly better graph.
Figure 46b	Press to see this new graph. Again, more details should help. Move to TRACE mode via .
Figure 46c	Now we see that there are 2 instances of values greater than or equal to 9 but less than 16.
Figure 46d	Moving to the right twice, that column represents the 9 values greater than or equal to 23 and less than 30. This histogram is a slight improvement in that we now have 6 classes (columns) that have data in them, corresponding to the 6 distinct values in our data. However, we are still missing the spread of the data because our class width is so large tht we do not see the breaks between most of the data.
Figure 46e	Here are new WINDOW settigns that make an attempt to give an even better picture of the original data. making the Xscl value be 2 will increase our number of classes but it will also show the separation of the distinct values that we do have.
Figure 46f	In this historgram we have a more accurate representation of the data and the spread of the data. THinking aboutt he changes that we made in the WINDOW settings, we might be tempted to return to those and change the Xscl value to be 1. That way we would have separate classes (columns) even if we had distinct data values such as 14 and 15. Using the settings of Figure 46e these would have been combined into the first class. However, the calculator has a limitation that it will not do a histogram if it has more than 47 classes. With a class width of 1 we would need more than that many classes.
Figure 47	We can try another type of plot, a Box-and-whisker plot, to look at this same data. We return to the Plot1 settings screen and change the Type: to . Then we go through the sequence to do the ZoomStat process and generate the image shown in Figure 48.
Figure 48	This plot gives us a feeling for the spread of the data, showing us the quartile points and giving us a good feeling about the "middle" of the data. Seeing the long whisker on the right raises a concern about just how extreme the rightmost, the highest, values are. Perhaps it would have been better for us to have chose a modified Box-andWhisker plot.
Figure 49	We return to the Plot1 settings and choose the icon for the modified Box-and-whisker plot, . Then we can return to the graph via .
Figure 50	With teh modified Box-and-whisker plot we see that we have at least one outlier at the right side of the plot. We could return to the information of Figure 40a to see that Q3=35 and Q1=22. This gives the IQR= Q3–Q1=13. If we take 1.5*IQR we get 1.5*13=19.5. Going 19.5 above Q3 puts the upper limit at 35+19.5=54.5. Thus, our two instances of 61 can be considered outliers.
Figure 51	Moving into TRACE mode, via , and then using the key to move to the right, we can highlight the point at the end of the right whisker. The calcualtor tells us that the value there is 53, our highest data value less than or equal to the upper limit that we found to be 54.5.
Figure 52	Moving to the right one more time, we see that the value of the outlier is 61, although this plot does not tell us that such a value has two instances in our data set.