Basic Statistics on the TI-86

The first problem to look at is to calculate basic statistics, mean and standard deviation, for the following set of data: 2290, 2281, 2237, 2309, 2442, 2118, 1941, 1942, 1866, 2028, and 1865. These are the reported fall enrollments from 1987 through 1997 at Alpena Community College. We will do this work on the TI-86. After doing the initial problem we will do the same analysis for similar data from Bay de Noc Community College.

Figure 1 We start by entering the data values as elements of a list. We use the to open the List Menu, shown at the bottom of Figure 1. Then the key to generate the left brace, followed by the eleven values separated by commas (using the key, and closing the list with the right key to generate the right brace. The key generates the and shifts the calculator to alpha mode. We assign the list to ALP via the key sequence, and submit the command via . The calculator displays the start of the ALP list, using the ... to inidcate that more appears off the screen.
Figure 2 We can exit the List menu, via , and initiate the Stat menu via . We then open the OneVar submenu via , and then we press again to generate the OneVar text on the screen. We follow that with the name ALP by pressing . These keystrokes should result in a screen such as the one shown in FIngure 2.
Figure 3 pressing the key instructs the TI-86 to perform the basic one variable statistics and to display the results. The first portion of those results are given in Figure 3. The mean, x-bar, is given as 2119.90909, along with the sum of the values, and the sum of the squares of the values. Finally, on Figure 3, the TI-86 displays the estimate of the underlying population standard deviation, based ont he eleven item sample in the list. The TI-86 calcualtes this value even though there is no such underlying population, and even though the eleven value list is the list of all the points in our population. We will just ignore the value.
Figure 4 Pressing the three times results in Figure 4. This shows more of the basic statistical values calculated by OneVar. Now we see x, the standard deviation of the values assuming the values are a population. In this case, x is given as 192.978781. We also note that there are 11 values (n=11) and that the smallest is 1865.
Figure 5 Another three keys produces Figure 5. Here we see that the first quartile point is 1941. Thus, 25% of the values in the list are below 1941. The median is 2118, so half the values are above and half are below this median value. And, the third quartile point is 2442, so 75% of the values are less than 2442.
Figure 6 One more shows the final basic statistic, the maximum value.
As a consequence of doing a statistical ananlysis, the TI-86 actually copies the list of values being used into the standard list xStat. In addition, the TI-86 sets the standard list fStat to hold the frequency of each corresponding value in xStat. We can observe this, and get a chance to see the list editor.

Figure 7 We get to Figure 7 by selecting the EDIT function from the top menu of Figure 6. The keys to use are . In Figure 7 we can see the first 6 items in the xStat and fStat lists. The yStat list has no values on this calculator at this time (although it may have residual values on yours, i.e., values left over from some earlier command).
Figure 8 We use the cursor keys to move around on the list edit screen. In this case we have used the to move to the name field at the top of the xStat list.
Figure 9 We can move three columns to the right by using the key three times, producing Figure 9. At this point we could type in a name of either an existing list or the name of a new list. If we enter an existing list name, then that list will be displayed and we can view or edit the list. We will take the shorter route to entering a name by using the NAMES sub-menu. We move from Figure 9 to Figure 10 by pressing
Figure 10 We wish to select the ALP list to edit. Therefore, we use the key to select the ALP sub-menu item, as shown in Figure 11.
Figure 11 Now all that is needed is the key to accept our choice.
Figure 12 In Figure 12 we can see that the ALP list is displayed in the editor. It would be easy to change the items in this list if we so desire. We are supposed to enter new values for the Bay de Noc item. It would be nice to use the editor to do this. However, let us find a way to do this without losing the ALP values.
Figure 13 First we exit the list editor, via . Then we open the List menu with the sequence and we use to open the NAMES sub menu. Now the key pastes ALP to the screen, which we follow by the to generate the command ALPBAY. Finally, the key accepts and performs the command. Figure 13 reflects the completed command.
Figure 14 Figure 14 shows us moving back to the list editor. We do this by the keys to select the fourth item, EDIT, from the top menu of Figure 13.
Figure 15 Again, we use the cursor keys to move up, and to the right , selecting the name field in the next open column. By using the key we select the NAMES sub-menu, arriving at Figure 15.
Figure 16 We want to edit the BAY list, so we move from Figure 15 by pressing the key to paste BAY to the screen, then to accept the command, and finally to move the list editor to the first item in the list. This is the status shown in Figure 16. Note that the value is both highlighted in the list column, and it is displayed just above the menu box.
Figure 17 The new value for item 1 is 2084. We type those characters and the screen updates as in Figure 17. Note that the original value is still highlighted in the edit column. The old value appears just above the menu box.
Figure 18 We press (or use the cursor down arrow) to accept the new value and highlight the next value for editting. Figure 18 reflects this condition.
Figure 19 Figure 19 shows the list after changing all six of the initial values.
Figure 20 Figure 20 demonstrates the screen scrolling as we move down one more row of the list editor. Note that the line above the menu box clearly indicates that we are looking at item 7 of the list.
Figure 21 Figure 21 shows the completely edited list.
Figure 22 Figure 21 reflects the situation if we move down one more item. Now the calculator is waiting for us to add another value to the BAY list. We have no more values to add, so we leave Figure 22 via the key.
Figure 23 THis returns us to the normal screen. Now we are ready to do the statistical alanlysis of the BAY data. We will need to form the OneVar BAY command.
Figure 24 We use the keys to open the Stat menu. selects CALC and opens the sub menu. selects the OneVar command. We complete the command via giving us Figure 24.
Figure 25 To accept the command in Figure 24, press . Again, the resulting statistics are displayed.
Figure 26 We can move down to see more of those statistics via the down arrow keys. However, it might help somewhat to close the menu lines so that we have more lines available on the screen. will close the menu lines. Then we use the to move down to see more of the values.
Figure 27 A final gives the last value.

Figure 1	We start by entering the data values as elements of a list. We use the to open the List Menu, shown at the bottom of Figure 1. Then the key to generate the left brace, followed by the eleven values separated by commas (using the key, and closing the list with the right key to generate the right brace. The key generates the and shifts the calculator to alpha mode. We assign the list to ALP via the key sequence, and submit the command via . The calculator displays the start of the ALP list, using the ... to inidcate that more appears off the screen.
Figure 2	We can exit the List menu, via , and initiate the Stat menu via . We then open the OneVar submenu via , and then we press again to generate the OneVar text on the screen. We follow that with the name ALP by pressing . These keystrokes should result in a screen such as the one shown in FIngure 2.
Figure 3	pressing the key instructs the TI-86 to perform the basic one variable statistics and to display the results. The first portion of those results are given in Figure 3. The mean, x-bar, is given as 2119.90909, along with the sum of the values, and the sum of the squares of the values. Finally, on Figure 3, the TI-86 displays the estimate of the underlying population standard deviation, based ont he eleven item sample in the list. The TI-86 calcualtes this value even though there is no such underlying population, and even though the eleven value list is the list of all the points in our population. We will just ignore the value.
Figure 4	Pressing the three times results in Figure 4. This shows more of the basic statistical values calculated by OneVar. Now we see x, the standard deviation of the values assuming the values are a population. In this case, x is given as 192.978781. We also note that there are 11 values (n=11) and that the smallest is 1865.
Figure 5	Another three keys produces Figure 5. Here we see that the first quartile point is 1941. Thus, 25% of the values in the list are below 1941. The median is 2118, so half the values are above and half are below this median value. And, the third quartile point is 2442, so 75% of the values are less than 2442.
Figure 6	One more shows the final basic statistic, the maximum value.

Figure 7	We get to Figure 7 by selecting the EDIT function from the top menu of Figure 6. The keys to use are . In Figure 7 we can see the first 6 items in the xStat and fStat lists. The yStat list has no values on this calculator at this time (although it may have residual values on yours, i.e., values left over from some earlier command).
Figure 8	We use the cursor keys to move around on the list edit screen. In this case we have used the to move to the name field at the top of the xStat list.
Figure 9	We can move three columns to the right by using the key three times, producing Figure 9. At this point we could type in a name of either an existing list or the name of a new list. If we enter an existing list name, then that list will be displayed and we can view or edit the list. We will take the shorter route to entering a name by using the NAMES sub-menu. We move from Figure 9 to Figure 10 by pressing
Figure 10	We wish to select the ALP list to edit. Therefore, we use the key to select the ALP sub-menu item, as shown in Figure 11.
Figure 11	Now all that is needed is the key to accept our choice.
Figure 12	In Figure 12 we can see that the ALP list is displayed in the editor. It would be easy to change the items in this list if we so desire. We are supposed to enter new values for the Bay de Noc item. It would be nice to use the editor to do this. However, let us find a way to do this without losing the ALP values.
Figure 13	First we exit the list editor, via . Then we open the List menu with the sequence and we use to open the NAMES sub menu. Now the key pastes ALP to the screen, which we follow by the to generate the command ALPBAY. Finally, the key accepts and performs the command. Figure 13 reflects the completed command.
Figure 14	Figure 14 shows us moving back to the list editor. We do this by the keys to select the fourth item, EDIT, from the top menu of Figure 13.
Figure 15	Again, we use the cursor keys to move up, and to the right , selecting the name field in the next open column. By using the key we select the NAMES sub-menu, arriving at Figure 15.
Figure 16	We want to edit the BAY list, so we move from Figure 15 by pressing the key to paste BAY to the screen, then to accept the command, and finally to move the list editor to the first item in the list. This is the status shown in Figure 16. Note that the value is both highlighted in the list column, and it is displayed just above the menu box.
Figure 17	The new value for item 1 is 2084. We type those characters and the screen updates as in Figure 17. Note that the original value is still highlighted in the edit column. The old value appears just above the menu box.
Figure 18	We press (or use the cursor down arrow) to accept the new value and highlight the next value for editting. Figure 18 reflects this condition.
Figure 19	Figure 19 shows the list after changing all six of the initial values.
Figure 20	Figure 20 demonstrates the screen scrolling as we move down one more row of the list editor. Note that the line above the menu box clearly indicates that we are looking at item 7 of the list.
Figure 21	Figure 21 shows the completely edited list.
Figure 22	Figure 21 reflects the situation if we move down one more item. Now the calculator is waiting for us to add another value to the BAY list. We have no more values to add, so we leave Figure 22 via the key.
Figure 23	THis returns us to the normal screen. Now we are ready to do the statistical alanlysis of the BAY data. We will need to form the OneVar BAY command.
Figure 24	We use the keys to open the Stat menu. selects CALC and opens the sub menu. selects the OneVar command. We complete the command via giving us Figure 24.
Figure 25	To accept the command in Figure 24, press . Again, the resulting statistics are displayed.
Figure 26	We can move down to see more of those statistics via the down arrow keys. However, it might help somewhat to close the menu lines so that we have more lines available on the screen. will close the menu lines. Then we use the to move down to see more of the values.
Figure 27	A final gives the last value.