### Basic Statistics on the TI-85

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-85. After doing the initial problem we will do the same analysis for similar data from Bay de Noc Community College.

One of the interesting and important consequences of doing statistics on the TI-85 is the fact that the TI-85 automatically copies the xlist to xStat and the ylist to yStat. We can see this, and learn something about the edit mode in the Stat menu, by moving to that mode.

Not only can we move around in the list, we can insert new elements or we can delete elements by using the menu items. Having seen the List Editor, let us use it to create the list of values needed for Bay de Noc. First we will get out of the editor via and to Figure 17 by starting the List menu, , and selecting the NAMES submenu via .

 Figure 17 Figure 17 shows us creating the list BAY by copying ALP to BAY. Once that is done, we move to start the List Editor by pressing . Figure 18 Again, as in Figure 14, we need to supply the name of the list to edit. In Figure 18 we choose BAY via . Figure 19 We move from FIgure 18 by pressing . The calculator responds with Figure 19, and we are now ready to change the values in the list to conform to the values we want for Bay de Noc. Figure 20 As we finish replacing values in the list, we use the key to move to the next element. Figure 20 shows this process after we have entered the first 6 elements. We have completed element 6, so we move to Figure 21 by pressing the key. Figure 21 Figure 21 shows that as we move down from element 6, the calculator shifts the display so that we now see the old element 7, and we have lost sight of element 1. Figure 22 We continue making the changes to get all eleven values for Bay de Noc. Then we can leave the List Editor via the key and move to Figure 23. Figure 23 Just to verify our work, in Figure 23 we have entered the name BAY and pressed to cause the calculator to display the new list. Figure 24 We start the STAT menu and select the CALC option as shown in FIgure 24. Figure 25 This time we want to do the statistics on the values in BAY, and we already have the desired frequencies in yStat. Therefore, we choose to find the BAY item in the submenu, and then to select BAY. We follow that with to move to the ylist which we can leave as yStat. We press to accept our choices. Figure 26 The TI-85 confirms our choices and waits for the next command, as in FIgure 26. We select to perform our 1-VAR option. The resulting display is shown in FIgure 27. Figure 27 Figure 27 has the calculated statistics for Bay De Noc.

The material presented in Figures 1 through 27 demonstrated using the menu system to enter and edit lists of values and to do basic 1-variable statistics on those lists. One requirement outlined above is that we need two lists. The xlist holds the values to be used, and the ylist holds the frequency for each value in the xlist. For most of our work, that ylist will be a list of 1's. If our xlist is called ALP, as it was above, we found that we could generate the required frequency list, which we called ALPF, via the statement ALP==ALPALPF. Furthermore, once we have done a statistical analysis on our lists, ALP and ALPF, those lists are copied to the standard lists xStat and yStat, respectively. As long as the length of the list does not change, as was the case for the new list BAY, we can use the old frequency list, either yStat or ALPF, to help in the computation of the 1-variable statistics for the new list.

The TI-85 has a second method for doing 1-variable statistical analyses. That second method does not use the STAT menu, but rather it uses two commands, OneVar and ShwSt. Figures 28 through 38 demonstrate finding, using, and saving these special commands. One big advantage of using the OneVar command is that it does not require a second frequency list. For OneVar, if the frequency list is not given, then it is assumed to be a list of 1's. Furthermore, doing the OneVar command without a frequency list will cause the standard list yStat to become the required frequency list of 1's. Let us look at using these commands.