II. Menu Keys - Keys that offer choices

M. STAT (statistics)

The statistics menu is accessed by pressing . The statistics menu is quite extensive, and most of it is used in analyzing data. However, there are some aspects of this application that can be used in algebra, trigonometry, and calculus. Specifically, data can be plotted and regression techniques applied to find a curve of best fit. Most of the remaining menu items are not applicable in a significant way to algebra, trigonometry, or calculus. This tutorial will concentrate on how to enter the data (see lists), how to plot the data, how to find a curve of best fit, and how to graph the curve to compare it to the data points.

Example:
(a)
Put the values{-4,-2,0,2} in the list xStat, and the values {4,2,0,2} in the list yStat. For instructions on how to enter the values, go to list.

Enter the values
in xStat
and yStat.

(b) Plot the data on the graph screen. The data will be plotted by turning on one of the Plot graphs. Notice in the second picture below that xStat and yStat are entered as the default. You can change these to other lists if you are using other sets of data to plot. In order to plot the points, we will use a scatter plot. The lists must contain the same number of values for the points to be plotted.

Turn Plot1 on by
pressing ,
move the cursor to On
and press .

The type of plot
can be changed by
pressing .
The types are listed
in the menu.

Access the
menu and set
a WINDOW.
Graph the point by
pressing .

(c) Find the curve of best fit. The TI-86 can find a curve of best fit for the data, but you must decide which regression to use. The data above closely approximates a parabola, which is the graph of a quadratic (second degree) function. Once the calculator has found a curve of best fit, you can have the calculator graph the curve to compare the data points with the curve. If the curve is not a good fit, then you can try a different type of function.

Press to
get to (P2Reg) .
This is the quadratic
regression function.
Press .
Enter the names
xStat and yStat.
Press
and use the menu to
enter the function names.
Press to
see the quadratic
function found.

(d) Graph the curve on the graph screen. From the last screen above, the calculator has found that the quadratic is the curve that best approximates the data points. To see just how closely the curve follows the points, you can graph the function. While this function is quite easy to enter into the graph menu, many times the coefficients are quite long and it can be difficult to enter the values. This problem is solved for you, however, because this equation is stored in a STAT variable named RegEq.

Press .
Press .
Press and
then .
Press to
enter the function
found above.
Press .

It appears that the graph is a close approximation to the data points.