Texas Instruments TI-82 STATS User manual

PART A

TEXAS INSTRUMENTS TI-82/TI-83 GRAPHICS

CALCULATORS

Setup

When using this Guide, you should always, unless instructed otherwise, use the calculator setup

specified below:

FOR THE TI-82 Before you begin, check the TI-82Õs basic setup by pressing MODE . Choose the

settings shown in Figure 1. Check the statistical setup by pressing STAT (CALC) 3(SetUp) .

Choose the settings shown in Figure 2. Check the window format by pressing ENTER (FORMAT),

and choose the settings shown in Figure 3.

¥ If you do not have the darkened choices shown in each of the figures below, use the arrow

keys to move the blinking cursor over the setting you want to choose and press ENTER .

¥ Press 2nd MODE (QUIT) to return to the home screen.

TI-82 Basic Setup TI-82 Statistical Setup TI-82 Window Setup

FIGURE 1 FIGURE 2 FIGURE 3

FOR THE TI-83 Before you begin, check the TI-83Õs basic setup by pressing MODE .Choose the

settings shown in Figure 4. Specify the statistical setup by pressing

2nd MODE (QUIT) STAT 5(SetUpEditor) followed by 2nd 12nd 22nd 32nd 4

2nd 6. Choose the settings shown in Figure 2. Press ENTER to view the screen in Figure 5. Also,

A-2 TI-82/TI-83 Graphics Calculators

check the window format by pressing 2nd ZOOM (FORMAT) , and choose the settings shown in Figure

¥ If you do not have the darkened choices shown in each of the figures below, use the arrow

keys to move the blinking cursor over the setting you want to choose and press ENTER .

¥ Press 2nd MODE (QUIT) to return to the home screen.

TI-83 Basic Setup TI-83 Statistical Setup TI-83 Window Setup

FIGURE 4 FIGURE 5 FIGURE 6

Basic Operation

You should be familiar with the basic operation of your calculator. With calculator in hand, go

through each of the following.

1. CALCULATING You can type in lengthy expressions; just make sure that you use

parentheses when you are not sure of the calculator's order of operations. As a general rule,

numerators and denominators of fractions and powers consisting of more than one term should be

enclosed in parentheses.

Evaluate

4*15 +895

Evaluate

(-3)4-5

8+1.456 . (Use (–) for the negative symbol and

-for the subtraction sign.)

Evaluate e3*0.027 and e3*0.027.

The calculator will assume you mean the first expression unless

you use parentheses around the two values in the exponent. (It

is not necessary to type in the 0 before the decimal point.)

2. USING THE ANS MEMORY Instead of again typing an expression that was evaluated

immediately prior, use the answer memory by pressing 2nd (–) (ANS) .

Chapter 1 A-3

Calculate

415 895

÷using this nice shortcut.

If you wish to clear the home screen, press CLEAR .

3. ANSWER DISPLAY When the denominator of a fraction has no more than three digits,

your calculator can provide the answer in fraction form. When an answer is very large or very

small, the calculator displays the result in scientific notation.

The Òto a fractionÓ key is obtained by pressing

MATH 1(‹Frac) .

The calculator's symbol for Òtimes 1012Ó is È12. Thus,

7.945È12 means 7,945,000,000,000.

The result 1.4675È–6 means 1.4675*10–6, the scientific

notation expression for 0.0000014675.

4. STORING VALUES Sometimes it is beneficial to store numbers or expressions for later

recall. To store a number, type the number on the display and press STO‹ALPHA , type the letter

in which you wish to store the value, and then press ENTER . To join several short commands

together, use 2nd (:).

Store 5 in Aand 3 in B, and then calculate 4 AÐ 2B.

To recall a value stored in a variable, use ALPHA to type the

letter in which the expression or value is stored and then press

ENTER . The value stays stored until you change it.

5. ERROR MESSAGES When your input is incorrect, an error message is displayed.

If you have more than one command on a line without the

commands separated by a colon (:), an error message results

when you press ENTER .

TI-82 Choose 1(Goto) to position the cursor to the place

the error occurred so that you can correct the mistake or

choose 2(Quit) to begin a new line on the home screen.

A-4 TI-82/TI-83 Graphics Calculators

TI-83 Choose 2(Goto) to position the cursor to the place

the error occurred so that you can correct the mistake or

choose 3(Quit) to begin a new line on the home screen.

Chapter 1 Ingredients of Change:

Functions and Linear Models

&1.1 Fundamentals of Modeling

There are many uses for a function that is entered in the graphing list. Graphing the function

in an appropriate viewing window is one of these. Because you must enter all functions on one

line (that is, you cannot write fractions and exponents the same way you do on paper) it is

very important to have a good understanding of the calculatorÕs order of operations and to

use parentheses whenever they are needed.

1.1.1 ENTERING AN EQUATION IN THE GRAPHING LIST Press Y=to access

the graphing list. The graphing list contains space for 10 equations, and the output

variables are called by the names Y1, Y2,..., and Yo. When you intend to graph an equation

you enter in the list, you must use Xas the input variable.

If there are any previously entered equations that you

will no longer use, delete them from the graphing list.

Position the cursor on the

line with the equation,

and press CLEAR .

TI 82 Suppose you want to graph A= 1000(1 + 0.05)t.

For convenience, we use the first, or Y1, location in the list.

We intend to graph this equation, so enter the right hand

side as 1000(1 + 0.05)^X.

(Type Xby pressing X,T,q, not the times sign ✕.)

TI 83 Suppose you want to graph A= 1000(1 + 0.05)t.

For convenience, we use the first, or Y1, location in the list.

We intend to graph this equation, so enter the right hand

side as 1000(1 + 0.05)^X.

(Type Xby pressing X,T,q,n , not the times sign ✕.)

Plot1,Plot2,and Plot3 at the top of the Y= list should not

be darkened. If any of them are, use until you are on

the darkened plot name. Press ENTER to make the

name(s) not dark.

1.1.2 DRAWING A GRAPH If you have not already done so, enter the equation in the Y=

list using Xas the input variable before drawing a graph. We now draw the graph of

y= 1000(1 + 0.05)x.

A-6 TI-82/TI-83 Graphics Calculators

Press ZOOM 4(ZDecimal) .

Notice that the graphics screen is blank.

Press WINDOW to see the view set by ZDecimal.

Xmin and Xmax are the settings of the left and right edges

of the viewing screen, and Ymin and Ymax are the settings

for the lower and upper edges of the viewing screen.

Xscl and Yscl set the spacing between the tick marks on

the x- and y-axes.

The view you see is –4.7 £x£4.7, –3.1 £y£3.1.

Follow the procedures shown in either 1.1.3 or 1.1.4 to draw a graph with your calculator.

Whenever you draw a graph, you have the option of manually changing the view or having

the calculator automatically find a view of the graph.

1.1.3 MANUALLY CHANGING THE VIEW OF A GRAPH If you do not have a

good view of the graph or if you do not see the graph, change the view with one of t h e

ZOOM options or manually set the WINDOW. (We later discuss the ZOOM options.)

TI-82 Press WINDOW , and set Xmin to 0, Xmax to

10, leave Xscl at 1, set Ymin to 900, Ymax to 2000, and

Yscl to 50.

TI-83 Press WINDOW and set Xmin to 0, Xmax to 10,

leave Xscl at 1, set Ymin to 900, Ymax to 2000, and

Yscl to 50.

For all applications in this Guide, have Xres set to 1.

Both Press GRAPH to draw the graph of

Y1= 1000(1 + 0.05)^Xusing the new view.

1.1.4 TI-82: AUTOMATICALLY CHANGING THE VIEW OF A GRAPH

If your view of the graph is not good or if you do not see the graph, change the view using the

TI-82 program AUTOSCL. If you do not have this program, either enter it now using the code

given in the TI-82 Appendix or have someone transfer it to you from another calculator.

Chapter 1 A-7

Caution: When using this TI-82 program, the function you

are graphing must be entered in the Y1 location of the Y=

graphing list. If other functions are entered in the graph-

ing list, this program will not find an appropriate view

for all the functions.

Y1= 1000(1 + 0.05)x

(Delete other functions

that may be entered in

the other locations in

the Y= list.)

Press PRGM followed by the number corresponding to the

location of program AUTOSCL. Press ENTER .

Note: Your program list may or may not look exactly like

the one that is shown to the right.

You are asked to enter Xmin, the value at which the left

side of the view is set. Type 0 and press ENTER .

Next, you are asked to enter Xmax, the value at which the

right side of the view is set. Type 10 and press ENTER .

Program AUTOSCL now draws the graph.

Note: In some cases, the graph drawn by the program will

not be the best view. If this happens, follow the instructions

in part 8 to manually set Ymin and Ymax (and/or the scale

values) to obtain a better view.

1.1.4 TI-83: AUTOMATICALLY CHANGING THE VIEW OF THE GRAPH

If your view of the graph is not good or if you do not see the graph, change the view using the

built-in autoscaling feature of the TI-83. This option will automatically find a view to see

all the functions that you have turned on in the graphing list.

Be sure the function you are graphing, y= 1000(1 + 0.05)x,

is entered in the Y1 location of the Y= list. (Delete all

other functions that may be entered in other locations.)

Press WINDOW , set Xmin to 0 and Xmax to 10. (It does

not matter what values are set in the Ymin and Ymax

positions.)

Press ZOOM (0: ZoomFit)ENTER .

The TI-83 automatically sets the vertical view and

(based on the Xmin and Xmax you set) draws a graph

of the function.

1.1.5 TRACING You can display the coordinates of certain points on the graph by tracing.

The x-values shown when you trace depend on the horizontal view that you choose, and t he

y-values are calculated by substituting the x-values into the equation that is being graphed.

A-8 TI-82/TI-83 Graphics Calculators

TI-82 Press TRACE , use to move the trace cursor to

the right, and use to move the trace cursor to the left.

The number 1in the upper right hand corner of the screen

tells you that you are tracing on the equation in Y1.

TI-83 Press TRACE , use to move the trace cursor to

the right, and use to move the trace cursor to the left.

The equation that you are tracing appears at the top of

the graphing screen.

Both Trace past the edge of the screen and notice that

even though you cannot see the trace cursor, the x- and

y- values of points on the line are still displayed at the

bottom of the screen. Also notice that the graph scrolls

to the left or right as you move the cursor past the edge

of the current viewing screen.

1.1.6 ESTIMATING OUTPUTS You can estimate outputs from the graph using TRACE. I t

is important to realize that such outputs are never exact values unless the displayed x-value

is identically the same as the value of the input variable.

Estimate the value of Awhere A= 1000(1 + 0.05)x when

x= 5, x= 7, and x= 10.

Press WINDOW . If you do not have the settings shown

to the right, reset to these values.

(Note: TI-83 windows do not have FORMAT at the top

of this screen.)

Press GRAPH . After the graph is drawn, press ZOOM

3(Zoom Out) ENTER .

After the zoomed graph is drawn, again press ENTER

to enlarge your view of the graph.

(Press WINDOW and observe the values now defining

the graphics screen.) Press GRAPH .

Note that (5, 1450) is a point

on the screen, not a point on

the graph of the function.

Chapter 1 A-9

Press TRACE and use to move as close as you can

to x = 5. (Your screen may look slightly different than

the one shown to the right.)

Continue pressing and notice that the values 7 and

10 cannot be obtained by tracing in this view. Therefore,

choose values close to these numbers to obtain estimates

such as Ais approximately $1386.80 when x = 7 and A

is about $1637.37 when x= 10.

Because the number 5, not a

value close to 5 is shown,

A= $1276.28 when x= 5.

¥ If you had used the original WINDOW with Xmax = 10 and traced, you should obtain the

exact value A= 1500 when x = 10 because 10, not a value close to 10, is shown when tracing.

A-10 TI-82/TI-83 Graphics Calculators

¥ If you want Ònice, friendlyÓ values displayed for x when tracing, set Xmin and Xmax so

that Xmax - Xmin is a multiple of 9.4, the width of the ZDecimal viewing screen. For

instance, if you set Xmin = 0 and Xmax = 18.8 in the example above, the exact values when

x= 5, x= 7, and x= 10 are displayed when you trace since 18.8 = 2(9.4). Try it!

1.1.7 EVALUATING OUTPUTS The values obtained by this evaluation process are

actual output values of the equation, not estimated values such as those generally obtained

by tracing. Begin by entering the equation whose output you want to evaluate in the Y= list.

Using xas the input variable, enter the function in the

Y= list. Return to the home screen by pressing 2nd

MODE (QUIT) as many times as necessary.

Y1= 1000(1 + 0.05)x

(You could use any of the 10

function locations.)

TI-82 Go to the Y-VARS menu by pressing 2nd VARS

(Y-VARS).

TI 83 Go to the Y-VARS menu by pressing VARS

(Y-VARS).

Both Choose 1: Function by pressing 1or ENTER ,

and choose 1: Y1by pressing 1or ENTER .

(To choose another Y= location, simply press the num-

ber corresponding to that function.)

Y1shows on your screen. Type the x-value at which you

want to evaluate the equation, and press ENTER . Now,

evaluate Y1 at x= 5.

(Note: You can, but do not have to, type in the closing

parentheses on the right.)

Evaluate Y1at x= 7 by recalling the previous entry with

2nd ENTER (ENTRY) , edit the 5 to 7 by pressing

and typing over the 5, and press ENTER .

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