Table of Contents What do the keys do?.. 3 Basic Calculator Use 6 Scientific Notation 9 Evaluations of Fracions 11 Now I Own a Graphing Calculator, How do I use it? Using the TI 83 and 84 Graphing Calculators Entering Absolute Values 12 Entering Powers and Roots 13 Operations: Pi, i and e 16 Common Menu Screens 17 Basics of Graphing 19 Graphing Inequality 26 Finding Coordinates of x-intercepts 27 Intersection of Two Graphs 28 Window Alternations 30 "Adapted with permission from Russ Baker, Howard Community College, Columbia, MD. The original can be found at http://www.howardcc.edu/math/calculator/ti83frame.htm" Plotting Points 32 Using Tables 33 Graphs of Vertical Lines 35 Graphing of Piecewise Function 36 Finding MAX and MIN Coordinates 38 Using Statistics 41 Data Analysis 43 Graphing Regression Equations 44 Miscellaneous 47 1 2
What do the keys do? y = Window Zoom All of those keys are used for graphing and will be explained when Trace graphing. Graph On Turns the calculator on APPS PRGM VARS CLEAR 5. x (- any root larger than a cubed root. (Must put in what x equals first) 6-10. are not used in Basic Algebra Applications not used in Basic Algebra, may be used in other courses Not used in Basic Algebra May be used later in Basic Algebra Clears the screen on the calculator 2 nd Use this key to get to items printed on the base of the calculator that are printed in yellow. Mode - Hit key - Normal needed for all math things we will do - Float sets the position of the decimal point and will round to that position - Radian degree used in trig. must be in degree to work for angles, radians for circles - Others are not used in Basic Algebra X -1 Negative 1 exponent key inverts a number Sin Cos Trigonometry keys not used in Basic Algebra Tan ^ The exponent key place in the base, hit the key then enter the exponent value x 2 Squares a number DEL Over arrow keys Alpha X,T,,N Delete key used to remove a single entry off the calculators screen. (Enter a wrong number? Use delete to change it) Work the same as the over arrow keys on computers and remote controls Used to get to letters printed in teal. Must be hit to bring up a letter used to place the letter X in an equation, Comma - separates inputs into programs that are placed in the calculator. Not used in Basic Algebra ( ) Parenthesis keys used in order of operations lets the calculator know to do what is inside first Log Not used in Basic Algebra LN Not used in Basic Algebra STAT -hit this key -Edit will discuss this later -Calc used to calculate -LinReg #4 by us STO,,-,+ Used to store information on the calculator. Must assign the value of a letter Used for math operations MATH hit key MATH 1. Frac used at the end of a problem. The answer will be in fractional form (not reduced) 2. Dec used at the end of a problem, the answer will be a decimal 3. 3 raising a number to the 3 power cubed 4. 3 (- cube root) of a number. (Finish the problem in parentheses) 2 nd Function Keys Must use the 2 nd function key for all items printed in yellow Quit Not used in this class INS Used to insert material into a problem. Locate position to change the 3 4
problem, hit 2 nd INS, then enter material Arrow Keys A-Lock 2 nd Up arrow darkens the screen 2 nd Down arrow lightens the screen Locks the calculator so different letters can be placed on the screen Link Links one calculator to another to send information. Not used in Basic Algebra List Used to enter data as lists into the calculator for graphing Test Used to check equalities not used in Basic Algebra L1 L6 Used to pull up lists of values used in graphing not used in Basic Algebra RCL Used to recall stored information MEM Memory this key removes material from the memory Off Turns the calculator off CATALOG i Not used in Basic Algebra Angle Draw DISTR MATRIX Not used in Basic Algebra Not used in Basic Algebra Not used in Basic Algebra Not used in Basic Algebra ANS Takes an answer and inserts it into a problem ENTRY Returns the calculator to the previous problem that has been worked out. Up to ten problems can be retrieved. Sin -1 Cos -1 Trigonometry Functions Tan -1 Pi used to find circumference and area for circles Square root key EE Scientific notation key Braces used in order of operations e Not used in Basic Algebra 10 x Used to raise a base of 10 to a power Basics Calculator Use Clearing an entry or error 1. If you have entered the wrong number or letter, set the cursor on the error and press the correct key 2. If you need to delete a number or letter, set the cursor on the error and press the DEL key. 3. To erase the entire line, press CLEAR once. 4. To clear the whole screen, press CLEAR twice. U V Not used in Basic Algebra W Brackets used in order of operations e x Not used in Basic Math 5 6
Inserting a character 1. To insert a number or letter, set the cursor on the character to the right and then press INS (2nd key + DEL).You may enter as many characters as you wish without re-entering the INS. 2. To use the previous answer in the next calculation, but NOT in the first position, press ANS ( 2nd + (-) ) [in the lower right] Returning to the home screen 1. To get to any other menu screen from whatever it s showing, press the button for the desired menu. 2. To get back to the home screen, from which you perform calculations, press QUIT (2nd + MODE). Making the screen lighter or darker 1. To make the screen darker, press 2nd + UP arrow 2. To make the screen lighter, press 2nd + DOWN arrow. Turning it OFF 1. First, relax. The TI-83 turns itself off if you forget. 2. To turn off the calculator, press 2nd + ON The calculator will always come back on at the home calculator screen, and remembers what was on it last. It's a good idea to clear the screen before you turn it off. Repeat steps until the screen is at the desired brightness. A box appears in the upper right corner of the screen with a number from 0 to 9. 0 is the lightest and 9 is as dark as it can be. Repeat entry button Find the ENTRY button at the bottom right of the calculator As battery power diminishes, you'll need to darken the screen to see it well. When the number reaches 8 and is still too light, go buy batteries. 1. The ENTRY function is above the ENTER key. It will reprint any line already entered for editing or recalculating. Using a previous answer Enter several simple calculations, like these: 1. To use the last answer as the first number of the next calculation, just enter the operation sign that goes after it. The calculator will show ANS in the first spot. 7 8
Now enter one more: Use the right arrow key to highlight the SCI and press ENTER. Now press 2nd-QUIT keys to return to the home screen. One of the "problems" has scrolled off the screen. To view it again, press 2nd-Enter four times. You will see each problem re-listed at the bottom until the first one shows, like this: 2. Entering numbers to be displayed as scientific notation Key in the number and press ENTER: The "E" means the X 10 and the 4 is the exponent, or 1.2569 x 10 4 3. Entering numbers already in scientific notation From here you can edit the problem, or just see the answer again. Anytime you have to use the same calculation with only minor changes, or you discover an error in keying in a calculation, use the ENTRY function to re-write and change it. It will save a lot of keying. Enter the numeric part, press 2nd -, (the EE key) and ENTER. NEVER use the times key when doing scientific notation. Scientific Notation When working with very large or small numbers, scientific notation is very handy. The calculator will automatically give an answer in scientific notation if the answer cannot be displayed in 10 places. To have the calculator display ALL numbers in scientific notation, use the MODE key: It looks like this: 4. Numbers that are not in correct scientific notation form will be fixed automatically by the calculator. 5. To display a standard numeral given scientific form, change the MODE back to NORMAL, return to the home screen and press ENTER. Fractions Fractions look like division problems on the TI83. It will NOT display mixed fractions, nor will it allow denominators more than 4 digits To have the calculator display and answer as a fraction, use the MATH key 9 10
3. Again, for expressions with only one variable, use the LIST functions. Press 2nd- ( and enter the numbers to plug in, separated by a comma. For example: {1,2,3,4,5} Close the grouping with 2nd - ) 1. Enter a calculation (don't forget the order of operations) Press STO key Press 2nd-L1 or any other L# key. Press ENTER 2. Press MATH-1 (or MATH-ENTER): Type in the expression with L1 in place of the variable. The results are all the answers in order. Press ENTER to see the answer. 4. If the expression has more than one variable, try the following: Remember, you can enter ANY letter with ALPHA key and the correct key with the letter above it. It is in improper fraction form, and in lowest terms. Evaluation of functions Evaluating a given function for a given value can be done several ways. Here are some good options Problem: if x = 3 find the value of x 2 + 2x -1 1. The most obvious solution: enter 3 2 + 2*3-1 into the calculator. If you need to do another substitution, use the 2nd-Entry keys and edit the numbers. 2. For multiple substitutions, place the expression in y= menu (only one variable can be used here) and use TABLES to get answers. If x = 3, press 3 STO x ENTER If y = -2 press -2 STO -ALPHA-1 (that's y). Press ENTER continue if there are more variables. type in the expression, for example, 5x - 2y. Press ENTER Entering Absolute Values The absolute value function is a required function. Apply it from two different sources. 1. Press MATH 2. Use the right arrow key to put the 11 12
cursor over NUM 2. Press either 1 or ENTER, since the absolute value function is first on the list. 3. Enter the expression to be inside the absolute value lines and close the parentheses. 3. Enter the exponent. If it is an expression, be sure to put it in parentheses. There are special keys for some powers: 1. To square a number, variable, or expression, enter it, then press the x 2 button. 2. To cube a number, variable, or expression, enter it, then press MATH - 3 4. If you started in the home screen, the calculator will evaluate the expression using whatever variable values are stored, take its absolute value and show the answer. 5. If you started in the Y= menu screen, the calculator will be able to graph the absolute value function. A second way to access the absolute value function is by pressing 2nd- CATALOG: (this is a listing of all the functions in the calculator. It is handy here because abs(... is the first item) Press ENTER and you are done. ROOTS Since roots are just fractional powers, one way is to use the ^ key and be sure to enclose the fraction in parentheses. Entering Powers and Roots As with other operations and functions, there are multiple options for both powers and roots. POWERS 1. Enter the base 2. Press the ^ key (far right column, below CLEAR). Roots can also be done with special function keys. Square roots: Press 2nd-x 2 to access the square root Enter the number, variable, or expression. Cube roots: Press MATH - 4-ENTER Enter the number, variable, or expression OtherEnter the INDEX of the root 13 14
Operations: Pi, i, and e Pi, i, and e are all numeric values that can be accessed using the calculator keys. Pi i 1. The Pi key is 2nd - ^. 2. Use it in expressions as if it were a number like any other. The advantage of using the pi key over entering 3.14 is the rounding error introduced by entering 3.14. 3. Press the Y= key. roots: Press MATH - 5 - ENTER Enter the number, variable, or expression. For example: Find the sixth root of 64 The i key is at the bottom of the calculator. Press 2nd-decimal point. i is the square root of -1 and leads to work with complex numbers. The Ti-83 will do complex number arithmetic as well as real number calculations. When dividing, use the MATH-FRAC option to give fractional values for A and B in the A + Bi form. e e, like pi, is a constant, irrational number. To enter e into an expression, press 2nd-division. If a power of e is needed, use the 2nd-LN keys, and then enter whatever power is needed. 15 16
Common Menu Screens A brief look at a few often-used menu screens and a brief look at what they do. Details on other pages. There are more choices out of sight that can be seen by pushing the down arrow. Starting across the top of the calculator: y = Put equations solved for y in this menu. CALC (2nd key + trace) Shows a list of routines to find coordinates of special points on a graph. We will use only the numbers 1 through 5. WINDOW This is the standard window. Other buttons: MATH Has selections for fractional output, cubing, cube root and any root. It shows the standard window values of numbers on the x and y axis. The Xscl and Yscl tell the scale. One tick mark on the axis = one unit. To turn the scales OFF, enter a zero for Xscl or Yscl. That is often good to do when the intervals used are very large. ZOOM Just select the number of the function you wish to apply. Works from regular calculator screen or from y = menu and in programming. There are lots more menu screens, but these are the most commonly used. Other important screens are introduced in the skills for which they are needed. This screen will allow quick changes to the window based on what you choose. 17 18
Basics of Graphing Errors when graphing New users often find that when the graph button is pushed, an error message is returned. Most often, it is one of these screens: Graphing a simple equation 1. Press y= button 1. In either case, the problem can be fixed by looking at the y= menu page. 2. Type in the equation. The button with x, T, 0, n on it is the best way to enter a variable. : 2. Note that the PLOT1 is darkened, indicating that it is turned ON. 3. Press GRAPH To see the equation in the upper left, press TRACE The PLOT functions are in the LISTS (found in STAT-EDIT) and use two of the lists for coordinates. If there are no data in the lists, the Invalid Dim message occurs. If there are unequal numbers of values in the lists, the Dim Mismatch message occurs. 3. THE FIX: Use the UP-ARROW key to move the cursor to the PLOT1 that is dark (if it is Plot2 or PLOT3, you need the right arrow key too). If you do not see what you expected, see "Finding a Good Window". 4. Press ENTER to turn the PLOT OFF 5. Pressing GRAPH will draw the graph you are trying to display. 19 20
Zoom menu The center key in the top row is the Zoom menu key. Pressing it shows this screen: And scrolled down to see the rest: Turning graphs on/off 1. To turn a graph OFF, use the Left arrow key to put the cursor over the equal sign. 2. Press ENTER. In this screen, Y1 and Y3 will graph, but y2 is turned off. 3. Moving the cursor over to the far left allows different graph styles from dotted to pathway motions, to inequality shading. Experiment. Below, Y3 is set to shade above the graph. How to use the most common options: 1 Selecting the first option, ZBOX, allows the user to enlarge the graph within a specific rectangle. a) Here is a graph in the standard screen: Pressing the TRACE key shows the equation and the coordinates. 4. And next, Y1 will be graphed with a THICK line: b) When ZBOX is selected a blinking "+" will show in the graph screen. Move it with the arrow keys so a corner of the box you will make is where you wish it to be, and then press ENTER. c) Use the arrow keys to trace out the box with the desired graph inside it. 21 22
After using the down arrow: 3 ZOOM OUT does the opposite of ZOOM IN and works exactly the same way. This is handy if a key point in your graph is not visible because the window is too small. It is sometimes not so great if you find you really only wanted to change the scale of one axis and not both. After using the right arrow: Press ZOOM OUT once to get: This cubic graph is incomplete. d) When the box is complete, Press ENTER. Now the intercept can be seen with more accuracy. This skill is very handy when analyzing graphs for roots of equations. First choose ZOOM OUT, then choose the center of the zoomed in graph. Here is a good choice: 2 ZOOM IN does just that. Select it, move the "+" to the center of the section you want to see close up, and press ENTER. (OR press ZOOM and 1) The window automatically resets with that point in the center of the screen. This process can be repeated over and over. Press ZOOM IN once to get: So the new view looks like: Now all key points can be seen. 23 24
5 ZSQUARE adjusts the screen to make the slope of a straight line and circles closer to scale. The normal screen has pixels, i.e., graph grid squares that are not square. ZSQUARE fixes that. Here is a circle and line of slope 2 on the standard screen: And now after pressing ZOOM 5: Remember, this is a tricky function. The new graph will use whatever x-axis boundaries are set. If you don't like what you see, try changing the x-values in the window. Graphing Inequalities Shading above or below a graph can be done by accessing the Y= menu 6 ZSTANDARD is the most-used option. Whenever you want to graph an equation, and you are not sure what values are set in the window, press ZOOM 6 and the equation will graph in the standard window, which is -10 to +10 in both x and y axes. 1. Press Y= and enter the desired function. For example: 2. Use the left-arrow key to move the cursor to the far left. 3. Press the ENTER key twice. 4. The triangle is blinking. 5. Press GRAPH to see it. This is the GREATER THAN option. 9 ZOOMSTAT is a more advanced option and will be taken up in another section. 0 ZOOMFIT can be a helpful tool to find a good window. This routine takes whatever DOMAIN values (x-values or horizontal axis) there are and adjusts the RANGE values (y-values or vertical axis) so the graph is on screen throughout the interval. It is a bit tricky to use, as the Domain must be just right to get a good result. Sometimes even then, manipulating the Domain and Range in the WINDOW screen is a better option. Here is an example: standard screen: 6. The graph should look like this: Go back to the Y= screen and press ENTER again. This is the LESS THAN option. This cubic equation graph has a relative minimum that is off the screen. And here is the ZOOM 0 screen: Now the minimum is seen. Graph inequality SYSTEMS the same way 25 26
Notice that the calculator changes the shading so that the solution to the system is visible. HINT: The graph cannot distinguish between "less than" and "less than or equal to" graphs. The same for "greater than" and "greater than or equal to" graphs. that is to the LEFT of the intercept. Do this by either entering a number, OR moving the arrow keys. Then hit ENTER Follow the same procedure for the RIGHT bound. The smaller the interval, the better. Finding coordinates of x-intercepts x-intercepts are not just important "anchor" points on a graph. They are the roots to a related equation. 1. Press Y= and enter the desired function. For example: y = x 3-5x 2. Press GRAPH: "Guess" means, essentially, that the calculator wants a place in the interval to begin looking. Either enter a number OR move the cursor as close to the intercept as possible, then press ENTER. The coordinates displayed at the bottom of the screen are those of the x-intercept. Round as needed. 3. To find an x-intercept, Press 2nd-TRACE (CALC) 4. Press the "2 since zero is another name for x-intercept and root. 5. Now the routine begins: We will find the left-most zero The calculator needs an interval to "look" in. So first, choose a spot along the graph Find any other x-intercepts in the same way. HINT: Sometimes, due to rounding errors, the Y value may not be exactly 0. It may look like this: 1.03456787e-12 Don't panic. It's a number in scientific notation and is VERY small. So small, it can be accepted as zero. 27 28
Intersection of two graphs The solution to a system of equations is an intersection of the graphs of the equations. 1. Press the Y= key and enter the equations 2. Press GRAPH (standard screen) 3. Press 2nd-TRACE (CALC) 4. Choose option 5 by pressing the key Repeat to find other intersection coordinates. Window alterations 1. Press the WINDOW key on the top row to see this screen: These numbers are the dimensions for the standard graphing screen. 5. Use the left or right arrow key to see which graph is to be the first. 6. Do the same to select the second graph. HINT: If you have only two graphs on the screen, press ENTER twice. If you have more than two, use UP and DOWN arrow keys to select which two to use. Xmin = left edge of the screen Xmax = right edge of the screen Xscl = scale - each mark on the axis = this value Ymin = bottom edge of screen Ymax = top edge of screen Yscl = scale - each mark on the axis = this value Xres = resolution-- do not alter. Often after Zooming or setting a window, the axes look double width or have dotted lines next to them. This is a scaling problem that may be fixed two ways: 7. The GUESS step requires moving the cursor as close to the intersection point as possible. That is where the calculator will begin its calculations. The result is the intersection point. FIRST WAY: Setting the scales = 0 will turn off the axes markings. Use this when the Range or Domain are large or very small and the scale isn't critical to the solution. SECOND WAY: If you want or need markings, find the difference between max and min, and then divide by 20 or 25, rounding to a whole number. 29 30
Plotting Points For example: if Xmax = 400, and Xmin = -200, the difference = 600. 600 divided by 20 = 30, so Xscl = 30 and each mark on the x-axis = 30 units. Plotting points is a first step in doing Data Analysis. Press STAT to see: 2. How to choose the correct window is a difficult concept for some students. 1. Press ENTER or 1 to see the EDIT screen, which will be empty if you have never used it. a. Sometimes the problem gives Domain and Range: Plug the given values in: Domain = x-values, Range = y-values. b. Sometimes the problem gives only Domain: 2. Enter the x-values in the first column (L1), pressing ENTER after each number. 3. Enter y-values in the second column (L2),pressing ENTER after each number. 4. Be sure you have the same number of entries in both lists. Use the Domain as the x-values. Use ZOOMFIT or use trial and error to get a good graph. 4. Press the Y= key. c. Sometimes the problem only implies the Domain and Range. Use math skills: For example, radicals must have positive radicands (Domain restriction) and are always positive values (Range restriction). 5. Use the up-arrow key to highlight PLOT1 and press ENTER to turn PLOT1 On. Use common sense: If the problem is about bacteria counts, it must be a positive number (Domain). Read carefully and think about the context of the problem. 6. Pressing GRAPH will plot the points. Use ZOOM-9 to automatically find a window that will display 31 32
all the points. "Indpnt: Auto Ask" Set it to ASK as shown in the window. Helpful Hints: To clear a column of data, use the arrow-up key to move the cursor over the column title (L1, L2, etc.). Press CLEAR, then the down-arrow. All the entries in the column will be erased when the down-arrow is pressed. If you get an error message when you press GRAPH, check your WINDOW. The coordinates of all the points must be within the chosen window. For example, if you choose the standard window, neither (5,12) nor (12, 5) could be graphed, and an error message will result. ALSO, if you are trying to graph an equation later, and the calculator "doesn't work", check the Plots. Usually turning them off cures the problem. 2. Next, press 2nd - Graph (TABLE). If you haven't used it before, or used the AUTO mode last, the screen will be almost blank: The calculator is waiting for a value to be keyed in. You may enter a number, Pi, e, or even a formula, which will show across the bottom. 3. The calculator will show the x-value you want and function values for any equations you have listed in the y= screen. You may have to scroll over using the arrow keys to see all the y-values. Using Tables Decide first whether you want to choose your own x-values or have the calculator build a complete table. Now for automatic table building. This is a good option if the values you need are at equal intervals and close together. 1. Press TBLSET (2nd Window): Also, at least ONE equation must be entered in the y= menu screen. This is a good option if x-values are more-or-less random, with no equal interval or quite far apart. 2. Place the cursor over the 0 in TblStart and set it to the first x-value you want in your table, here it is 5. Press ENTER. 1. Press 2 nd then WINDOW keys: That's TBLSET on the top row to see this screen: 3. If you want the x-values to count by two's, enter a 2. If by 50's, enter 50. You may use any value you wish. Let's do 2's. Press 2 and ENTER. Ignore all but the line that reads: 4.To automatically build a table, set the third line to Auto. 33 34
Leave the Depend: set to AUTO Choose option 4 Enter the given value for x. Say, x = 5, and hit ENTER (NOT GRAPH) 5. Press TABLE (2nd-Graph) to see the table. Remember, there must be an equation in the y= screen. 6. To see more ordered pairs, use the arrow keys to scroll up or down. 2. Graphing a Moveable vertical line is also possible. Graphs of Vertical lines Start in the GRAPHING screen Press 2nd-PRGM (DRAW) to see the DRAW menu Choose option 4 Use the right and left arrow keys to move the vertical line across the screen. This is kind of fun for the vertical line test, and to "eyeball" critical points. Graphs of vertical lines can NOT be entered into the Y= menu, since their form is x = c. There are two methods to know. 1. Stationary vertical line Graphing a Piecewise Function Start from the HOME screen Press 2nd-PRGM (DRAW) to see the DRAW menu: It is possible to graph a function over a specific interval within the chosen window. 1. Press Y= and enter the desired function in parentheses. For example: 2. Press the ( button again. 35 36
3. Press the "x,t,0,n" key 4. Press 2nd-MATH, (TEST) 10. Use the right arrow key to highlight LOGIC 11. Because this is a "between" inequality, choose AND by pressing 1. 5. Choose an inequality. Try > for this example by pressing 3. 6. Enter the value that is the end point of the interval, say -4 and close the parentheses. 12. Now enter the rest of the inequality, the x < 7 part: 13. Close the parentheses 7. Graph in a standard window: 14. Press GRAPH This graph was made in DOT MODE. It may be easier to see the graph in DOT MODE. HINT: To do a domain with x< - 4, x > 6 use OR instead of AND. If the given domain is, for another example, - 2 < x < 7, follow these steps. Finding MAX or MIN coordinates 8. Follow steps 1-5 above to see this: 9. Press 2nd-MATH While finding a max or min point by "hand" can require calculus, the TI-83 can do it in a moment. 37 38
"Guess" means, essentially, that the calculator wants a place in the interval to begin looking. Either enter a number OR move the cursor as close to the minimum point as possible, then press ENTER. 1. Press Y= and enter the desired function. For example: y = x 3-5x 2. Press GRAPH: The coordinates displayed at the bottom of the screen are those of the minimum point. Round as needed. 3. To find the minimum point in quadrant IV, Press 2nd-TRACE (CALC) 4. Press the "3" since this is a minimum point. 7. Finding MAXIMUM points is done in the same way. REMINDER: Always choose a SMALL interval when prompted for LEFT and RIGHT bounds. Stay as close to the max or min point as you can. 5. Now the routine begins: The calculator needs an interval to "look" in. So first, choose a spot along the graph that is to the LEFT of the minimum point. Do this by either entering a number, OR moving the arrow keys. Then hit ENTER Follow the same procedure for the RIGHT bound. The smaller the interval, the better. 39 40
Basic Statistics Using Statistics Here is a first look at statistics with the Ti-83. It has remarkable capabilities not mentioned here. After entering data, the Ti will show the mean, median, and standard deviation of the data. Here's how: 1. To enter data, press the STAT button. This is the same as entering data to plot points. The data goes into a list. Sum of squares of entries Standard deviation of a sample (s) Standard deviation of the whole (population) (sigma) (Use this one most of the time) 2. AFTER entering data, use the right arrow key to highlight CALC, Press ENTER or 1 to see 1-variable statistics 3. Press 2nd-1 (that's L1) and ENTER. If you put data into another list, be sure to press the correct key. Number of items in data (n) Use the up or down-arrow to scroll through the data Smallest item in data (minimum) Value at the 1st quarter (1 st quartile) Median of the data (2 nd quartile) Value at the 3rd quarter (3 rd quartile) Largest value in data (maximum) 4. The results show... The mean (x bar) Sum of the entries 41 42
Regression Formulas Data Analysis In linear graphing, one skill learned is to find an equation of a line passing through two given points. There are mathematical techniques which will find the "best" approximation of a graph that passes through a larger set of points. These techniques are called Regression formulas. By hand, they are very tedious. With the calculator, they are a snap. 1. To start the procedure, enter some data into the lists as is done in the plotting points routine. 2. Press the STAT key, then the Right arrow key to see the screen at the right. The regression formulas begin at option 4, which is a linear equation, and continues with quadratic (5), cubic (6) etc. Scrolling down reveals more options, most of which will not be used in basic or intermediate algebra. Select the one you think will give the best approximation, i.e., the one that will touch the most points. 3. If we choose (5), this screen appears: 4. Enter the x- and y- value list names with a comma between them. The L1 and L2 lists are the default lists. If your data is in these two lists, just press ENTER. How good a fit is it? Could we do better with a different regression formula? To answer these questions, continue to the next data analysis topic, graphing regression equations. Graphing Regression Equations Before proceeding, be sure you understand how to find a regression equation using the calculator. Once you have a regression equation from a set of data, it is good to see the graphs. Starting with the data previously shown in the regression formula demonstration, we can plot both the data and the equation. 1. Here are the results of the regression procedure. 2. Press the Y= key and set the cursor in the space next to y 1= or y 2= or any of the other numbered equation lines. 3. To enter the regression equation, press the VARS key. 4. Option 5 is the Statistics option, so press 5 5. The next screen reveals the results of the regression calculation. The calculated approximation is y = -.75x 2 +2.05x + 4.25 And here is the data from which the equation was found: 5. Use the right arrow key to highlight EQ and get 43 44
Since choice 1 is highlighted and that is our option, press ENTER 4. The next screen is the Y= menu again, with the equation entered, in this case, as Y1. 5. To see the points as well as the graph, turn on the PLOT feature. Our data is in L1 and L2 so we will use Plot1. Use the UP arrow key to highlight it and press ENTER. 6. Press GRAPH Linear regression Both are better than the quadratic, but the cubic is the best of the three. How good a fit is it? Not great. Could we do better with a different regression formula? Here are some other results: Cubic regression: 45 46
Miscellaneous Linking to another calculator One of the best features of the Ti-83 is the ability to transfer data from one calculator to another. To do this requires the linking cable that comes with the calculator. The program should transfer without a hitch. If not, check your steps and try again. Sequences 1. Plug the cable into both calculators. (Press hard. It should click) 2. On the RECEIVING calculator, press 2nd - X,t,0,n (LINK) 3. Use the right arrow key to highlight RECEIVE. Press ENTER. The screen will say "waiting..." 4. Press LINK on the SENDING calculator: 5. Choose what to transfer. Choose 3, to transfer a program. 6. Use the UP and DOWN arrow keys to point to, and ENTER to select the programs to transfer. The Ti-82 and 83 will both list the terms of a sequence and find the sum of any number of terms. 1) Listing terms of a sequence. Before using the calculator, you must know the formula for the general term of the sequence you are listing. Press 2nd - STAT(LIST) - OPS 5 seq( - ENTER first look pointing to QUADFOR after To generate the list, put each of the following after seq( first, the general term and a comma. next, the letter that is the variable (probably always x )and a comma then the NUMBER of the first term you wish to list and a comma ENTER With the selections complete, arrow key to highlight and then press ENTER. use the right TRANSMIT, 47 48
finally, the NUMBER of the last term you wish to list. This will generate a list of the first five terms of a sequence with a formula of 3x + 4. Press ENTER 2. To find the sum of a certain number of terms, try the following: Press 2nd - STAT (list) - MATH - 5 (sum( ) - ENTER When you press ENTER, you will see the sum of the terms. After ENTER, your screen will look like this: Now repeat the steps for a sequence list so the screen looks like this: 49 50