Appendix B: Reference Information

User Variablesp. 383

These are the names you may store to. Names that are limited to one data type refuse anything else: for example, storing a plain number to a list name gives ERR:DATA TYPE.

Archive Variablesp. 383

Data, programs and most other variables can be moved from RAM to the user data archive. There they cannot be edited or deleted by accident, and the RAM they occupied is free for other work.

An archived variable is shown with an asterisk (*) in front of its name in memory listings. Trying to use or edit one gives ERR:ARCHIVED, and archiving when the archive has no room gives ERR:ARCHIVE FULL (see ERR:ARCHIVED and ERR:ARCHIVE FULL).

System Variablesp. 383

System variables are the settings and results that the calculator keeps for itself. Some of them you may store to, and some are read-only.

Logisticp. 384

Logistic regression fits y = c ÷ (1 + a·e^(−bx)). It uses a nonlinear, recursive least-squares search to estimate a, b and c, trying to make this cost function J as small as possible:

J is the sum of the squares of the residual errors. Here x is the independent-variable list, y is the dependent-variable list and N is the dimension of the lists.

SinRegp. 384

Sine regression fits y = a·sin(bx + c) + d. It applies the same kind of nonlinear, recursive least-squares search, estimating a, b, c and d so that the cost function J is as small as possible:

Again x is the independent-variable list, y is the dependent-variable list and N is the dimension of the lists.

ANOVA(p. 385

The one-way ANOVA F statistic is the ratio of two mean squares. Each mean square is a sum of squares divided by its degrees of freedom.

2-SampFTestp. 385

The statistic is the squared ratio of the two sample standard deviations, F = (Sx₁ ÷ Sx₂)². Sx₁ and Sx₂ have n₁ − 1 and n₂ − 1 degrees of freedom. In the formulas below f(x, n₁−1, n₂−1) is the F probability density function (Fpdf) with those degrees of freedom, and p is the reported p-value.

For the two-sided test, [Lbnd, Ubnd] are the lower and upper limits. The F statistic is used as whichever bound gives the smaller integral, and the other bound is chosen so that the two integrals are equal.

2-SampTTestp. 386

The two-sample t statistic is t = (x̄₁ − x̄₂) ÷ S. How S and the degrees of freedom df are computed depends on whether you choose to pool the variances.

For pooled variances, Sxp is the pooled sample standard deviation: Sxp = √( [ (n₁−1)·Sx₁² + (n₂−1)·Sx₂² ] ÷ df ).

Time Value of Moneyp. 386

Everything starts from one equation that ties together N, PV, PMT, FV and the periodic interest rate i. When PMT is not zero, the calculator finds i by iteration (see below); the other unknowns are solved from the formulas in the table.

When PMT = 0 there is no need to iterate: i = (−FV ÷ PV)^(1 ÷ N) − 1.

Amortizationp. 388

Balance, principal and interest are worked out payment by payment. RND means "round to the number of decimal places set in the display mode" and RND12 means "round to 12 decimal places". The result depends on PMT, PV, I% and the two payment numbers pmt1 and pmt2.

Cash Flowp. 388

Net present value depends on the initial cash flow CF₀, the later cash flows CFⱼ, how many times each one repeats (nⱼ) and the interest rate i, where i = I% ÷ 100. Sⱼ is the running total of the repeat counts: Sⱼ = n₁ + n₂ + … + nⱼ for j ≥ 1, and S₀ = 0.

The internal rate of return depends only on the initial cash flow CF₀ and the later cash flows CFⱼ and their frequencies.

Interest Rate Conversionsp. 389

Eff is the effective annual rate (percent), Nom is the nominal annual rate (percent) and CP is the number of compounding periods per year.

Days between Datesp. 389

The dbd( function accepts or computes dates from January 1, 1950 through December 31, 2049. It uses the actual/actual day-count method: real month lengths and real year lengths.

The result is dbd( = (number of days for the second date) − (number of days for the first date), where each date is counted from a base date:

TI-84 Plus Resultsp. 391

When an answer is not what you expected, the cause is nearly always the order of operations or a mode setting.

The calculator uses its Equation Operating System (EOS) to decide what to evaluate first. From first to last, the order is:

1. Functions that come before their argument, such as square root, sin( or log(.
2. Functions that come after their argument: exponents like ², factorial, r (radians), ° (degrees) and unit conversions.
3. Powers and roots, such as 2^5 or 5 times a square root.
4. Permutations (nPr) and combinations (nCr).
5. Multiplication, implied multiplication and division.
6. Addition and subtraction.
7. Relational functions such as > or <.
8. The logic operator and.
9. The logic operators or and xor.

Within the same level, EOS works from left to right, and anything in parentheses is calculated first. When the rules of algebra might be unclear, add parentheses. The guide notes that from OS 2.53 MP onward, parentheses can be pasted into an expression to show how the calculator interpreted it.

Trigonometric functions and polar/rectangular conversions depend on the angle mode. Radian and Degree control how the calculator reads angle values. To change it:

1. Press MODE to show the mode settings.
2. Select Degree or Radian.
3. Press ENTER to save the setting.

ERR:DIM MISMATCH Errorp. 392

You get ERR:DIM MISMATCH when an operation uses two or more lists or matrices whose sizes do not agree. For example, if L₁ = {1,2,3,4,5} and L₂ = {1,2}, then L₁×L₂ fails because the lists have different numbers of elements.

There is a full entry, with a hands-on example, at ERR:DIM MISMATCH.

ERR:INVALID DIM Errorp. 392

ERR:INVALID DIM can appear when you graph a function that has nothing to do with statistics. The cause is a stat plot that is still switched on. Turn the stat plots off: press 2ndSTAT PLOT to open the STAT PLOTS menu and choose 4:PlotsOff.

The error has other causes too. See ERR:INVALID DIM.

Link-Receive L1 (or any file) to Restore Messagep. 392

The real calculator shows "Link-Receive L1 (or any file) to Restore" when it has been disabled for testing (for example an exam mode) and not switched back on. To restore it, you link it to another TI-84 Plus and send any file, or download any file from a computer with TI Connect software.

To send a file from another calculator: on the receiving unit press 2ndLINK and select RECEIVE; on the sending unit press 2ndLINK, pick a category and then a file, and select TRANSMIT.

Contrast Featurep. 392

If the contrast is set to its darkest (9) or lightest (0) level, the calculator can look broken or switched off. Adjust it with 2nd▲︎ to darken or 2nd▼︎ to lighten: press and release 2nd, then press and hold ▲︎ or ▼︎.

TI-84 Plus Identification Codep. 393

A real TI-84 Plus has a unique 14-character ID (digits 0–9 and letters A–F) that you can register with Texas Instruments or use to identify a lost calculator. The About screen shows the operating system version, product number, ID and certificate revision number.

Open the About screen with 2ndMEM (MEM) and choose 1:About.

Backupsp. 393

A calculator stores files and Apps just as a computer does, so it is a good habit to back them up using TI Connect software and a USB cable. TI Connect's own Help file has the step-by-step procedure.

Appsp. 393

Apps are software you add to the calculator the way you would add programs to a computer, to tailor it to a subject or course. Texas Instruments publishes apps for the TI-84 Plus at education.ti.com. Press APPS to see the ones installed.

TI-Cares KnowledgeBasep. 393

The TI-Cares KnowledgeBase is a website where you can search known solutions to frequently asked questions at any time of day: education.ti.com/support.

ERR:ARCHIVEDp. 394

You tried to use, edit or delete a variable that is in the user data archive. For example, dim(L₁) gives this error when L₁ is archived.

ERR:ARCHIVE FULLp. 394

You tried to archive a variable and the archive does not have enough space to hold it.

ERR:ARGUMENTp. 394

A function or instruction was given the wrong number of arguments.

Check Appendix A for the exact arguments and punctuation of each function. Arguments in brackets are optional; separate arguments with commas. For example, stdDev(list[,freqlist]) can be entered as stdDev(L₁) or stdDev(L₁,L₂) because the frequency list is optional.

ERR:BAD ADDRESSp. 394

An error such as electrical interference occurred while sending or receiving an application.

ERR:BAD GUESSp. 394

• In a CALC operation, the Guess you gave is not between Left Bound and Right Bound.
• For the solve( function or the equation solver, your guess is not between lower and upper.
• Your guess and several points around it are undefined.

ERR:BOUNDp. 394

• In a CALC operation or with Select(, you defined Left Bound > Right Bound.
• In fMin(, fMax(, solve( or the equation solver, you entered lower ≥ upper.

ERR:BREAKp. 394

You pressed ON to break out of a running program, to halt a DRAW instruction or to stop the calculation of an expression. This is not a fault; it just confirms that execution was stopped.

ERR:DATA TYPEp. 394

You supplied a value or variable of the wrong data type.

• A function (including implied multiplication) or instruction received an argument of an invalid type, such as a complex number where a real number is required. Check Appendix A and the relevant chapter.
• You entered a type the editor does not allow, for example a matrix as an element in the stat list editor.
• You tried to store the wrong kind of data, for example a matrix into a list. See User Variables for what each variable name accepts.

ERR:DIM MISMATCHp. 394

The operation involves two or more lists or matrices whose dimensions do not match. For example, multiplying L₁ by L₂ when L₁ = {1,2,3,4,5} and L₂ = {1,2} gives ERR:DIM MISMATCH because L₁ and L₂ do not have the same number of elements.

ERR:DIVIDE BY 0p. 395

• You tried to divide by zero. This error is not returned while graphing: the graph simply leaves undefined values out.
• You tried a linear regression on a vertical line.

ERR:DOMAINp. 395

• You gave a function or instruction an argument outside its valid range. This error is not returned while graphing. See Appendix A for each function's range.
• You tried a logarithmic or power regression with a negative X, or an exponential or power regression with a negative Y.
• You tried ΣPrn( or ΣInt( with pmt2 < pmt1.

ERR:DUPLICATEp. 395

You tried to create a group with a name that is already used by another group.

ERR:Duplicate Namep. 395

A variable you tried to send cannot be transmitted because the receiving calculator already has a variable with that name.

ERR:EXPIREDp. 395

You tried to run an application that had a limited trial period, and that period has ended.

ERR:Error in Xmitp. 395

• The calculator could not transmit an item. Check that the cable is firmly connected at both ends and that the receiving unit is in receive mode.
• You pressed ON to break during the transmission.
• You tried to back up from a TI-82 to a TI-84 Plus.
• You tried to send data other than L₁ through L₆ from a TI-84 Plus to a TI-82.
• You tried to send L₁ through L₆ to a TI-82 without using 5:Lists to TI82 on the LINK SEND menu.

ERR:ID NOT FOUNDp. 395

This happens when the SendID command runs but the calculator ID it needs cannot be found.

ERR:ILLEGAL NESTp. 395

You used a function that is not allowed inside an argument of another function, for example seq( within the expression argument of seq(.

ERR:INCREMENTp. 395

• The increment in seq( is 0 or has the wrong sign. This error is not returned while graphing.
• The increment in a For( loop is 0.

ERR:INVALIDp. 395

You referenced a variable or used a function where it is not valid.

• A function like Yₙ cannot refer to Y, Xmin, ΔX or TblStart, for example.
• You referenced a variable or function transferred from a TI-82 that is not valid on the TI-84 Plus (for example Uₙ₋₁).
• In Seq mode you tried to graph a phase plot without defining both of its equations.
• In Seq mode you tried to graph a recursive sequence without giving the right number of initial conditions.
• In Seq mode you referred to terms other than (n−1) or (n−2).
• You chose a graph style that is not valid in the current graph mode.
• You used Select( without at least one xyLine or scatter plot turned on.

ERR:INVALID DIMp. 396

• You tried to graph a function that does not involve stat plots while a stat plot is switched on. Turn stat plots off: 2ndSTAT PLOT, then 4:PlotsOff (see ERR:INVALID DIM Error).
• You gave a list dimension that is not an integer between 1 and 999.
• You gave a matrix dimension that is not an integer between 1 and 99.
• You tried to invert a matrix that is not square.

ERR:ITERATIONSp. 396

• solve( or the equation solver used more iterations than allowed. Look at a graph of the function; if the equation has a solution, change the bounds, the initial guess or both.
• irr( used more iterations than allowed.
• The maximum number of iterations was exceeded while computing I% in the TVM Solver.

ERR:LABELp. 396

The label named in a Goto instruction is not defined by any Lbl instruction in the program. Check the spelling of both, and that the Lbl is in the same program.

ERR:LINK L1 (or any other file) to Restorep. 396

The calculator has been disabled for testing. To restore it, download any file from a computer with TI Connect software, or receive any file from another TI-84 Plus. See Link-Receive L1 (or any file) to Restore Message.

ERR:MEMORYp. 396

There is not enough memory to do what you asked. Delete items from memory first (MEMORY menu, 2:Mem Mgmt/Del…) or archive some variables.

• Recursive definitions give this error, for example graphing Y₁ = Y₁.
• Branching out of an If/Then, For(, While or Repeat block with Goto can also give it, because the End that closes the block is never reached.

ERR:MemoryFullp. 396

• You cannot transmit an item because the receiving unit does not have enough memory. You can skip the item or leave receive mode.
• During a backup, the receiving unit does not have room for everything in the sending unit. A message tells you how many bytes the sending unit has to delete. Delete items and try again.

ERR:MODEp. 396

You tried to store to a window variable that belongs to a different graphing mode, or to run an instruction in the wrong mode. For example, DrawInv only works in Func mode.

ERR:NO SIGN CHNGp. 396

• solve( or the equation solver found no sign change.
• You tried to compute I% when FV, (Σ PMT) and PV are all ≥ 0 or all ≤ 0.
• You tried irr( when neither CFList nor CF0 is greater than 0, or when neither is less than 0.

ERR:NONREAL ANSp. 396

In Real mode, a calculation produced a complex result. This error is not returned while graphing: the graph leaves such points out.

ERR:OVERFLOWp. 396

You entered, or calculated, a number beyond the range of the calculator (about 10 to the power 100). This error is not returned while graphing.

ERR:RESERVEDp. 397

You used a system variable in a way that is not allowed, such as storing to one of the reserved statistics variables. See Appendix A and System Variables.

ERR:SINGULAR MATp. 397

• A singular matrix (determinant = 0) was used as the argument of x⁻¹, which is not valid.
• SinReg or a polynomial regression produced a singular matrix because it could not find a solution, or none exists.

This error is not returned while graphing.

ERR:SINGULARITYp. 397

The expression in solve( or the equation solver contains a singularity, a point where the function is not defined.

ERR:STATp. 397

You asked for a statistics calculation on lists that are not suitable.

• Statistical analyses need at least two data points.
• Med-Med needs at least three points in each of its three partitions.
• When you use a frequency list, every element must be ≥ 0.
• For a histogram, (Xmax − Xmin) ÷ Xscl must be ≤ 47.

ERR:STAT PLOTp. 397

You tried to display a graph while a stat plot that uses an undefined list is turned on. Define the list, fix the list name in the stat plot, or turn the plot off (4:PlotsOff on the STAT PLOTS menu).

ERR:SYNTAXp. 397

The command has a syntax error. Look for misplaced functions, arguments, parentheses or commas. Appendix A shows the arguments and punctuation each function needs. For example stdDev(list[,freqlist]) can be entered as stdDev(L₁) or stdDev(L₁,L₂), since the frequency list is optional.

ERR:TOL NOT METp. 397

You requested a tolerance that the algorithm cannot reach. Use a looser (larger) tolerance.

ERR:UNDEFINEDp. 397

You referenced a variable that is not defined right now. For example, you used a statistics variable when no calculation is current (because a list was edited), or one that does not apply to the latest calculation, such as a after Med-Med.

ERR:VALIDATIONp. 397

Electrical interference made a link fail, or this calculator is not authorized to run the application.

ERR:VARIABLEp. 397

You tried to archive a variable that cannot be archived, or to unarchive an application or group.

Variables that cannot be archived include the real numbers LRESID, R, T, X, Y and θ, the statistics variables under VARS, the Yvars and the AppIdList.

ERR:VERSIONp. 397

You tried to receive a variable whose version is not compatible with this calculator.

ERR:WINDOW RANGEp. 398

There is a problem with the window variables. Typical causes:

• Xmax ≤ Xmin or Ymax ≤ Ymin.
• θmax ≤ θmin with θstep > 0 (or the reverse).
• Tstep = 0.
• Tmax ≤ Tmin with Tstep > 0 (or the reverse).
• The window values are too small or too large to graph. You may have zoomed in or out beyond the numerical range of the calculator.

ERR:ZOOMp. 398

• A point or a line, instead of a box, was defined in ZBox.
• A ZOOM operation returned a math error.

Computational Accuracyp. 398

To keep results accurate, the calculator carries more digits internally than it shows.

How the window maps to pixels. Xmin is the centre of the leftmost pixel column and Xmax is the centre of the next-to-last column (the last column is reserved for the busy indicator). ΔX is the distance between the centres of two neighbouring pixels. Ymin is the centre of the next-to-bottom pixel row, Ymax is the centre of the top row and ΔY is the distance between the centres of adjacent rows.

The relationship also works in reverse: if you store a value in ΔX or ΔY from the home screen or from a program, the calculator recalculates Xmax or Ymax.

Cursor Coordinates and Calculation Tolerancesp. 399

In Float mode the cursor coordinates are shown as eight-character numbers (the sign, decimal point and exponent count as characters). X and Y are updated with at most eight digits of accuracy.

On the CALCULATE menu, minimum and maximum are found with a tolerance of 1E−5, and ∫f(x)dx with a tolerance of 1E−3. So the number displayed may not be accurate to all eight shown digits, although for most functions at least five digits are right.

For fMin(, fMax( and fnInt( on the MATH menu, and for solve( in the CATALOG, you can specify the tolerance yourself.

Function Limitsp. 399

The range of input values each function accepts. Going outside gives ERR:DOMAIN or ERR:OVERFLOW. Powers of ten are written like 10^100.

Function Resultsp. 399

The inverse trigonometric functions always return an angle in a fixed range, whichever of the many possible angles you might expect.