Interactive Manual › Chapter 12

Chapter 12: Statistics

Enter and edit data in the stat list editor, calculate one- and two-variable statistics, fit regression models, draw stat plots (scatter, xyLine, histogram, box plots, normal probability) and use the statistical variables, from the home screen or a program.

Getting Started: Pendulum Lengths and Periodsp. 178

This long example takes you through a whole statistical analysis: enter data, plot it, fit a model, check the fit with a residual plot, try a better model and finally use it to make predictions. It is split into seven short tutorials. Each one rebuilds the data it needs, so you can start with any of them.

A group of students wants to know how the length of a pendulum is related to its period (the time for one full swing). They hang a weight on a string from the ceiling and time the swing for 12 string lengths. The measurements (adapted from Contemporary Precalculus Through Applications, North Carolina School of Science and Mathematics) are:

Length (cm)	Time (sec)	Length (cm)	Time (sec)
6.5	0.51	24.4	1.01
11.0	0.68	26.6	1.08
13.2	0.73	30.5	1.13
15.0	0.79	34.3	1.26
18.0	0.88	37.6	1.28
23.1	0.99	41.5	1.32

Note The steps here follow the stat wizard that the emulator (like OS 2.55MP) shows when STAT WIZARDS is ON. Every other stat command works the same way with the wizard off: you type the command and its arguments yourself.

1. Set up the stat list editor and enter the datap. 178

Lengths go in L₁ and periods go in L₂. First make sure the calculator is in Func graphing mode and that the list editor shows L₁ to L₆ in columns 1 to 6.

Tutorial

Enter the pendulum lengths and times

You will select Func mode, reset the stat list editor and type the two data columns.

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Open the MODE screen and select Func on the graphing-mode line (three lines down from the top, then ENTER).
MODE▼︎▼︎▼︎ENTER
Leave the MODE screen with 2ndQUIT (QUIT).
2ndQUIT
Open the STAT menu and choose 5:SetUpEditor. The command is pasted on the home screen.
STAT5
Press ENTER to run it. SetUpEditor with no list names clears all the columns of the list editor and then stores L₁ to L₆ in columns 1 to 6. (Removing a list from the editor does not delete it from memory.)
ENTER
Choose 1:Edit on the STAT EDIT menu to open the stat list editor. If L₁ and L₂ already contain old data, press ▲︎ to move onto the list name, then CLEAR ENTER to empty the list; do the same for L₂. Then move back to the first row of L₁.
STAT1
Type the 12 string lengths. After each number, ENTER stores it and moves down to the next row.
6.5ENTER11ENTER13.2ENTER15ENTER18ENTER23.1ENTER24.4ENTER26.6ENTER30.5ENTER34.3ENTER37.6ENTER41.5ENTER
Press ▶︎ to move to L₂. The cursor lands on the first (empty) row of the second column.
▶︎
Type the 12 times in seconds the same way.
.51ENTER.68ENTER.73ENTER.79ENTER.88ENTER.99ENTER1.01ENTER1.08ENTER1.13ENTER1.26ENTER1.28ENTER1.32ENTER

2. Plot the data as a scatter plotp. 179

A scatter plot shows at a glance whether the data lie roughly on a line. Plot 1 will use L₁ for X and L₂ for Y.

Note Before plotting, no Y= function should be selected and no other stat plot should be on, or they will be drawn too. After a RAM reset that is already the case. Otherwise open the Y= editor (Y=), clear or deselect the functions and turn off the plots on the top line.

Tutorial

Define Plot 1 and show it with ZoomStat

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Press 2ndSTAT PLOT (STAT PLOT) and choose 1:Plot1. The stat plot editor for Plot 1 appears.
2ndSTAT PLOT1
Turn the plot on. The cursor starts on the current setting (Off), so press ◀︎ to move onto On and then ENTER.
◀︎ENTER
Move down to Type: and press ENTER to select the first type, the scatter plot.
▼︎ENTER
Move down to Xlist: and enter L₁ with 2ndL1. Then move down to Ylist: and enter L₂ with 2ndL2.
▼︎2ndL1▼︎2ndL2
Move down to Mark:, press ▶︎ to choose the + mark and press ENTER.
▼︎▶︎ENTER
Return to the home screen with 2ndQUIT, then choose 9:ZoomStat from the ZOOM menu. ZoomStat sets the window to fit all the data and draws the plot.
2ndQUITZOOM9

The points rise in a nearly straight band, so a line is worth trying first.

3. Fit a line to the datap. 179

With STAT WIZARDS on, choosing a regression from the STAT CALC menu opens a form where you give the list names and, if you like, a Y= variable that should receive the equation.

Tutorial

Calculate LinReg(ax+b) and store it in Y₁

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Press STAT, move to the CALC menu with ▶︎ and choose 4:LinReg(ax+b).
STAT▶︎4
Fill in the wizard. Xlist: gets L₁ (2ndL1), Ylist: gets L₂ (2ndL2). (They are already filled in with these defaults, but typing them is the habit to learn.)
2ndL1▼︎2ndL2
Skip FreqList: (every point counts once) and go to Store RegEQ:. Press ALPHAF4 to open the Y-VARS shortcut menu and choose 1:Y₁.
▼︎▼︎ALPHAF4ENTER
Move down onto Calculate.
▼︎
Press ENTER. A temporary result screen shows the equation form and the coefficients a and b. The regression equation has been stored in Y₁, and the residuals have been stored in the list RESID.
ENTER
Press CLEAR to leave the result screen. The result is not kept in the home-screen history, but the completed command (LinReg(ax+b) L₁,L₂,,Y₁) is, so you can recall it with 2ndENTRY later. The coefficients live in the VARS Statistics menu (VARS5).
CLEAR
Press GRAPH to see the regression line drawn through the scatter plot.
GRAPH

Tip Each regression also stores its equation in the variable RegEQ (VARS5 then the EQ tab), whether or not you name a Y= variable. The number of decimals shown in the results follows the Float/Fix setting on the MODE screen.

The line follows the middle of the data well, but a residual plot will show whether the fit is really good.

4. Examine the residualsp. 180

A residual is the actual Y value minus the value the model predicts for the same X. The calculator stores them for you in the list RESID each time you run a regression. Adding RESID to the list editor lets you read them, and plotting RESID against the lengths shows any pattern the line missed.

Tutorial

Show RESID in the list editor

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Open the stat list editor.
STAT1
Press ▲︎ to move up to the list names, then ▶︎ twice to rest on L₃.
▲︎▶︎▶︎
Press 2ndINS (INS) to insert an empty column in front of L₃. The Name= prompt appears and alpha-lock is on, so the keys type their green letters.
2ndINS
Type R E S I D (with alpha-lock on, press the keys ×, SIN, LN, x², x⁻¹). You could also paste the name from the LIST NAMES menu (2ndLIST).
×SINLNx²x⁻¹
Press ENTER to store the name in the column. RESID now fills column 3 and L₃ to L₆ shift one column to the right.
ENTER
Press ▼︎ to step into the list and keep pressing it to read the residuals. The first three are negative, the next five are positive and three of the last four are negative: that is a pattern, not random scatter.
▼︎

Tutorial

Plot the residuals (Plot 2) against the lengths

Plot 2 will show RESID on the Y axis. Plot 1 and the regression line are switched off so only the residual plot is drawn.

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Open the stat plot editor for Plot 2.
2ndSTAT PLOT2
Turn it on and keep the scatter type. Move onto On with ◀︎, press ENTER, then ▼︎ ENTER for the scatter type.
◀︎ENTER▼︎ENTER
Xlist: is L₁. For Ylist: open the LIST NAMES menu with 2ndLIST and choose RESID (the seventh item) so the right list name is pasted.
▼︎2ndL1▼︎2ndLIST7
Move down to Mark: and press ENTER to keep the box mark.
▼︎ENTER
Open the Y= editor. Press ◀︎ to move onto the = sign of Y₁ and ENTER to deselect it. Press ▲︎ to reach the plot names on the top line, then ENTER to turn Plot 1 off (Plot 1 is the highlighted one).
2ndQUITY=◀︎ENTER▲︎ENTER
Go back to the home screen and run 9:ZoomStat. The window now fits the residuals: Y runs from about −0.08 to +0.05.
2ndQUITZOOM9
The residuals form a group of negatives, then positives, then negatives again. That arc means the line misses a downward curve in the data, so a model that bends downward (such as a power function) should fit better.

5. Try a power regressionp. 182

A power model has the form y = a·x^b. This fits curves that bend, such as a square-root shape. First put the original scatter plot back on screen, then run the regression.

Tutorial

Calculate PwrReg and store it in Y₁

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Open the Y= editor and press CLEAR to erase the linear equation from Y₁. Then press ▲︎ ENTER to turn Plot 1 on and ▶︎ ENTER to turn Plot 2 off.
Y=CLEAR▲︎ENTER▶︎ENTER
Return home and run 9:ZoomStat to redraw the original data plot.
2ndQUITZOOM9
Choose A:PwrReg from the STAT CALC menu (STAT ▶︎ then ALPHAA, the letter A).
STAT▶︎ALPHAA
Enter L₁ and L₂, then go to Store RegEQ: and paste Y₁ with ALPHAF4 ENTER. (You could also use VARS ▶︎ 1:Function 1:Y₁.)
2ndL1▼︎2ndL2▼︎▼︎ALPHAF4ENTER
Move onto Calculate and run it.
▼︎ENTER
The model is y ≈ 0.192·x^0.522, close to a square root. Leave the result screen and press GRAPH to see the curve through the points.
CLEARGRAPH

6. Check the new residualsp. 183

Running the power regression produced a new RESID list. Plot 2 still plots RESID against L₁, so turning Plot 2 on (and Plot 1 and Y₁ off) shows the residuals of the power model.

Tutorial

Plot and trace the power-model residuals

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

In the Y= editor press ◀︎ ENTER to deselect Y₁, ▲︎ ENTER to turn Plot 1 off and ▶︎ ENTER to turn Plot 2 on.
Y=◀︎ENTER▲︎ENTER▶︎ENTER
Go home and run 9:ZoomStat.
2ndQUITZOOM9
The residuals now change sign at random, which is what a good model gives, though they grow with the string length. Press TRACE, then ▶︎ and ◀︎ to move from point to point and read the Y values. The largest positive residual is about 0.041 and the most negative about −0.027; all others are under 0.02 in size.
TRACE▶︎▶︎

7. Predict periods for new lengthsp. 183

Use the model Y₁ like any function: type Y₁(length) on the home screen. Predict the period for lengths of 20 cm and 50 cm.

Tutorial

Use Y₁ to predict the period for 20 cm and 50 cm

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Open VARS, switch to the Y-VARS menu with ▶︎, choose 1:Function and then 1:Y₁. (The ALPHAF4 shortcut menu does the same job.)
VARS▶︎11
Enter the length 20 in parentheses and press ENTER. The predicted time is about 0.92 seconds, probably accurate to within 0.02 s because of the residual sizes.
(20)ENTER
Recall the last entry with 2ndENTRY, move three places to the left (onto the 2 of 20) and type 5 to turn 20 into 50. Press ENTER. The prediction is about 1.48 seconds.
2ndENTRY◀︎◀︎◀︎5ENTER
50 cm is beyond the longest string measured (41.5 cm), and the residuals were growing with length, so this extrapolated estimate is less trustworthy than the 20 cm one.

Note You can also predict from a table: with the TABLE SETUP options Indpnt: Ask and Depend: Auto (Chapter 7), type any length and read the period.

Setting Up Statistical Analysesp. 184

All statistical data lives in lists. The calculator always has six ready-made list variables, L₁ to L₆, and you can also create lists with your own names (see Chapter 11). Most analyses follow the same five steps:

Enter the data into one or more lists.
Plot the data.
Calculate statistics or fit a model to the data.
Graph the regression equation over the plotted data.
Graph the residuals for the chosen model.

Displaying the stat list editorp. 184

The stat list editor is a table in which you can store, edit and look at up to 20 lists at a time. It is also where you create new list names. Open it with STAT and 1:Edit.

The screen has three zones. The top line shows the list names (after a memory reset: L₁ to L₆ in columns 1 to 6) and, at the right, the number of the current column. The bottom line is the entry line; all typing happens here, and what it shows depends on what you are doing. The middle area shows up to seven rows of three lists at a time, abbreviating long numbers; the entry line always shows the full value of the current element.

Tutorial

Open the stat list editor

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Press STAT to display the STAT menu. The EDIT tab is shown first.
STAT
Choose 1:Edit. The cursor sits on the first element of L₁ and the entry line shows L₁(1)=4.
1

Using the Stat List Editorp. 185

This section covers everyday editing: giving columns list names, removing lists from the editor, emptying lists and changing individual values.

Entering a list name in the stat list editorp. 185

To put a list into a column you first need the Name= prompt. There are two ways to get it:

Move the cursor onto an existing list name and press 2ndINS (INS). An empty column opens in front of it and the other lists shift one column to the right.
Press ▲︎ to reach the list-name row and then ▶︎ until you reach the empty column after the last list.

At the prompt alpha-lock is already on, so you simply press the keys for the letters. Then enter one of these:

a name chosen from the LIST NAMES menu (2ndLIST, see Chapter 11)
L₁, L₂, L₃, L₄, L₅ or L₆ from the keyboard (2ndL1 to 2ndL6)
the name of a list you created earlier, typed directly
a brand-new name of your own

Press ENTER or ▼︎ to store the name (and any elements it already has) in the column. Press ▼︎ again to start entering or scrolling through the elements, which shows the rectangular cursor.

Note If the name you enter is already shown in another column, that list moves to the current column and the remaining columns shift to close the gap. If all 20 columns are full, remove one name before you ask for another empty column. You do not need the small ʟ symbol that user-list names normally need elsewhere; it is not required at the Name= prompt.

Tutorial

Insert a new list name with INS

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Open the stat list editor.
STAT1
Press ▲︎ to move onto the list name L₁.
▲︎
Press 2ndINS (INS). The Name= prompt appears and alpha-lock is on.
2ndINS
Type the new name WTS (the green letters on −, 4 and LN).
−4LN
Press ENTER. WTS is now an (empty) list in column 1, and L₁ has moved to column 2.
ENTER
Press ▼︎ to enter the list and type two values, pressing ENTER after each.
▼︎3ENTER5ENTER

Creating a name in the stat list editorp. 186

To make a new list, display the Name= prompt as above and type the name. A name must follow these rules:

It is one to five characters long.
The first character is a letter from A to Z or θ; it cannot be a digit.
The remaining zero to four characters may be letters, θ or digits.

Press ENTER or ▼︎ to store the name in the current column. The new name also appears as an item on the LIST NAMES menu.

Tutorial

Create a new list called TEMP

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Open the stat list editor (after a reset it shows L₁ to L₆).
STAT1
Press ▲︎ for the name row, then ▶︎ six times: five moves reach L₆ and the sixth lands on the empty column, where the Name= prompt appears.
▲︎▶︎▶︎▶︎▶︎▶︎▶︎
Type TEMP: the green letters on 4, SIN, ÷ and 8.
4SIN÷8
Press ENTER to create the list and place it in column 7.
ENTER
Enter a first value.
▼︎20ENTER

Removing a list from the stat list editorp. 186

Move the cursor onto the list name and press DEL. The list is only taken out of the editor; it stays in memory with all its data and the columns to its right shift left.

Note To delete a list from memory, use the MEMORY MANAGEMENT/DELETE menu (Chapter 18). If you archive a list it also disappears from the stat list editor.

Tutorial

Remove L₁ from the editor (not from memory)

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Open the editor and move onto the name L₁.
STAT1▲︎
Press DEL. L₂ slides into column 1.
DEL
L₁ is no longer displayed in the editor, but it still exists with its three elements.

Removing all lists and restoring L₁ through L₆p. 186

To clear every user-created list out of the editor and put L₁ to L₆ back in columns 1 to 6, either run SetUpEditor with no arguments, or reset all memory (Chapter 18).

Tutorial

Restore L₁ to L₆ with SetUpEditor

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

At the start only L₂ is displayed in the editor. Choose 5:SetUpEditor from the STAT menu.
STAT5
Press ENTER to run it.
ENTER
Open the editor. L₁ to L₆ are back in columns 1 to 6.
STAT1

Clearing all elements from a listp. 187

There are five ways to empty a list:

ClrList clears the lists you name.
In the stat list editor, move onto the list name and press CLEAR ENTER.
In the editor, press DEL on every element, one at a time.
On the home screen or in a program, store 0 to the dimension: 0→dim(listname).
ClrAllLists clears every list in memory (Chapter 18).

Tutorial

Clear a list with CLEAR ENTER

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Open the editor and press ▲︎ to select the name L₁.
STAT1▲︎
Press CLEAR then ENTER. All elements are gone.
CLEARENTER

Tutorial

Clear a list by setting its dimension to 0

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

On the home screen type 0, then STO►.
0STO►
Paste dim( from the LIST OPS menu: 2ndLIST, ▶︎ to OPS, then 3:dim(.
2ndLIST▶︎3
Enter the list name L₁ and close the parenthesis, then press ENTER.
2ndL1)ENTER

Editing a list elementp. 187

To change an element, move the cursor onto it. Then do any of the following:

Replace the value: just start typing. The first character you type clears the old value.
Edit the value: press ENTER to move it to the entry line, then use ◀︎ and ▶︎ to move through it, DEL to delete a character and 2ndINS to insert characters.
Store the change: press ENTER, ▲︎ or ▼︎. If you typed an expression it is evaluated, and if you typed a variable its stored value becomes the element.
Cancel the edit: press CLEAR ENTER to restore the original element.

The list in memory is updated the moment you store the edit. Expressions and variables are allowed as elements. If you enter a fraction with the n/d template it is shown in the editor with a thick bar between numerator and denominator, unlike the thin bar of ordinary division on the home screen.

Note Order of operations still applies. For example, 1/2+3 is divided first and then added, so to divide the whole sum by something put parentheses around the numerator.

Tutorial

Replace, edit, insert and delete elements

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Open the editor. The cursor is on L₁(1).
STAT1
Type 4 and press ENTER. Typing without pressing ENTER first replaced the old value 1.
4ENTER
The cursor is on the second row. Press ENTER to open the element in the entry line, type 10 over the old value and press ENTER.
ENTER10ENTER
On the third row, type an expression: 3+4. It is evaluated when you press ENTER.
3+4ENTER
The cursor is now on the empty row below the data. Press 2ndINS (INS) to insert a new element, which starts as 0.
2ndINS
Press DEL to delete the element again; the elements below it move up.
DEL

Attaching Formulas to List Namesp. 188

You can attach a formula to a list name so that the list is calculated from other lists and recalculated whenever they change. The formula must evaluate to a list. Chapter 11 explains the idea in detail; this section shows how to do it from the stat list editor.

Attaching a formula to a list name in the stat list editorp. 188

Open the stat list editor (STAT ENTER).
Press ▲︎ to move to the list-name row.
Use ◀︎ and ▶︎ to select the list that will hold the formula. If a formula in quotation marks already shows in the entry line, one is attached already; press ENTER to edit it.
Press ALPHA" for the opening quotation mark, type the formula, then press ALPHA" again for the closing mark.
Press ENTER. Every element is calculated and stored, and a lock symbol appears next to the list name.

Note Without the quotation marks the calculator computes the same list once but does not attach the formula, so later changes are not picked up. Any user-created list name inside a formula must carry the small ʟ symbol (Chapter 11); L₁ to L₆ do not.

Tutorial

Make L₂ always equal to 2 × L₁

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Open the editor, press ▲︎ for the name row and ▶︎ to select L₂.
STAT1▲︎▶︎
Type the formula in quotation marks: ALPHA", L₁ (2ndL1), ×, 2, ALPHA".
ALPHA"2ndL1×2ALPHA"
Press ENTER. L₂ is calculated and locked.
ENTER
Move left to L₁, down to its second element and enter 5. The formula list updates immediately.
◀︎▼︎5ENTER

Using the stat list editor when formula-generated lists are displayedp. 189

Editing an element of a list that a formula refers to updates the matching element of the formula list straight away. While a formula-generated list is on screen, every edit or entry in another visible list takes slightly longer, because the formula lists must be recalculated.

Tip To keep editing fast, scroll sideways until no formula list is in view, or rearrange the columns so formula lists are not displayed.

Handling errors resulting from attached formulasp. 189

On the home screen you can attach a formula that uses a list of dimension 0. However, the formula list cannot be displayed in the stat list editor or on the home screen until the list it depends on has at least one element.

Every element of a referenced list has to be valid for the formula. For example, with Real mode on and the formula log(L₁), every element of L₁ must be greater than 0, since the logarithm of a negative number is complex. When you use the shortcut templates, the values must suit the template: the n/d template needs an integer numerator and denominator.

If an error menu appears when you try to display a formula list in the editor, you have two ways out:

Select 2:Goto, write down the formula, then press CLEAR ENTER to detach it. Now you can use the editor to hunt for the faulty element, fix it, and re-attach the formula.
Select 1:Quit, show the referenced list on the home screen, find the faulty element and correct it there by storing to listname(element#) (Chapter 11).

Detaching a formula from a list namep. 190

A formula can be detached in several ways. Which elements stay behind depends on the method:

Method	Result
Select the list name in the editor and press `ENTER` `CLEAR` `ENTER`	All elements stay. The formula is gone and the lock symbol disappears.
Select an element of the list, press `ENTER`, edit it and press `ENTER`	That element changes, the formula is detached and the other elements stay.
`ClrList listname`	The elements of the named lists are cleared, their formulas are detached; the list names stay.
`ClrAllLists` (Chapter 18)	Every list in memory is cleared and loses its formula; all the names stay.

Tutorial

Detach a formula by editing one element

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Open the editor and move to the first element of L₂ (the cell shows a locked list).
STAT1▶︎
Press ENTER (required to edit a locked element), type 9 and press ENTER.
ENTER9ENTER
The formula is now detached. Change L₁(2) to 7 and check that L₂(2) stays at 4.
◀︎7ENTER

Tutorial

Detach a formula with ClrList

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Choose 4:ClrList on the STAT EDIT menu and enter L₂.
STAT42ndL2
Press ENTER. L₂ is emptied and no longer has a formula.
ENTER
Change L₁ in the stat list editor or store a new list in it: L₂ stays empty, because it no longer follows L₁.

Tutorial

Detach a formula from the list name

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Open the editor, press ▲︎ and ▶︎ to select the name L₂. The entry line shows the formula in quotation marks.
STAT1▲︎▶︎
Press ENTER CLEAR ENTER. The formula and the lock symbol go, but the elements 2, 4, 6 remain.
ENTERCLEARENTER

Editing an element of a formula-generated listp. 190

Because changing an element of a formula list detaches the formula, the calculator protects you from doing it by accident: you must press ENTER before you can type a new value into an element of such a list. It also refuses to delete an element of a list that has a formula. Detach the formula first (any method above) if you need to remove elements.

Switching Stat List Editor Contextsp. 190

The stat list editor works in four contexts. The keys have a different meaning in each one, and the entry line tells you which one you are in. The editor starts in view-elements context.

Context	What it is for
View-elements	Scroll the cells; the entry line shows the list name, the position and the full value of the current element.
View-names	Move across list names; the entry line shows the name and its elements. This is where you can remove or insert lists.
Edit-elements	Edit a single element, or the elements of the whole list.
Enter-name	The `Name=` prompt with alpha-lock on.

Tutorial

Walk through the four contexts

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Select 1:Edit from the STAT EDIT menu. You start in view-elements context.
STAT1
Press ▲︎ to move onto a list name: view-names context. Use ◀︎ and ▶︎ to look at other names.
▲︎
Press ENTER to switch to edit-elements context. All the elements of the list appear in braces on the entry line.
ENTER
Press ENTER again to return to view-elements context.
ENTER
Press ENTER once more to edit the current element in the entry line.
ENTER
Press ▲︎ until the cursor is on a list name, then 2ndINS to reach enter-name context.
▲︎▲︎2ndINS
Press CLEAR to leave the prompt without a name; you are back in view-names context.
CLEAR
Press ▼︎ to return to view-elements context.
▼︎

View-elements contextp. 192

The entry line shows the list name, the number of the current element and its full value, up to 12 characters at a time; an ellipsis (...) means the value continues. Useful keys here:

ALPHA▼︎ pages down six elements and ALPHA▲︎ pages up six elements.
DEL deletes the current element; those below it move up one row.
2ndINS (INS) inserts a new element with the default value 0.

Edit-elements contextp. 192

What the entry line shows depends on where you came from:

From view-elements context, it shows the full value of the current element. Edit it, then use ▼︎ and ▲︎ to edit other elements.
From view-names context, it shows all elements of the list in braces (with an ellipsis if they do not fit). Use ◀︎ and ▶︎ to reach any element.

Note A formula can only be attached to a list name when you entered edit-elements context from view-names context.

View-names contextp. 193

The entry line shows the list name and its elements. Press DEL to remove the list from the editor (the columns on the right move left one place; the list stays in memory). Press 2ndINS (INS) to insert a name in the current column; the others shift right one column.

Enter-name contextp. 193

The entry line shows the Name= prompt and alpha-lock is on. You can create a new list name, type one of L₁ to L₆, or paste an existing name from the LIST NAMES menu. The small ʟ is not required here. To leave without entering a name, press CLEAR; the editor goes back to view-names context.

STAT EDIT Menup. 193

Press STAT to open the STAT menu. It has three tabs, EDIT, CALC and TESTS; the EDIT tab (below) is the one shown first. CALC is described in STAT CALC Menu, and TESTS belongs to hypothesis testing (Chapter 13).

SortA( and SortD(p. 194

SortA(

SortA(listname)SortA(keylistname,dependlist1[,dependlist2,...,dependlist n])

Sorts list elements from low to high. With one list it sorts that list in memory. With two or more lists it sorts the first (key) list and then rearranges each dependent list into the same order, so paired data stay paired; all lists must have the same dimension. Complex lists are sorted by magnitude (modulus). The sorted lists are updated in memory.

Where: STAT 2:SortA( (also LIST OPS 1:SortA()

Keys: STAT2

SortA(L₁,L₂) sorts L₁ ascending and moves L₂ along with it.

SortD(

SortD(listname)SortD(keylistname,dependlist1[,dependlist2,...,dependlist n])

Sorts list elements from high to low, in the same two ways as SortA(. Complex lists are sorted by magnitude.

Where: STAT 3:SortD( (also LIST OPS 2:SortD()

Keys: STAT3

SortD(L₁) sorts L₁ from largest to smallest.

Note These are the same commands as SortA( and SortD( on the LIST OPS menu.

Tutorial

Sort data pairs with SortA( using L₁ as the key

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Choose 2:SortA( from the STAT menu.
STAT2
Enter the key list L₁, a comma and the dependent list L₂, then close the parenthesis.
2ndL1,2ndL2)
Press ENTER. L₁ is now {2,3,5} and L₂ was rearranged to {2,3,1} so each pair stayed together.
ENTER

Tutorial

Sort one list in descending order

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Choose 3:SortD( and enter L₁.
STAT32ndL1)
Press ENTER. L₁ becomes {5,3,2}.
ENTER

ClrListp. 194

ClrList

ClrList listname1,listname2,...,listname n

Clears (empties) the named lists in memory and detaches any formula attached to them. The list names stay. To empty every list at once use ClrAllLists (Chapter 18).

Where: STAT 4:ClrList

Keys: STAT4

ClrList L₁,L₂ empties both lists.

Tutorial

Clear two lists with ClrList

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Choose 4:ClrList from the STAT menu.
STAT4
Enter L₁, a comma and L₂.
2ndL1,2ndL2
Press ENTER. Both lists are now empty.
ENTER

SetUpEditorp. 194

SetUpEditor

SetUpEditor [listname1,listname2,...,listname n]

Removes every list name from the stat list editor and then stores the listed names in columns 1, 2, 3... in the order you give. You may give zero to 20 names. A name that does not exist yet is created in memory and added to the LIST NAMES menu. A name that is archived is unarchived automatically. With no arguments, L₁ to L₆ are restored to columns 1 to 6.

Where: STAT 5:SetUpEditor

Keys: STAT5

SetUpEditor L₂,L₁ shows L₂ in column 1 and L₁ in column 2.
SetUpEditor restores the six default lists.

Tutorial

Show only L₂ and L₁ in the editor, in that order

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Choose 5:SetUpEditor and enter the names in the order you want them.
STAT52ndL2,2ndL1
Press ENTER. The editor has been rebuilt with two columns.
ENTER
Open the editor. L₂ is in column 1 and L₁ in column 2.
STAT1

Regression Model Featuresp. 195

Items 3 through C of the STAT CALC menu (Med-Med to SinReg) are regression models. They all share two automatic features, the residual list and the regression equation, and some of them can also report diagnostics (r, r², R²).

Automatic residual listp. 195

Each time you run a regression model, the calculator computes the residuals and stores them in the list RESID. RESID then becomes an item on the LIST NAMES menu (2ndLIST, Chapter 11). Each residual is the data value minus the model value:

RESID = Ylistname − RegEQ(Xlistname)

RegEQ is explained next. RESID is overwritten by the next regression you run, so copy it to another list if you need to keep it.

Automatic regression equationp. 196

Every regression model has an optional last argument, regequ. Give it a Y= variable such as Y₁ and, when the command runs, the regression equation is stored in that variable and the Y= function is selected (turned on). In the stat wizard this argument is the Store RegEQ: field.

Whether or not you name a Y= variable, the equation is always stored in the variable RegEQ. It is item 1 on the EQ tab of the VARS Statistics menu (VARS5).

Note The Fix (fixed-decimal) setting on the MODE screen controls how many digits are stored after the decimal point in the regression equation. A very small number of digits can make the fit noticeably worse.

Diagnostics display modep. 196

Some regression models also compute a correlation coefficient r and the coefficient of determination r², or just R². They are always calculated and stored, but only shown in the result screen when diagnostics are switched on. The default is off.

Model	Diagnostics available
LinReg(ax+b), LinReg(a+bx), LnReg, ExpReg, PwrReg	r² and r
QuadReg, CubicReg, QuartReg	R²
Med-Med, Logistic, SinReg	none

Note For LnReg, ExpReg and PwrReg, r and r² are computed from the linearly transformed data. For ExpReg (y=ab^x) they describe the straight-line fit of ln y = ln a + x·ln b.

Turn the display on or off in either of two ways:

On the MODE screen, set STAT DIAGNOSTICS to ON or OFF.
Run DiagnosticOn or DiagnosticOff, both found in the CATALOG (2ndCATALOG).

DiagnosticOn

DiagnosticOn

Turns diagnostics on: regression results now also show r² and r (or R²) for the models that compute them. Same as setting STAT DIAGNOSTICS to ON on the MODE screen.

Where: 2ndCATALOG (CATALOG), then scroll to DiagnosticOn

DiagnosticOff

DiagnosticOff

Turns diagnostics off (the default): regression results show only the equation and coefficients. Same as setting STAT DIAGNOSTICS to OFF on the MODE screen.

Where: 2ndCATALOG (CATALOG), then scroll to DiagnosticOff

Tutorial

Turn on StatDiagnostics from the MODE screen

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Open the MODE screen and press ▼︎ twelve times to reach the STAT DIAGNOSTICS line.
MODE▼︎▼︎▼︎▼︎▼︎▼︎▼︎▼︎▼︎▼︎▼︎▼︎
Press ▶︎ to move onto ON and ENTER to select it.
▶︎ENTER
Return home. Run LinReg(ax+b) (STAT CALC item 4) with the wizard defaults: four ▼︎ presses reach Calculate.
2ndQUITSTAT▶︎4▼︎▼︎▼︎▼︎ENTER

Tutorial

Turn on diagnostics with DiagnosticOn from the CATALOG

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Open the CATALOG and jump to the D entries with the letter D (alpha lock is on in the CATALOG).
2ndCATALOGALPHAD
Scroll down ten items to DiagnosticOn (past dayOfWk(, dbd(, DEC, ►Dec, Degree, DelVar, DependAsk, DependAuto, det(, DiagnosticOff) and press ENTER to paste it.
▼︎▼︎▼︎▼︎▼︎▼︎▼︎▼︎▼︎▼︎ENTER
Press ENTER to run the instruction.
ENTER
Now run a regression: LinReg(ax+b) shows r² and r.
STAT▶︎4▼︎▼︎▼︎▼︎ENTER

STAT CALC Menup. 198

Press STAT ▶︎ to open the STAT CALC menu. After a calculation, the statistical variables are available from the VARS menu (Statistical Variables).

1:1-Var Stats	Calculates 1-variable statistics.
2:2-Var Stats	Calculates 2-variable statistics.
3:Med-Med	Calculates a median-median line.
4:LinReg(ax+b)	Fits a linear model to data.
5:QuadReg	Fits a quadratic model to data.
6:CubicReg	Fits a cubic model to data.
7:QuartReg	Fits a quartic model to data.
8:LinReg(a+bx)	Fits a linear model to data.
9:LnReg	Fits a logarithmic model to data.
0:ExpReg	Fits an exponential model to data.
A:PwrReg	Fits a power model to data.
B:Logistic	Fits a logistic model to data.
C:SinReg	Fits a sinusoidal model to data.
D:Manual-Fit	Fits a linear equation interactively to a scatter plot (shown as "Manual Linear Fit" in the manual).

Note The TESTS tab of the STAT menu holds the hypothesis tests and confidence intervals, described in Chapter 13.

For each item, if you give neither an Xlistname nor a Ylistname, the default lists are L₁ and L₂. If you give no freqlist, every list element counts once.

STAT WIZARDS in STAT CALCp. 198

When STAT WIZARDS is ON on the MODE screen (the default), choosing a STAT CALC item opens a wizard: a small form that asks for the required and optional arguments. Choose Calculate and the finished command is pasted to the home screen and its results appear in a temporary result view. Press CLEAR to dismiss the results; the pasted command stays in the home-screen history, and the statistical variables are in the VARS menu.

The wizard fields differ per command: List: and FreqList: for 1-Var Stats; Xlist:, Ylist: and FreqList: for 2-Var Stats; and for each regression model Xlist:, Ylist:, FreqList: and Store RegEQ: (SinReg adds Iterations: and Period:). Press ▼︎ to move to the next field.

Tutorial

Run 1-Var Stats through the stat wizard

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Press STAT, ▶︎ and choose 1:1-Var Stats.
STAT▶︎1
The data are in L₁, so List: is right. FreqList: is optional and can stay empty. Press ▼︎ twice to reach Calculate.
▼︎▼︎
Press ENTER. The statistics appear on a temporary result screen. Press ▼︎ to scroll through them.
ENTER
Scroll down to see the quartiles, median and extremes.
▼︎▼︎▼︎▼︎▼︎▼︎▼︎
Press CLEAR to clear the result view. The home screen holds the command that was run.
CLEAR

Tutorial

Turn STAT WIZARDS off and type the command yourself

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Open the MODE screen and press ▼︎ thirteen times to reach the STAT WIZARDS line.
MODE▼︎▼︎▼︎▼︎▼︎▼︎▼︎▼︎▼︎▼︎▼︎▼︎▼︎
Press ▶︎ to move onto OFF and press ENTER.
▶︎ENTER
Return home and choose 1:1-Var Stats again. This time the command is pasted on the home screen instead of opening a form.
2ndQUITSTAT▶︎1
Type the list name, L₁, and press ENTER. Without a list name the command would use L₁ anyway.
2ndL1ENTER

Note With STAT WIZARDS off, the default lists are L₁ and L₂ and an unspecified freqlist means one occurrence of each element. Commands inserted from the CATALOG are always pasted without a wizard, and in the program editor the wizard pastes the finished command into the program.

Frequency of occurrence for data pointsp. 199

Most STAT CALC items accept a freqlist. Each element tells how many times the matching data point (or data pair) occurs. For example, with L₁={15,12,9,14} and a frequency list {1,4,1,3}, 1-Var Stats L₁,freqlist means 15 occurs once, 12 four times, 9 once and 14 three times.

Every element of freqlist must be 0 or greater, and at least one must be greater than 0.
Non-integer frequencies are valid, for example frequencies written as percentages or parts that add up to 1.
With any non-integer frequency, Sx and Sy are undefined and are not displayed.

Tutorial

Use a frequency list with 1-Var Stats

The frequency list is kept in L₂ here; you may use any list of the same length (the manual example names it FREQ).

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Choose 1:1-Var Stats from the STAT CALC menu.
STAT▶︎1
Move down to FreqList: and enter L₂ with 2ndL2. Then move down onto Calculate.
▼︎2ndL2▼︎
Press ENTER. The nine data points are counted: n = 9, the sum is 114 and the mean is about 12.67.
ENTER
Press CLEAR to return to the home screen. The pasted command is in the history, ready to recall with 2ndENTRY if you want to run it again.
CLEAR

1-Var Statsp. 200

1-Var Stats

1-Var Stats [Xlistname,freqlist]

Analyzes data with one measured variable. Each element of freqlist (if given) is the number of times the matching Xlistname element occurs; the elements must be real numbers 0 or greater. Results: x̄, Σx, Σx², Sx, σx, n, minX, Q1, Med, Q3 and maxX. They are shown on a result screen and stored in the statistical variables.

Where: STAT ▶︎ 1:1-Var Stats

Keys: STAT▶︎1

1-Var Stats L₁ for the list L₁
1-Var Stats L₁,L₂ with L₂ as the frequency list

See STAT WIZARDS in STAT CALC and Frequency of occurrence for data points for walkthroughs, and Statistical Variables for the variable names.

2-Var Statsp. 200

2-Var Stats

2-Var Stats [Xlistname,Ylistname,freqlist]

Analyzes paired data. Xlistname is the independent variable and Ylistname the dependent one. Each element of freqlist is the number of times the data pair (X,Y) occurs. Results: x̄, Σx, Σx², Sx, σx, n, ȳ, Σy, Σy², Sy, σy, Σxy, minX, maxX, minY and maxY.

Where: STAT ▶︎ 2:2-Var Stats

Keys: STAT▶︎2

Tutorial

Calculate two-variable statistics

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Choose 2:2-Var Stats. The wizard asks for Xlist:, Ylist: and FreqList:.
STAT▶︎2
Press ▼︎ three times to get onto Calculate and press ENTER.
▼︎▼︎▼︎ENTER

Med-Med (ax+b)p. 200

Med-Med

Med-Med [Xlistname,Ylistname,freqlist,regequ]

Fits the model y=ax+b to the data with the median-median (resistant line) technique. It computes the summary points x₁, y₁, x₂, y₂, x₃ and y₃ (the medians of the lower, middle and upper thirds) and displays a (slope) and b (y-intercept). Outliers have little effect on this line.

Where: STAT ▶︎ 3:Med-Med

Keys: STAT▶︎3

Tutorial

Fit a median-median line

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Choose 3:Med-Med. The form has the usual four fields.
STAT▶︎3
Move to Store RegEQ: and paste Y₁ with ALPHAF4 ENTER.
▼︎▼︎▼︎ALPHAF4ENTER
Move onto Calculate and press ENTER. The summary points are (2,3), (5,7) and (8,11); the line has slope 4/3 and y-intercept 1/3.
▼︎ENTER

LinReg(ax+b)p. 201

LinReg(ax+b)

LinReg(ax+b) [Xlistname,Ylistname,freqlist,regequ]

Fits the model y=ax+b by least squares. Displays a (slope) and b (y-intercept); with DiagnosticOn it also shows r² and r.

Where: STAT ▶︎ 4:LinReg(ax+b)

Keys: STAT▶︎4

A complete example, including a residual plot, is in 3. Fit a line to the data. Here is the shortest possible use:

Tutorial

Fit a least-squares line and predict a value

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Choose 4:LinReg(ax+b), go to Store RegEQ: and paste Y₁.
STAT▶︎4▼︎▼︎▼︎ALPHAF4ENTER
Move onto Calculate and press ENTER. The slope is 1.5 and the intercept 1.3.
▼︎ENTER

QuadReg (ax²+bx+c)p. 201

QuadReg

QuadReg [Xlistname,Ylistname,freqlist,regequ]

Fits the second-degree polynomial y=ax²+bx+c to the data. It displays a, b and c; with DiagnosticOn it also shows R². With exactly three data points the result is a polynomial fit; with four or more it is a polynomial regression. At least three points are required.

Where: STAT ▶︎ 5:QuadReg

Keys: STAT▶︎5

Tutorial

Fit a parabola

The data come from y = 2x² − 3x + 1, so the fit is exact.

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Open the STAT CALC menu and choose QuadReg. The wizard form opens with L₁ and L₂ already filled in.
STAT▶︎5
Move down to Store RegEQ: and paste Y₁ with ALPHAF4 ENTER, so the fitted equation lands in the Y= editor.
▼︎▼︎▼︎ALPHAF4ENTER
Move onto Calculate and press ENTER. The result screen lists the coefficients.
▼︎ENTER

CubicReg (ax³+bx²+cx+d)p. 201

CubicReg

CubicReg [Xlistname,Ylistname,freqlist,regequ]

Fits the third-degree polynomial y=ax³+bx²+cx+d to the data. It displays a, b, c and d; with DiagnosticOn it also shows R². With four points the result is a polynomial fit; with five or more it is a polynomial regression. At least four points are required.

Where: STAT ▶︎ 6:CubicReg

Keys: STAT▶︎6

Tutorial

Fit a cubic

The data come from y = x³ − 2x.

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Open the STAT CALC menu and choose CubicReg. The wizard form opens with L₁ and L₂ already filled in.
STAT▶︎6
Move down to Store RegEQ: and paste Y₁ with ALPHAF4 ENTER, so the fitted equation lands in the Y= editor.
▼︎▼︎▼︎ALPHAF4ENTER
Move onto Calculate and press ENTER. The result screen lists the coefficients.
▼︎ENTER

QuartReg (ax⁴+bx³+cx²+dx+e)p. 202

QuartReg

QuartReg [Xlistname,Ylistname,freqlist,regequ]

Fits the fourth-degree polynomial y=ax⁴+bx³+cx²+dx+e to the data. It displays a, b, c, d and e; with DiagnosticOn it also shows R². With five points the result is a polynomial fit; with six or more it is a polynomial regression. At least five points are required.

Where: STAT ▶︎ 7:QuartReg

Keys: STAT▶︎7

Tutorial

Fit a quartic

The data come from y = x⁴ − x; L₂ is calculated from L₁ in the setup.

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Open the STAT CALC menu and choose QuartReg. The wizard form opens with L₁ and L₂ already filled in.
STAT▶︎7
Move down to Store RegEQ: and paste Y₁ with ALPHAF4 ENTER, so the fitted equation lands in the Y= editor.
▼︎▼︎▼︎ALPHAF4ENTER
Move onto Calculate and press ENTER. The result screen lists the coefficients.
▼︎ENTER

LinReg(a+bx)p. 202

LinReg(a+bx)

LinReg(a+bx) [Xlistname,Ylistname,freqlist,regequ]

Fits the model y=a+bx by least squares. Displays a (y-intercept) and b (slope); with DiagnosticOn it also shows r² and r. It gives the same line as LinReg(ax+b), with the coefficients named the other way round.

Where: STAT ▶︎ 8:LinReg(a+bx)

Keys: STAT▶︎8

Tutorial

Fit y = a + bx

The data come from y = 3 + 2x.

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Open the STAT CALC menu and choose LinReg(a+bx). The wizard form opens with L₁ and L₂ already filled in.
STAT▶︎8
Move down to Store RegEQ: and paste Y₁ with ALPHAF4 ENTER, so the fitted equation lands in the Y= editor.
▼︎▼︎▼︎ALPHAF4ENTER
Move onto Calculate and press ENTER. The result screen lists the coefficients.
▼︎ENTER

LnReg (a+b ln(x))p. 202

LnReg

LnReg [Xlistname,Ylistname,freqlist,regequ]

Fits the model y=a+b ln(x) by least squares, using the transformed values ln(x) and y. Displays a and b; with DiagnosticOn it also shows r² and r (computed on the transformed data). All X values must be greater than 0.

Where: STAT ▶︎ 9:LnReg

Keys: STAT▶︎9

Tutorial

Fit a logarithmic curve

L₂ is calculated as 2 + 3 ln(L₁), so the fit finds a = 2 and b = 3.

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Open the STAT CALC menu and choose LnReg. The wizard form opens with L₁ and L₂ already filled in.
STAT▶︎9
Move down to Store RegEQ: and paste Y₁ with ALPHAF4 ENTER, so the fitted equation lands in the Y= editor.
▼︎▼︎▼︎ALPHAF4ENTER
Move onto Calculate and press ENTER. The result screen lists the coefficients.
▼︎ENTER

ExpReg (ab^x)p. 202

ExpReg

ExpReg [Xlistname,Ylistname,freqlist,regequ]

Fits the model y=ab^x by least squares, using the transformed values x and ln(y). Displays a and b; with DiagnosticOn it also shows r² and r (computed on the transformed data). All Y values must be greater than 0.

Where: STAT ▶︎ 0:ExpReg

Keys: STAT▶︎0

Tutorial

Fit an exponential curve

L₂ is calculated as 2 × 1.5^L₁, so a = 2 and b = 1.5.

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Open the STAT CALC menu and choose ExpReg. The wizard form opens with L₁ and L₂ already filled in.
STAT▶︎0
Move down to Store RegEQ: and paste Y₁ with ALPHAF4 ENTER, so the fitted equation lands in the Y= editor.
▼︎▼︎▼︎ALPHAF4ENTER
Move onto Calculate and press ENTER. The result screen lists the coefficients.
▼︎ENTER

PwrReg (ax^b)p. 203

PwrReg

PwrReg [Xlistname,Ylistname,freqlist,regequ]

Fits the model y=ax^b by least squares, using the transformed values ln(x) and ln(y). Displays a and b; with DiagnosticOn it also shows r² and r (computed on the transformed data). All X and Y values must be greater than 0.

Where: STAT ▶︎ A:PwrReg

Keys: STAT▶︎ALPHAA

See 5. Try a power regression for a worked example with the pendulum data.

Tutorial

Fit a power curve

L₂ is calculated as 3 × L₁^0.5, so a = 3 and b = 0.5.

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Open the STAT CALC menu and choose PwrReg. The wizard form opens with L₁ and L₂ already filled in.
STAT▶︎ALPHAA
Move down to Store RegEQ: and paste Y₁ with ALPHAF4 ENTER, so the fitted equation lands in the Y= editor.
▼︎▼︎▼︎ALPHAF4ENTER
Move onto Calculate and press ENTER. The result screen lists the coefficients.
▼︎ENTER

Logistic (c/(1+a·e^(−bx)))p. 203

Logistic

Logistic [Xlistname,Ylistname,freqlist,regequ]

Fits the model y=c/(1+a·e^(−bx)) by an iterative least-squares procedure. Displays a, b and c; c is the limiting value the curve levels off at.

Where: STAT ▶︎ B:Logistic

Keys: STAT▶︎ALPHAB

Tutorial

Fit a logistic curve

L₂ comes from y = 10/(1+3e^(−0.5x)), so the fit finds a = 3, b = 0.5 and c = 10.

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Open the STAT CALC menu and choose Logistic. The wizard form opens with L₁ and L₂ already filled in.
STAT▶︎ALPHAB
Move down to Store RegEQ: and paste Y₁ with ALPHAF4 ENTER, so the fitted equation lands in the Y= editor.
▼︎▼︎▼︎ALPHAF4ENTER
Move onto Calculate and press ENTER. The result screen lists the coefficients.
▼︎ENTER

SinReg (a sin(bx+c)+d)p. 203

SinReg

SinReg [iterations,Xlistname,Ylistname,period,regequ]

Fits the model y=a·sin(bx+c)+d by an iterative least-squares procedure. Displays a, b, c and d. At least four data points are required, and at least two per cycle to avoid an aliased (wrong) frequency.

Where: STAT ▶︎ C:SinReg

Keys: STAT▶︎ALPHAC

iterations is the maximum number of passes of the algorithm: an integer from 1 to 16 (default 3). The search may stop sooner. More iterations usually take longer but give a better fit.
period is an optional first guess for the length of one cycle. If you leave it out, the X values must be equally spaced and in increasing order. If you give it, the X values may be unevenly spaced, and the search may converge faster or may succeed where it would otherwise fail.
The output is always in radians, whatever the Radian/Degree mode setting.

Tip For noisy data, give an accurate period. To estimate it, plot the data, trace to find the X distance spanned by one cycle (or by N cycles, divided by N). After a first run that looks roughly right but not optimal, run SinReg 16,Xlistname,Ylistname,2π/b with the b you obtained, to refine the fit.

SinReg example: hours of daylight in Alaskap. 204

The hours of daylight at a place in Alaska follow a smooth yearly cycle, which is a good job for SinReg. The tutorial uses stand-in data with the same shape (12 readings at 30-day intervals, generated from a sine wave with a 365-day period) so that you can check the answer. The period guess is 365 days.

Tutorial

Fit a yearly daylight cycle with SinReg

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Choose C:SinReg. The form has five fields: Iterations: (default 3), Xlist:, Ylist:, Period: and Store RegEQ:.
STAT▶︎ALPHAC
Ask for the maximum 16 iterations: type 1 6 on the first line.
16
Move down to Period: and enter the guess, 365.
▼︎▼︎▼︎365
Move to Store RegEQ: and paste Y₁ with ALPHAF4 ENTER.
▼︎ALPHAF4ENTER
Move onto Calculate and press ENTER. The amplitude a is about 6.4, b about 2π/365 = 0.0172 and d about 12.2 hours.
▼︎ENTER

Manual Linear Fitp. 205

Manual Linear Fit lets you fit a line to a scatter plot by eye. It is item D on the STAT CALC menu. First enter the list data and display the stat plot, then start Manual-Fit.

Manual-Fit

Manual-Fit [equname]

Draws a line through two points that you pick on the displayed scatter plot and shows its equation as Y=mX+b. You can then change m and b by hand. When you finish with 2ndQUIT the equation is stored in Y₁, or in the Y= variable you gave as equname (for example Y₄), and that function is selected for graphing.

Where: STAT ▶︎ D:Manual-Fit

Keys: STAT▶︎ALPHAD

Manual-Fit Y₄ stores the fitted line in Y₄.

Press STAT, ▶︎ for CALC and choose D:Manual-Fit. On the home screen it is pasted (you may add a Y= variable such as Y₄ after it); press ENTER and the graph screen opens with a free-floating cursor in the centre.
Use the cursor keys to move the cursor to the first point and press ENTER.
Move the cursor to a second location and press ENTER. A line through the two points is drawn and its equation is shown in the form Y=mX+b, with the first parameter, m, highlighted.
To change a parameter, use ◀︎ and ▶︎ to switch between m and b, then type a new value (or press ENTER and then type; it may be an expression) and press ENTER. The value is stored and the graph is redrawn with the new line.
Press 2ndQUIT (QUIT) to finish. The line mX+b is stored in Y₁ (or the Y= variable you chose) and selected.

Tutorial

Fit a line by hand and change its slope

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Choose D:Manual-Fit from the STAT CALC menu. It is pasted to the home screen.
STAT▶︎ALPHAD
Press ENTER to start it. The graph of the scatter plot appears with a cursor in the centre of the screen.
ENTER
Move the cursor to the lower left of the data (20 steps left, 3 down) and press ENTER to mark the first point.
◀︎◀︎◀︎◀︎◀︎◀︎◀︎◀︎◀︎◀︎◀︎◀︎◀︎◀︎◀︎◀︎◀︎◀︎◀︎◀︎▼︎▼︎▼︎ENTER
Move the cursor to the upper right (40 steps right, 16 up) and press ENTER. The line through the two points appears.
▶︎▶︎▶︎▶︎▶︎▶︎▶︎▶︎▶︎▶︎▶︎▶︎▶︎▶︎▶︎▶︎▶︎▶︎▶︎▶︎▶︎▶︎▶︎▶︎▶︎▶︎▶︎▶︎▶︎▶︎▶︎▶︎▶︎▶︎▶︎▶︎▶︎▶︎▶︎▶︎▲︎▲︎▲︎▲︎▲︎▲︎▲︎▲︎▲︎▲︎▲︎▲︎▲︎▲︎▲︎▲︎ENTER
The line passes through the points you chose. Type 2 and press ENTER to replace the highlighted slope m by 2.
2ENTER
Press 2ndQUIT (QUIT) to finish. The equation 2X+b is now stored in Y₁ and selected.
2ndQUIT

Statistical Variablesp. 206

Every STAT CALC calculation stores its results in statistical variables. To use one in an expression, press VARS, choose 5:Statistics and then pick the variable from one of the tabs: XY, Σ, EQ, TEST or PTS. Editing a list or running a different kind of analysis clears all the statistical variables.

Which calculation produces which variable, and where to find it on the VARS Statistics menu
Variable	1-Var Stats	2-Var Stats	Other	VARS tab
mean of x values	x̄	x̄		XY
sum of x values	Σx	Σx		Σ
sum of x² values	Σx²	Σx²		Σ
sample standard deviation of x	Sx	Sx		XY
population standard deviation of x	σx	σx		XY
number of data points	n	n		XY
mean of y values		ȳ		XY
sum of y values		Σy		Σ
sum of y² values		Σy²		Σ
sample standard deviation of y		Sy		XY
population standard deviation of y		σy		XY
sum of x × y		Σxy		Σ
minimum of x values	minX	minX		XY
maximum of x values	maxX	maxX		XY
minimum of y values		minY		XY
maximum of y values		maxY		XY
1st quartile	Q1			PTS
median	Med			PTS
3rd quartile	Q3			PTS
regression/fit coefficients			a, b	EQ
polynomial, Logistic and SinReg coefficients			a, b, c, d, e	EQ
correlation coefficient			r	EQ
coefficient of determination			r², R²	EQ
regression equation			RegEQ	EQ
summary points (Med-Med only)			x₁, y₁, x₂, y₂, x₃, y₃	PTS

Note Q1 and Q3: the first quartile (Q1) is the median of the data points from minX up to the median Med, and the third quartile (Q3) is the median of the points from Med up to maxX.

Tutorial

Use statistical variables in an expression

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

The setup ran 1-Var Stats L₁. Open VARS and choose 5:Statistics. The XY tab opens first.
VARS5
Choose 2:x̄ (the mean of x). It is pasted to the home screen. Multiply it by 2 and press ENTER.
2×2ENTER
Now use a variable from the Σ tab: open VARS 5, press ▶︎ for Σ, choose 1:Σx and press ENTER. The sum of the data is 15.
VARS5▶︎1ENTER
The quartiles are on the PTS tab. Press ◀︎ from the first tab to wrap round to PTS and choose 7:Q₁.
VARS5◀︎7ENTER

Statistical Analysis in a Programp. 207

Statistical data can be entered, analysed and fitted by a program, just as on the home screen. You can fill lists directly inside the program (see Chapter 11).

To put a calculation in a program, start on a blank line of the program editor and:

Choose the calculation from the STAT CALC menu. In the program editor the stat wizard pastes the finished command into the program instead of running it.
Give the names of the lists to use, separated by commas.
If you want the regression equation in a Y= variable, add a comma and the variable name.

Tutorial

Write and run a program that fits a line

The program STATS stores two lists and runs LinReg(ax+b), storing the line in Y₁.

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Press PRGM, move to the NEW tab with ▶︎ ▶︎ and choose 1:Create New. The Name= prompt opens with alpha-lock on.
PRGM▶︎▶︎1
Type STATS (the green letters on LN, 4, MATH, 4, LN) and press ENTER. The program editor opens.
LN4MATH4LNENTER
On the first line enter the x-data list: {1,2,3,4,5}→L₁.
2nd{1,2,3,4,52nd}STO►2ndL1ENTER
On the next line enter the y-data: {3,5,4,8,9}→L₂.
2nd{3,5,4,8,92nd}STO►2ndL2ENTER
Now choose 4:LinReg(ax+b) from the STAT CALC menu. In a program the wizard offers Paste instead of Calculate.
STAT▶︎4
Go to Store RegEQ:, paste Y₁, move onto Paste and press ENTER. The command LinReg(ax+b) L₁,L₂,,Y₁ is inserted in the program.
▼︎▼︎▼︎ALPHAF4ENTER▼︎ENTER
Leave the editor with 2ndQUIT (QUIT). Press PRGM and choose the program from the EXEC menu, then ENTER to run it.
2ndQUITPRGM1ENTERENTER

Note In a program the results of a stat calculation are written to the home screen. A program can also define stat plots (Statistical Plotting in a Program).

Statistical Plottingp. 208

You can plot data stored in lists and have up to three stat plots defined at once. There are six types: scatter plot, xyLine, histogram, modified box plot, regular box plot and normal probability plot. The steps are always the same:

Store the data in one or more lists.
Select or deselect Y= functions as needed (selected functions are drawn with the plots).
Define the stat plot.
Turn on the plots you want.
Set the viewing window.
Display the graph and explore it.

The six plot types and the settings each one asks for
Plot type	Xlist	Ylist	Mark	Freq	Data List	Data Axis
Scatter	yes	yes	yes
xyLine	yes	yes	yes
Histogram	yes			yes
ModBoxplot	yes		yes	yes
Boxplot	yes			yes
NormProbPlot			yes		yes	yes

Scatterp. 208

A scatter plot draws each pair from Xlist and Ylist as a point, shown as a box, a cross (+) or a dot. Xlist and Ylist must have the same length. The same list may be used for both. A complete example is in 2. Plot the data as a scatter plot.

xyLinep. 208

xyLine is a scatter plot whose points are joined by line segments in the order they appear in Xlist and Ylist. You will usually want to sort the lists first with SortA( or SortD( so the line runs left to right.

Tutorial

Sort the data and draw an xyLine plot

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

The points are not in order of X. Sort L₁ ascending and carry L₂ along: SortA(L₁,L₂).
STAT22ndL1,2ndL2)ENTER
Open the Plot1 editor and turn the plot on.
2ndSTAT PLOT1◀︎ENTER
Move down to Type:, press ▶︎ once to choose xyL (xyLine) and press ENTER.
▼︎▶︎ENTER
Set Xlist: to L₁ and Ylist: to L₂, then choose the + mark.
▼︎2ndL1▼︎2ndL2▼︎▶︎ENTER
Return home and press ZOOM 9 to draw the connected points.
2ndQUITZOOM9

Histogramp. 209

A histogram plots one-variable data as bars. The window variable Xscl is the width of each bar, and the first bar starts at Xmin. A value that falls exactly on the edge between two bars is counted in the bar to its right. ZoomStat sets Xmin, Xmax, Ymin and Ymax to include all the data and also adjusts Xscl.

Note The window must satisfy (Xmax − Xmin) ÷ Xscl ≤ 47, otherwise there would be too many bars to draw and you get an error.

Tutorial

Draw a histogram and change the bar width

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Open the Plot1 editor and turn the plot on.
2ndSTAT PLOT1◀︎ENTER
Move down to Type:, press ▶︎ twice to reach Hist (histogram) and press ENTER. The form now asks for Xlist: and Freq:.
▼︎▶︎▶︎ENTER
Set Xlist: to L₁ and leave Freq: at 1 (each value counts once).
▼︎2ndL1
Return home and run ZoomStat. The window is fitted to the data: X from 1 to 10 with bars 1 wide.
2ndQUITZOOM9
Open WINDOW, move down to Xscl=, type 2 and press ENTER to make the bars 2 wide. Then redraw with GRAPH.
WINDOW▼︎▼︎2ENTERGRAPH
Press TRACE. The cursor moves from the top centre of one bar to the next, starting at the first bar. Press ▶︎ to step to the second bar.
TRACE▶︎

ModBoxplotp. 209

A modified box plot plots one-variable data like the regular box plot, except that points more than 1.5 × the interquartile range beyond the quartiles are drawn separately, using the mark you chose (box, + or dot). These points are the outliers, and you can trace to them. The interquartile range is Q3 − Q1.

When you trace a modified box plot, the prompt for an outlier is x=, except when the outlier is the maximum (maxX) or minimum (minX). If outliers exist, the end of each whisker also shows x=; with no outliers the whisker ends show minX and maxX. Q1, Med (the median) and Q3 define the box.

Box plots depend on Xmin and Xmax but ignore Ymin and Ymax. With two box plots on, the first is drawn at the top of the screen and the second in the middle; with three, the third is at the bottom.

Tutorial

Draw a modified box plot and trace to the outlier

The value 9 is far above the other data (Q3 is 4 and the interquartile range is 2, so values above 7 are outliers).

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Open the Plot1 editor, turn the plot on and choose MBox (ModBoxplot) as the type: ▶︎ three times from Scat.
2ndSTAT PLOT1◀︎ENTER▼︎▶︎▶︎▶︎ENTER
Set Xlist: to L₁, keep Freq: at 1 and the box mark.
▼︎2ndL1▼︎▼︎
Return home and run ZoomStat.
2ndQUITZOOM9
Press TRACE. Tracing starts at Med. Press ▶︎ to move to Q3 and further right to the whisker end and the outlier.
TRACE▶︎▶︎▶︎

Boxplotp. 209

A regular box plot plots one-variable data. Its whiskers extend from the minimum data point (minX) to the first quartile (Q1) and from the third quartile (Q3) to the maximum (maxX). The box is defined by Q1, Med (the median) and Q3. It uses Xmin and Xmax and ignores Ymin and Ymax. When two box plots are on, the first is at the top of the screen and the second in the middle; with three, the first is at the top, the second in the middle and the third at the bottom.

Tutorial

Draw a box plot and trace it

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Open the Plot1 editor, turn the plot on and choose Box (Boxplot), which is the fifth type.
2ndSTAT PLOT1◀︎ENTER▼︎▶︎▶︎▶︎▶︎ENTER
Set Xlist: to L₁ and keep Freq: at 1.
▼︎2ndL1
Return home and run ZoomStat to draw the box plot.
2ndQUITZOOM9
Press TRACE: the cursor starts on Med (the median). Press ◀︎ to trace to Q1 and then minX, or ▶︎ to trace to Q3 and then maxX.
TRACE◀︎

NormProbPlotp. 210

A normal probability plot shows each observation X in Data List against the matching quantile z of the standard normal distribution. If the points lie close to a straight line, the data are roughly normally distributed.

Enter a list name for Data List: and choose X or Y for Data Axis:. With X the data are plotted along the x-axis and the z-values on the y-axis; with Y it is the other way round.

Tutorial

Draw a normal probability plot

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Open the Plot1 editor, turn the plot on and choose NPP (NormProbPlot), the sixth type.
2ndSTAT PLOT1◀︎ENTER▼︎▶︎▶︎▶︎▶︎▶︎ENTER
Set Data List: to L₁. Move down to Data Axis: and select X with ENTER.
▼︎2ndL1▼︎ENTER
Return home and run ZoomStat.
2ndQUITZOOM9

Defining the plotsp. 210

To define a stat plot:

Press 2ndSTAT PLOT (STAT PLOT). The STAT PLOTS menu shows the current definition of each plot.
Choose the plot you want. Its stat plot editor appears.
Select On to plot the data right away. The definition is stored whether you pick On or Off.
Select the type of plot. The editor then asks for the settings shown in the table above.
Fill in the list names or choices: Xlist: (independent data), Ylist: (dependent data), Mark: (box, + or dot), Freq: (frequency list for the Xlist elements; the default is 1), Data List: and Data Axis: (NormProbPlot).

Note The STAT TYPE and STAT PLOT MARK menus are the other two tabs of the STAT PLOTS menu. They are used when you define a stat plot inside a program (Statistical Plotting in a Program); in the stat plot editor you choose the type and mark directly with the cursor keys.

Displaying other stat plot editorsp. 211

Each plot has its own editor, and the name of the current one (Plot1, Plot2 or Plot3) is highlighted on the top line. To open the editor of a different plot, press ▲︎ and ▶︎ or ◀︎ to put the cursor on that name in the top line, then press ENTER. The editor for that plot is displayed and its name stays highlighted.

Turning on and turning off stat plotsp. 212

PlotsOff

PlotsOff [1,2,3]

Turns off stat plots from the home screen or a program. With no plot number it turns off all plots; with one or more plot numbers (1, 2, 3) it turns off just those plots.

Where: 2ndSTAT PLOT 4:PlotsOff

Keys: 2ndSTAT PLOT4

PlotsOff turns off every stat plot.
PlotsOff 1,3 turns off Plot1 and Plot3.

PlotsOn

PlotsOn [1,2,3]

Turns on stat plots from the home screen or a program. With no plot number it turns on all plots; with one or more plot numbers it turns on just those plots.

Where: 2ndSTAT PLOT 5:PlotsOn

Keys: 2ndSTAT PLOT5

PlotsOn 2 turns on Plot2.

Note You can also turn stat plots on and off in the top line of the Y= editor (Chapter 3): press ▲︎ from the first function, move onto the plot name and press ENTER.

Tutorial

Turn all stat plots off and back on

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Plot 1 is on. Choose 4:PlotsOff from the STAT PLOTS menu and press ENTER.
2ndSTAT PLOT4ENTER
With every plot off, ZoomStat has nothing to fit and reports an error.
ZOOM9
Quit the error, then choose 5:PlotsOn and press ENTER to turn the plot back on.
12ndSTAT PLOT5ENTER
ZoomStat now works.
ZOOM9

Defining the viewing windowp. 212

Stat plots are drawn on the current graph, so the viewing window matters. Press WINDOW and enter the window variables, or let ZoomStat choose a window that shows all the statistical data points.

ZoomStat

ZoomStat

Redefines the viewing window so that all the data points of the stat plots that are turned on are visible. For a histogram it also adjusts Xscl. It reports an error if no stat plot is on.

Where: ZOOM 9:ZoomStat

Keys: ZOOM9

See 2. Plot the data as a scatter plot.

Tracing a stat plotp. 212

Press TRACE to explore a stat plot:

Scatter plot or xyLine: tracing starts at the first element of the lists and moves from point to point.
Histogram: the cursor moves from the top centre of one bar to the top centre of the next, starting at the first bar.
Box plot: tracing starts at Med (the median). ◀︎ moves to Q1 and then minX; ▶︎ moves to Q3 and then maxX.
When you press ▲︎ or ▼︎ to move to another plot or another Y= function, the cursor jumps to the current or beginning point of that plot, not to the nearest pixel.

The ExprOn/ExprOff format setting (2ndFORMAT, Chapter 3) also applies to stat plots: with ExprOn, the plot number and the plotted lists are shown in the top-left corner while you trace.

Select( : choosing part of a plotp. 171

Select( is documented with the list operations in Chapter 11, but it works directly on a displayed scatter plot or xyLine plot, so a short version is given here. It lets you trace to a left and right bound on the plot and copies the points in between into two new lists, which you can then analyse.

Select(

Select(xlistname,ylistname)

Selects points from a scatter or xyLine plot and stores them in the two named lists. A scatter plot or xyLine plot must be on and displayed in the current window. You trace to the left bound point and press ENTER, then to the right bound point and press ENTER; the left bound must not be to the right of the right bound. The chosen x and y values (both bounds included) go into xlistname and ylistname, and a new stat plot of those lists replaces the original plot.

Where: 2ndLIST ▶︎ 8:Select(

Keys: 2ndLIST▶︎8

Tutorial

Select a stretch of points from a scatter plot

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

On the home screen choose 8:Select( from the LIST OPS menu.
2ndLIST▶︎8
Name the two lists that will receive the selected points, L₃ and L₄, and close the parenthesis. Press ENTER. The graph appears with Left Bound? at the bottom.
2ndL3,2ndL4)ENTER
The cursor is on the first point. Move to the second point with ▶︎ and press ENTER to mark it as the left bound. Right Bound? is now shown.
▶︎ENTER
Move two points to the right (the fourth point) and press ENTER. Points 2, 3 and 4 are stored in L₃ and L₄.
▶︎▶︎ENTER

Statistical Plotting in a Programp. 212

A program defines a stat plot with the Plot1(, Plot2( or Plot3( instruction and then displays the graph. These commands are not usually typed letter by letter; they are pasted from the STAT PLOTS menu.

Plot1(

Plot1(Scatter,Xlistname,Ylistname,mark)Plot1(xyLine,Xlistname,Ylistname,mark)Plot1(Histogram,Xlistname,freqlist)Plot1(ModBoxplot,Xlistname,freqlist,mark)Plot1(Boxplot,Xlistname,freqlist)Plot1(NormProbPlot,Datalistname,Data axis,mark)

Defines and turns on stat plot 1. The first argument is the plot type, followed by the lists and, for the types that use it, the mark (box, + or dot). Plot2( and Plot3( work the same way for plots 2 and 3. Define the plot first, then display it with DispGraph or a ZOOM instruction.

Where: 2ndSTAT PLOT 1:Plot1... (pastes Plot1( in the program editor)

Keys: 2ndSTAT PLOT1

Plot1(Scatter,L₁,L₂,+)

Plot2(

Plot2(type,list arguments,mark)

Defines and turns on stat plot 2. It takes the same arguments as Plot1(.

Where: 2ndSTAT PLOT 2:Plot2...

Keys: 2ndSTAT PLOT2

Plot3(

Plot3(type,list arguments,mark)

Defines and turns on stat plot 3. It takes the same arguments as Plot1(.

Where: 2ndSTAT PLOT 3:Plot3...

Keys: 2ndSTAT PLOT3

To define a stat plot in a program, start on a blank program line (after entering the data into lists) and:

Press 2ndSTAT PLOT to open the STAT PLOTS menu.
Choose the plot to define. Plot1(, Plot2( or Plot3( is pasted at the cursor.
Press 2ndSTAT PLOT ▶︎ to open the STAT TYPE menu and choose the type of plot. The type name is pasted.
Press , and enter the list names, separated by commas.
Press ,, then 2ndSTAT PLOT ◀︎ to open the STAT PLOT MARK menu, and choose the mark for the data points. (Skip this for a Histogram or a Boxplot.)
Press ) ENTER to finish the line.

Tutorial

Define a stat plot in a program

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Start a new program called PLOT: PRGM, ▶︎ ▶︎, 1:Create New, then the name (P = 8, L = ), O = 7, T = 4) and ENTER.
PRGM▶︎▶︎18)74ENTER
Paste Plot1( from the STAT PLOTS menu.
2ndSTAT PLOT1
Open the STAT TYPE menu with 2ndSTAT PLOT ▶︎ and choose 1:Scatter.
2ndSTAT PLOT▶︎1
Type the list names: comma, L₁, comma, L₂, comma.
,2ndL1,2ndL2,
Open the STAT PLOT MARK menu with 2ndSTAT PLOT ◀︎ and choose the + mark (item 2).
2ndSTAT PLOT◀︎2
Close the parenthesis and press ENTER. Add ZoomStat on the next line (press ZOOM 9) to display the plot when the program runs.
)ENTERZOOM9ENTER
Quit the editor and run the program from the EXEC menu.
2ndQUITPRGM1ENTERENTER

Displaying a stat plot from a programp. 213

A defined plot is only drawn when the graph is displayed. In a program, use the DispGraph instruction (Chapter 16) or any of the ZOOM instructions (Chapter 3), for example ZoomStat, which also fits the window to the data.

Common Errors in Statistics

These are the error messages you are most likely to meet when working with lists, stat calculations and stat plots. All of them are explained in full in the error list in Appendix B.

Error	Typical cause in this chapter
DIM MISMATCH	Xlist and Ylist (or a freqlist, or the lists given to SortA( and SortD( together) do not have the same number of elements.
STAT	A statistical calculation or plot cannot be done: for example ZoomStat when no stat plot is on, or a regression with too few data points (QuadReg needs 3, CubicReg 4, QuartReg 5, SinReg 4).
DOMAIN	A value is outside what a model allows, for example LnReg or PwrReg with an X value of 0 or less, or ExpReg and PwrReg with a Y value of 0 or less.
DATA TYPE	A list was expected but something else was given, or an element of a list is not a real number where one is needed.
Formula errors in the list editor	An error menu appears when a formula-generated list cannot be displayed. Select `2:Goto` to find the formula or `1:Quit` to leave (see Handling errors resulting from attached formulas).

1:Edit...	Displays the stat list editor.
2:SortA(	Sorts a list in ascending order.
3:SortD(	Sorts a list in descending order.
4:ClrList	Deletes all elements of a list.
5:SetUpEditor	Stores specified lists in the stat list editor.

1:Scatter	Scatter plot.
2:xyLine	Scatter plot with points joined in list order.
3:Histogram	Histogram of one-variable data.
4:ModBoxplot	Modified box plot with outliers.
5:Boxplot	Regular box plot.
6:NormProbPlot	Normal probability plot.

1:□	Box mark.
2:+	Cross mark.
3:·	Dot mark.