Chapter 11: Lists

Using the Built-in List Names L₁ through L₆p. 162

The calculator always has six lists named L₁, L₂, L₃, L₄, L₅ and L₆. They are the second functions of the number keys 1 to 6: press 2nd and then the digit to paste the name, for example 2ndL1 for L₁.

After a memory reset, L₁ through L₆ are stored in columns 1 through 6 of the stat list editor (see the Statistics chapter).

Creating a List Name on the Home Screenp. 162

To make a new list on the home screen, type its elements inside braces, separated by commas, then store it with STO► under a name. The elements can be real numbers, complex numbers or expressions.

1. Press 2nd{ to type {, enter one or more elements separated by commas, then press 2nd} to type }.
2. Press STO►.
3. Type the first letter of the name: any letter A to Z or θ (press ALPHA first).
4. Type up to four more letters, θ or digits to finish the name.
5. Press ENTER. The list is shown on the next line, and its name and elements are stored. The name is added to the LIST NAMES menu.

Other Places to Create a List Namep. 163

Besides the home screen, you can create a new list name in four other places:

• At the Name= prompt in the stat list editor.
• At an Xlist:, Ylist: or Data List: prompt in the stat plot editor.
• At a List:, List1:, List2:, Freq:, Freq1:, Freq2:, XList: or YList: prompt in the inferential statistics editors.
• On the home screen with SetUpEditor.

You can create as many lists as the memory of the calculator has room for.

Storing Elements to a Listp. 163

There are two ways to fill a list: type braces and STO► on the home screen (as above), or type values straight into the stat list editor (see the Statistics chapter).

A list can hold at most 999 elements.

Displaying a List on the Home Screenp. 163

Type the name of the list (with the ʟ symbol in front of a user-created name if needed) and press ENTER. If the list is too long for the screen, an ellipsis (...) appears at the end. Press ▶︎ repeatedly, or hold it down, to scroll through all the elements.

Copying One List to Anotherp. 163

To copy a list, store it into another list name: L₁→L₂ makes L₂ an exact copy of L₁ (and replaces whatever L₂ held).

Accessing a List Elementp. 164

Write the position of the element in parentheses after the list name: listname(element). You can read an element, or store a value into it. You may store to any position inside the current list, or to the position one past the end, which makes the list one element longer. Going further than that is an error.

Deleting a List from Memoryp. 164

To delete lists from memory, including L₁ to L₆, use the Memory Management / Delete menu (2ndMEM is MEM, then choose Mem Mgmt/Del...). Resetting memory brings L₁ to L₆ back. Removing a list from the stat list editor does not delete it from memory.

Using Lists in Graphingp. 164

To graph a whole family of curves at once you can put a list inside a Y= expression, or use the Transformation Graphing application (see the Function Graphing chapter for lists in Y=).

Using the LIST NAMES Menup. 164

The LIST NAMES menu starts with L₁ to L₆ and then lists every user-created list, sorted alphanumerically automatically. Only the first ten items are labelled, using the digits 1 to 9 and then 0. To jump to the first list whose name starts with a letter, press ALPHA and that letter (or θ).

Picking a name pastes it at the cursor. On the home screen (where other kinds of data are also valid) the name is pasted with the ʟ symbol in front. In places where only a list name makes sense, such as the Name= prompt of the stat list editor or the Xlist: and Ylist: prompts of the stat plot editor, it is pasted without ʟ.

Entering a User-Created List Name Directlyp. 165

1. Open the LIST OPS menu with 2ndLIST▶︎.
2. Choose item B:ʟ. It pastes the small ʟ symbol at the cursor (it is not always needed).
3. Type the letters and digits of the list name.

Attaching a Formula to a List on the Home Screen or in a Programp. 166

1. From a blank line, type an opening quotation mark with ALPHA", enter the formula (it must evaluate to a list), then type a closing quotation mark with ALPHA".
2. Press STO►.
3. Enter the name of the list that will carry the formula: L₁ to L₆ with 2nd and a digit, a user list from the LIST NAMES menu, or a user list typed directly after the ʟ symbol.
4. Press ENTER.

Detaching a Formula from a Listp. 166

There are several ways to remove an attached formula (the list keeps its current values):

• On the home screen, enter two quotation marks followed by STO► and the list name: ""→listname.
• Edit any element of the list.
• Remove it in the stat list editor (see the Statistics chapter).
• Use ClrList or ClrAllList (see the Memory chapter).

Using Lists with Math Functionsp. 167

Many math functions accept a list in place of a value (the function reference in Appendix A tells you which). The function is applied to each element and a list comes back.

• One list: the function must be valid for every element. A bad element makes the whole calculation an error. (In graphing, an invalid element is simply skipped: graphing Y₁=√({1,0,⁻1})X plots √1·X and √0·X but leaves out the invalid √⁻1·X.)
• Two lists with a two-argument function: the two lists must have the same dimension. The function is applied to corresponding elements.
• A list and a single value with a two-argument function: the single value is used together with every element of the list.

SortA( and SortD(p. 168

SortA( sorts from low to high, SortD( from high to low. A complex list is sorted by the size (modulus) of its elements.

With one list, the list itself is sorted and the new order is saved in memory. With two or more lists, the first (the key list) is sorted and every dependent list is rearranged to keep its elements lined up with the key list. All the lists must have the same dimension.

Using dim( to Find or Set a List Dimensionp. 169

Fill(p. 170

seq(p. 170

seq( evaluates an expression for each value of a variable from begin to end, stepping by increment, and returns the results as a list. The variable need not exist in memory. The increment may be negative, and defaults to 1. You cannot use seq( inside the expression, and complex lists are not valid.

cumSum(p. 170

ΔList(p. 171

Select(p. 171

Select( lets you pick a stretch of points from a plotted scatter or xyLine plot with the cursor and copies just those points into two lists. This is handy for analysing part of a data set, such as one section of data collected with a CBL 2, CBL or CBR.

Before using Select(:

1. Create two lists and enter the data.
2. Turn on a stat plot, choose a scatter plot or xyLine plot, and set Xlist: and Ylist: to the two lists (see the Statistics chapter).
3. Draw the plot with ZoomStat (see the Function Graphing chapter) so that all the points are visible.

Selecting the points:

1. From LIST OPS choose 8:Select(. It is pasted on the home screen.
2. Enter xlistname, a comma, ylistname and a closing parenthesis. These are the lists the selected data will be stored into.
3. Press ENTER. The graph appears with Left Bound? in the lower-left corner.
4. If more than one stat plot is on, use ▲︎ or ▼︎ to move the cursor to the plot you want.
5. Use ◀︎ and ▶︎ to move the cursor to the first point you want, then press ENTER. A ► marker shows the left bound and Right Bound? appears.
6. Move the cursor to the last point you want and press ENTER.

The x-values and y-values of the chosen points go into the two lists, and a new stat plot of those lists replaces the old one (the list names are updated in the stat plot editor). The new lists include the points you chose as the left and right bounds. The x-value of the left bound must be less than or equal to the x-value of the right bound.

augment(p. 173

List►matr(p. 173

Matr►list(p. 174

ʟ (the list-name symbol)p. 174

You generally need ʟ in front of a user-created list name wherever other kinds of input are also valid, such as on the home screen. Without it the calculator could read the letters as several variables multiplied together.

Where only a list name makes sense, such as the Name= prompt in the stat list editor or the Xlist: and Ylist: prompts in the stat plot editor, ʟ is not needed. If you type it there anyway, it is ignored.

min( and max(p. 175

With one list, min( and max( give the smallest or largest element. With two lists of the same length, they return a list holding the smaller or larger of each pair. For a complex list, the element with the smallest or largest magnitude (modulus) is returned.

mean( and median(p. 175

The optional freqlist says how many times each element of list occurs. Each frequency counts consecutive repeats of the matching element. When it is left out, every frequency is 1. Complex lists are not valid.

sum( and prod(p. 176

start and end are optional. They name the first and last element to include; if you leave them out, the whole list is used. The elements may be real or complex.

stdDev( and variance(p. 176

These give the sample standard deviation and sample variance of a list. The optional freqlist counts how many times each element occurs (default 1 each). Complex lists are not valid.