Casio CFX-9850G PLUS Instruction and safety manual

Chapter
17
List Function
A list is a kind of container that you can use to store multiple data
items.
This calculator lets you store up to six lists in a single file, and up
to six files in memory. Stored lists can be used in arithmetic,
statistical, and matrix calculations, and for graphing.
17-1 List Operations
17-2 Editing and Rearranging Lists
17-3 Manipulating List Data
17-4 Arithmetic Calculations Using Lists
17-5 Switching Between List Files
Element number Display range Cell
Row
List name
Column
List 1 List 2 List 3 List 4 List 5 List 6
156 1 107 3.5 4 0
237 2 75 6 0 0
321 4 122 2.1 0 0
469 8 87 4.4 2 0
540 16 298 3 0 0
648 32486.8 3 0
793 64 338 2 9 0
830 128 49 8.7 0 0
••••••
••••••
••••••
••••••

List Data Linking
230
Matrix Table
LIST
List operation
Example:
List 1 + List 2
{1, 2, 3} + {4, 5, 6}
List 1 + 3
From a graph to a list
Table data generated by
GRAPH TO TABLE to a list
↓w
List internal operations
↓w
Memory transfer
Generating a table by
defining a list as the
variable.
K
1(LIST)
2(LMEM)
4(List4)
Inside list
Copying the column of a
specific table to a specific list.
↓w
Memory transfer
Example: To send column 1
of Mat A to a list
GraphOperation
List graphing
Y1=List 1X

231
17-1 List Operations
Select the LIST icon in the Main Menu and enter the LIST Mode to input data into
a list and to manipulate list data.
uu
uu
uTo input values one-by-one
Use the cursor keys to move the highlighting to the list name or cell you want to
select. Note that cdoes not move the highlighting to a cell that does not contain
a value.
The screen automatically scrolls when the highlighting is located at either edge of
the screen.
The following example procedure is performed starting with the highlighting
located at Cell 1 of List 1.
1. Input a value and press wto store it in the list.
dw
2. The highlighting automatically moves down to the next cell for input.
•Note that you can also input the result of an expression in a cell. The following
operation shows how to input the value 4 in the second cell and then input the
result of 2 + 3 in the next cell.
ewc+dw

232
uu
uu
uTo batch input a series of values
1. Use the cursor keys to move the highlighting to another list.
2. Press !{, and then input the values you want, pressing ,between each
one. Press !}after inputting the final value.
!{g,h,i!}
3. Press wto store all of the values in your list.
w
•Remember that a comma separates values, so you should not input a
comma after the final value of the set you are inputting.
Right: {34, 53, 78}
Wrong: {34, 53, 78,}
You can also use list names inside of a mathematical expression to input values
into another cell. The following example shows how to add the values in each row
in List 1 and List 2, and input the result into List 3.
1. Use the cursor keys to move the highlighting to the name of the list where you
want the calculation results to be input.
2. Press Kand input the expression.
K1(LIST)1(List)b+
1(List)cw
17 - 1 List Operations

233
17-2 Editing and Rearranging Lists
kk
kk
kEditing List Values
uu
uu
uTo change a cell value
Use dor eto move the highlighting to the cell whose value you want to
change. Input the new value and press wto replace the old data with the new
one.
uu
uu
uTo delete a cell
1. Use the cursor keys to move the highlighting to the cell you want to delete.
ddc
3
2. Press 3(DEL) to delete the selected cell and cause everything below it to be
shifted up.
•Note that the above cell delete operation does not affect cells in other lists. If
the data in the list whose cell you delete is somehow related to the data in
neighboring lists, deleting a cell can cause related values to become
misaligned.
uu
uu
uTo delete all cells in a list
Use the following procedure to delete all the data in a list.
1. Use the cursor key to move the highlighting to any cell of the list whose data
you want to delete.
2. Press 4(DEL-A). The function menu changes to confirm whether you really
want to delete all the cells in the list.
3. Press 1(YES) to delete all the cells in the selected list or 6(NO) to abort
the delete operation without deleting anything.

234
uu
uu
uTo insert a new cell
1. Use the cursor keys to move the highlighting to the location where you want to
insert the new cell.
2. Press 5(INS) to insert a new cell, which contains a value of 0, causing
everything below it to be shifted down.
•Note that the above cell insert operation does not affect cells in other lists. If
the data in the list where you insert a cell is somehow related to the data in
neighboring lists, inserting a cell can cause related values to become
misaligned.
kk
kk
kSorting List Values
You can sort lists into either ascending or descending order. The highlighting can
be located in any cell of the list.
uu
uu
uTo sort a single list
Ascending order
1. While the lists are on the screen, press 1(SRT-A).
2. The prompt “How Many Lists? (H)” appears to ask how many lists you want to
sort. Here we will input 1 to indicate we want to sort only one list.
bw
17 - 2 Editing and Rearranging Lists

235
3. In response to the “Select List (L)” prompt, input the number of the list you want
to sort. Here we will input 2 to specify sorting of List 2.
cw
Descending order
Use the same procedure as that for the ascending order sort. The only difference
is that you should press 2(SRT-D) in place of 1(SRT-A).
uu
uu
uTo sort multiple lists
You can link multiple lists together for a sort so that all of their cells are rearranged
in accordance with the sorting of a base list. The base list is sorted into either
ascending order or descending order, while the cells of the linked lists are
arranged so that the relative relationship of all the rows is maintained.
Ascending order
1. While the lists are on the screen, press 1(SRT-A).
2. The prompt “How Many Lists? (H)” appears to ask how many lists you want to
sort. Here we will sort one base list linked to one other list, so we should input 2.
cw
3. In response to the “Select Base List (B)” prompt, input the number of the list
you want to sort into ascending order. Here we will specify List 1.
bw
4. In response to the “Select Second List (L)” prompt, input the number of the list
you want to link to the base list. Here we will specify List 2.
cw
Editing and Rearranging Lists 17 - 2

236
Descending order
Use the same procedure as that for the ascending order sort. The only difference
is that you should press 2(SRT-D) in place of 1(SRT-A).
•You can sort up to six lists at one time.
•If you specify a list more than once for a single sort operation, an error occurs.
An error also occurs if lists specified for sorting do not have the same number of
values (rows).
17 - 2 Editing and Rearranging Lists

237
17-3 Manipulating List Data
List data can be used in arithmetic and function calculations. In addition, various
list data manipulation functions makes manipulation of list data quick and easy.
You can use list data manipulation functions in the RUN,STAT,MAT,LIST,
TABLE,EQUA and PRGM Modes.
kk
kk
kAccessing the List Data Manipulation Function Menu
All of the following examples are performed in the RUN Mode.
Press Kand then 1(LIST) to display the list data manipulation menu, which
contains the following items.
•{List}/{L→M}/{Dim}/{Fill}/{Seq}/{Min}/{Max}/{Mean}/{Med}/{Sum}/{Prod}/
{Cuml}/{%}/{AA
AA
A}
Note that all closing parentheses at the end of the following operations can be
omitted.
uu
uu
uTo count the number of values [OPTN]-[LIST]-[Dim]
K1(LIST)3(Dim)1(List) <list number 1-6> w
•The number of cells that contain data in a list is called its “dimension.”
Example To enter the RUN Mode and count the number of values in List
1 (36,16,58,46,56)
AK1(LIST)3(Dim)
1(List) bw
uu
uu
uTo create a list or matrix by specifying the number of data
[OPTN]-[LIST]-[Dim]
Use the following procedure to specify the number of data items in the assignment
statement and create a list.
<number of data n>aK1(LIST)3(Dim)1(List)
<list number 1-6>w
n= 1 ~ 255

238
Example To create five data items (each of which contains 0) in List 1
AfaK1(LIST) 3(Dim)
1(List) bw
Use the following procedure to specify the number of data rows and columns, the
matrix name in the assignment statement, and to create a matrix.
!{<number of row m> ,<number of column n> !}a
K1(LIST)3(Dim)J2(MAT)1(Mat)a<matrix name>w
m,n= 1 ~ 255, matrix name; A ~ Z
Example To create a 2-row ×3-column matrix (with each cell
containing 0) in Matrix A
A!{c,d!}a
K1(LIST)3(Dim)J
2(MAT)1(Mat)aAw
uu
uu
uTo replace all cell values with the same value [OPTN]-[LIST]-[Fill]
K1(LIST) 4(Fill) <value> ,1(List) <list number 1-6> )w
Example To replace all values in List 1 with the number 3
AK1(LIST)4(Fill)
d,1(List)b)w
The following shows the new contents of List 1.
uu
uu
uTo generate a sequence of numbers [OPTN]-[LIST]-[Seq]
K1(LIST) 5(Seq) <expression> ,<variable name> ,<start
value> ,<end value> ,<pitch> )w
•The result of this operation is stored in ListAns Memory.
17 - 3 Manipulating List Data

239
Manipulating List Data 17 - 3
Example To input the number sequence 12,62,112into a list
Use the following settings.
Variable: xEnding value: 11
Starting value: 1 Pitch: 5
AK1(LIST)5(Seq)v
x,v,b,bb,f)w
Specifying an ending value of 12, 13, 14, or 15 produces the same result as
shown above since they are less than the value produced by the next increment
(16).
uu
uu
uTo find the minimum value in a list [OPTN]-[LIST]-[Min]
K1(LIST)6(g)1(Min)6(g)6(g)1(List) <list number 1-6>
)w
Example To find the minimum value in List 1 (36,16,58,46,56)
AK1(LIST)6(g)1(Min)
6(g)6(g)1(List)b)w
uu
uu
uTo find the maximum value in a list [OPTN]-[LIST]-[Max]
Use the same procedure as when finding the minimum value (Min), except press
2(Max) in place of 1(Min).
uu
uu
uTo find which of two lists contains the smallest value
[OPTN]-[LIST]-[Min]
K1(LIST)6(g)1(Min)6(g)6(g)1(List) <list number 1-6>
,1(List) <list number 1-6> )w
•The two lists must contain the same number of data items. Otherwise, an error
occurs.
•The result of this operation is stored in ListAns Memory.
Example To find whether List 1 (75,16,98,46,56) or List 2 (35,89,58,72,
67) contains the smallest value
K1(LIST)6(g)1(Min)
6(g)6(g)1(List)b,
1(List)c)w

240
uu
uu
uTo find which of two lists contains the greatest value
[OPTN]-[LIST]-[Max]
Use the same procedure as that for the smallest value, except press 2(Max) in
place of 1(Min).
•The two lists must contain the same number of data items. Otherwise, an error
occurs.
uu
uu
uTo calculate the mean of list values [OPTN]-[LIST]-[Mean]
K1(LIST)6(g)3(Mean)6(g)6(g)1(List) <list number 1-6>
)w
Example To calculate the mean of values in List 1 (36,16,58,46,56)
AK1(LIST)6(g)3(Mean)
6(g)6(g)1(List)b)w
uu
uu
uTo calculate the mean of values of specified frequency
[OPTN]-[LIST]-[Mean]
This procedure uses two lists: one that contains values and one that contains the
number of occurrences of each value. The frequency of the data in Cell 1 of the
first list is indicated by the value in Cell 1 of the second list, etc.
•The two lists must contain the same number of data items. Otherwise, an error
occurs.
K1(LIST)6(g)3(Mean)6(g)6(g)1(List)<list number 1-6
(data)>,1(List)<list number 1-6 (frequency)>)w
Example To calculate the mean of values in List 1 (36,16,58,46,56),
whose frequency is indicated by List 2 (75,89,98,72,67)
AK1(LIST)6(g)3(Mean)
6(g)6(g)1(List)b,
1(List)c)w
uu
uu
uTo calculate the median of values in a list [OPTN]-[LIST]-[Med]
K1(LIST)6(g)4(Med)6(g)6(g)1(List)<list number 1-6>
)w
Example To calculate the median of values in List 1 (36,16,58,46,56)
AK1(LIST)6(g)4(Med)
6(g)6(g)1(List)b)w
17 - 3 Manipulating List Data

241
uu
uu
uTo calculate the median of values of specified frequency
[OPTN]-[LIST]-[Med]
This procedure uses two lists: one that contains values and one that contains the
number of occurrences of each value. The frequency of the data in Cell 1 of the
first list is indicated by the value in Cell 1 of the second list, etc.
•The two lists must contain the same number of data items. Otherwise, an error
occurs.
K1(LIST)6(g)4(Med)6(g)6(g)1(List) <list number 1-6
(data)> ,1(List) <list number 1-6 (frequency)> )w
Example To calculate the median of values in List 1 (36,16,58,46,56),
whose frequency is indicated by List 2 (75,89,98,72,67)
AK1(LIST)6(g)4(Med)
6(g)6(g)1(List)b,
1(List)c)w
uu
uu
uTo calculate the sum of values in a list [OPTN]-[LIST]-[Sum]
K1(LIST)6(g)6(g)1(Sum)6(g)1(List)<list number 1-6>
w
Example To calculate the sum of values in List 1 (36,16,58,46,56)
AK1(LIST)6(g)6(g)
1(Sum)6(g)1(List)bw
uu
uu
uTo calculate the product of values in a list [OPTN]-[LIST]-[Prod]
K1(LIST)6(g)6(g)2(Prod)6(g)1(List)<list number 1-6>w
Example To calculate the product of values in List 1 (2,3,6,5, 4)
AK1(LIST)6(g)6(g)
2(Prod)6(g)1(List)bw
uu
uu
uTo calculate the cumulative frequency of each value
[OPTN]-[LIST]-[Cuml]
K1(LIST)6(g)6(g)3(Cuml)6(g)1(List) <list number 1-6>
w
•The result of this operation is stored in ListAns Memory.
Manipulating List Data 17 - 3

242
Example To calculate the cumulative frequency of each value in List 1
(2,3,6,5,4)
AK1(LIST)6(g)6(g)
3(Cuml)6(g)1(List)bw
uu
uu
uTo calculate the percentage represented by each value
[OPTN]-[LIST]-[%]
K1(LIST)6(g)6(g)4(%)6(g)1(List)<list number 1-6>w
•The above operation calculates what percentage of the list total is represented
by each value.
•The result of this operation is stored in ListAns Memory.
Example To calculate the percentage represented by each value in List 1
(2,3,6,5,4)
AK1(LIST)6(g)6(g)
4(%)6(g)1(List)bw
uu
uu
uTo calculate the differences between neighboring data inside a list
[OPTN]-[LIST]-[AA
AA
A]
K1(LIST)6(g)6(g)5(A)6(g)<list number 1-6>w
•The result of this operation is stored in ListAns memory.
Example To calculate the difference between the values in List 1
(1, 3, 8, 5, 4)
AK1(LIST)6(g)
6(g)5(A)bw
17 - 3 Manipulating List Data
2+3=
2+3+6=
2+3+6+5=
2+3+6+5+4=
2/(2+3+6+5+4)
× 100 =
3/(2+3+6+5+4) × 100 =
6/(2+3+6+5+4) × 100 =
5/(2+3+6+5+4) × 100 =
4/(2+3+6+5+4)
× 100 =
3 – 1 =
8 – 3 =
5 – 8 =
4 – 5 =

243
•You can specify the location of the new list (List 1 through List 6) with a
statement like: AList 1 →List 2. You cannot specify another memory or
ListAns as the destination of the AList operation. An error also occurs if you
specify a AList as the destination of the results of another AList operation.
•The number of cells in the new list is one less than the number of cells in the
original list.
•Note that an error occurs if you execute AList for a list that has no data or only
one data item.
uu
uu
uTo transfer list contents to Matrix Answer Memory
[OPTN]-[LIST]-[L→M]
K1(LIST)2(L→M)1(List) <list number 1-6> ,1(List) <list
number 1-6> )w
•You can input the following as many times as necessary to specify more than
one list in the above operation.
,<list number 1-6>
Example To transfer the contents of List 1 (2,3,6,5,4) and List 2 (11,12,
13,14,15) to Matrix Answer Memory
AK1(LIST)2(L→M)
1(List)b,1(List)c)w
Manipulating List Data 17 - 3

244
17-4 Arithmetic Calculations Using Lists
You can perform arithmetic calculations using either two lists or one list and a
numeric value.
List
Numeric Value
List
Numeric Value
+
−
×
÷
=List
ListAns Memory
Calculation results are
stored in ListAns Memory.
kk
kk
kError Messages
•Acalculation involving two lists performs the operation between corresponding
cells. Because of this, an error occurs if the two lists do not have the same
number of values (which means they have different “dimensions”).
•An error occurs whenever an operation involving any two cells generates a
mathematical error.
kk
kk
kInputting a List into a Calculation
There are two methods you can use to input a list into a calculation.
uu
uu
uTo input a specific list by name
Example To input List 6
1. Press Kto display the first Operation Menu.
•This is the function key menu that appears in the RUN Mode when you press
K.
1
2. Press 1(LIST) to display the List Data Manipulation Menu.
1
3. Press 1(List) to display the “List” command and input the number of the list
you want to specify.
uu
uu
uTo directly input a list of values
You can also directly input a list of values using {, }, and ,.

245
Arithmetic Calculations Using Lists 17 - 4
Example 1 To input the list: 56,82,64
!{fg,ic,
ge!}
41 6
Example 2 To multiply List 3
(
= 65
)
by the list 0
22 4
K1(LIST)1(List)d*!{g,a,e!}w
246
The resulting list 0is stored in ListAns Memory.
88
uu
uu
uTo assign the contents of one list to another list
Use ato assign the contents of one list to another list.
Example 1 To assign the contents of List 3 to List 1
K1(LIST)1(List)da1(List)bw
In place of 1(List) din the above procedure, you could input
!{eb,gf,cc!}.
Example 2 To assign the list in ListAns Memory to List 1
K1(LIST)1(List)!Ka1(List)bw
uu
uu
uTo input a single list cell value into a calculation
You can extract the value in a specific cell of a list and use it in a calculation.
Specify the cell number by enclosing it between square brackets using the [
and ]keys.
Example To calculate the sine of the value stored in Cell 3 of List 2
sK1(LIST)1(List)c![d!]w
uu
uu
uTo input a value into a specific cell
You can input a value into a specific cell inside a list. When you do, the value that
was previously stored in the cell is replaced with the new value you input.
Example To input the value 25 into Cell 2 of List 3
cfaK1(LIST)1(List)d![c!]w

246
kk
kk
kRecalling List Contents
Example To recall the contents of List 1
K1(LIST)1(List)bw
•The above operation displays the contents of the list you specify and stores
them in ListAns Memory, which allows you to use the ListAns Memory contents
in a calculation.
uu
uu
uTo use list contents in ListAns Memory in a calculation
Example To multiply the list contents in ListAns Memory by 36
K1(LIST)1(List)!K*dgw
•The operation K1(LIST) 1(List) !Krecalls ListAns Memory
contents.
•This operation replaces current ListAns Memory contents with the result of the
above calculation.
kk
kk
kGraphing a Function Using a List
When using the graphing functions of this calculator, you can input a function such
as Y1 = List1 X. If List 1 is {1, 2, 3}, this function will produces three graphs: Y = X,
Y = 2X, Y = 3X.
P. 111 There are certain limitations on using lists with graphing functions.
kk
kk
kInputting Scientific Calculations into a List
You can use the numeric table generation functions in the Table & Graph Menu to
input values that result from certain scientific function calculations into a list. To do
this, first generate a table. Next, use the “list copy” function to copy the values
from the table to the list.
kk
kk
kPerforming Scientific Function Calculations Using a List
Lists can be used just as numeric values are in scientific function calculations.
When the calculation produces a list as a result, the list is stored in ListAns
Memory. 41
Example 1 To use List 3 65 to perform sin (List 3)
22
Use radians as the angle unit.
sK1(LIST)1(List)dw
17 - 4 Arithmetic Calculations Using Lists
P. 216

247
–0.158
The resulting list 0.8268 is stored in ListAns Memory.
–8E–3
In place of the 1(List) doperation in the above procedure, you could input
!{eb,gf,cc!}.
1 4
Example 2 To use List 1 2and List 2 5 to perform List 1List 2
3 6
List1MList2w
This creates a list with the results of 14, 25, 36.
1
The resulting list 32 is stored in ListAns Memory.
729
Arithmetic Calculations Using Lists 17 - 4

248
17-5 Switching Between List Files
You can store up to six lists (List 1 to List 6) in each file (File 1 to File 6). A simple
operation lets you switch between list files.
uu
uu
uTo switch between list files
In the Main Menu, select the LIST icon and enter the LIST Mode.
Press !Zto display the LIST Mode set up screen.
Press the function key to select the file you want.
Example To select File 3
3(File3)
J
All subsequent list operations are applied to the lists contained in the file you
select (List File3 in the above example).