Casio FX-9750G User manual

List Function
Alist 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 you
can store 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
Chapter
17
Element number Display range Cell
Row
List name
Column
List 1 List 2 List 3 List 4 List 5 List 6
1 56 1 107 3.5 4 0
2 37 2 75 6 0 0
3 21 4 122 2.1 0 0
4 69 8 87 4.4 2 0
5 40 16 298 3 0 0
64832486.8 3 0
7 93 64 338 2 9 0
8 30 128 49 8.7 0 0
••••••
••••••
••••••
••••••

List Data Linking
264
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 Ato a list
GraphOperation
List graphing
Y1=List 1X

265
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 dand eto move between lists, and fand cto move between cells
inside of a list.
The screen automatically scrolls when the cursor is located at the edge of the screen.
•cdoes not move the cursor to a cell that does not contain a value.
For our example, we will start by locating the cursor in Cell 1 of List 1.
1. Input a value and press wto store it in the list.
dw
2. The cursor automatically moves down to the next cell for input.
• Note that you can also use the result of an expression as list input. The next
operation shows how to input the value 4 in the second row and then input the
result of 2 + 3 in the next row.
ewc+dw

266
uu
uu
uTo batch input a series of values
1. Use fto move the cursor to the list name.
ffff
2. Use dor eto move the cursor to another list.
e
3. Press !{, and then input the values you want, pressing ,between each
one. Press !}after inputting the final value.
!{g,h,i!}
4. 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 d, e, f, and cto move the cursor to the name of the list where you
want the calculation results to be input.
fe
17 - 1 List Operations

267
2. Press Kand input the expression.
K1(LIST)1(List)b+
1(List)cw
JJ
List Operations 17 - 1

268
17-2 Editing and Rearranging Lists
kk
kk
kEditing List Values
uu
uu
uTo change a cell value
Use dor eto move the cursor 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 d, e, f, or cto move the cursor to the cell you want to delete.
ddc
2. Press 3(DEL) to delete the selected cell and cause everything below it to be
shifted up.
3(DEL)
• 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
1. Use d, e, for cto move the cursor to the name of the list whose cells
you want to delete.
ffee
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269
2. Press 4(DEL-A). The function menu changes to confirm whether you really
want to delete all the cells in the list.
4(DEL-A)
3. Press 1(YES) to delete all the cells in the selected list or 6(NO) to abort the
delete operation without deleting anything.
1(YES)
uu
uu
uTo insert a new cell
Use d, e, f, or cto move the cursor to the location where you want to insert
the new cell. In this example, we will reinsert a cell containing the value 4, which we
deleted above.
1. Press 5(INS) to insert a new cell, which contains a value of 0, causing every-
thing below it to be shifted down.
ddc5(INS)
2. Input the value you want into the new cell (4 in our example) and press w.
ew
• 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.
123456
Editing and Rearranging Lists 17 - 2
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270
kk
kk
kSorting List Values
You can sort lists into either ascending order or descending order. The current cur-
sor location does not matter in the following procedures.
uu
uu
uTo sort a single list
Ascending order
1. While the lists are on the screen, press 1(SRT-A).
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
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
The values in List 2 are sorted into ascending order.
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 ascend-
ing order or descending order, while the cells of the linked lists are arranged so that
the relative relationship of all the rows is maintained.
17 - 2 Editing and Rearranging Lists

271
Ascending order
1. While the lists are on the screen, press 1(SRT-A).
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
The values in List 1 are sorted into ascending order, and the cells of List 2 are also
rearranged to keep the same relationship with the List 1 cells.
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).
Editing and Rearranging Lists 17 - 2

272
17-3 Manipulating List Data
List data can be used in arithmetic and function calculations. There is also a collec-
tion of powerful list data manipulation functions that let you do the following.
• Count the number values (Dim)
• Replace all cell values with the same value (Fill)
• Generate a sequence of numbers (Seq)
• Find the minimum value in a list (Min)
• Find the maximum value in a list (Max)
• Find which of two lists contains the smallest value (Min)
• Find which of two lists contains the greatest value (Max)
• Calculate the mean of list values (Mean)
• Calculate the mean of values of specified frequency (Mean)
• Calculate the median of values in a list (Med)
• Calculate the median of values of specified frequency (Med)
• Calculate the sum of values in a list (Sum)
• Calculate the sum of products (Prod)
• Calculate cumulative frequency of each value (Cuml)
• Calculate the percentage represented by each value (%)
• Transfer list contents to Matrix Answer Memory (List→Mat)
You 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 after entering the RUN Mode.
Press Kand then 1(LIST). This menu has three pages and you can advance to
the next page by pressing 6(g).
Note that all closing parentheses at the end of the following operations can be omitted.
uu
uu
uTo count the number of values (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

273
uu
uu
uTo replace all cell values with the same value (Fill)
K1(LIST) 4(Fill) <value> ,1(List) <list number 1-6> )w
Example To replace all values in List 1 (36,16,58,46,56) with 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 (Seq)
K1(LIST) 5(Seq) <expression> ,<variable name> ,<start
value> ,<end value> ,<pitch> )w
• The result of this operation is also stored in ListAns Memory.
Example To input the number sequence 12,62,112into a list
Use the following settings.
Variable: x
Starting value: 1
Ending value: 11
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, because all of them are less than the value produced by the next increment
(16).
The resulting sequence is input into ListAns Memory.
Manipulating List Data 17 - 3

274
uu
uu
uTo find the minimum value in a 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 (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 (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 values. If they don’t, an error (Dim
ERROR) occurs.
• The result of this operation is also stored in ListAns Memory.
Example To find whether List 1 (75,16,98,46,56) or List 2 (36,89,58,72,
67) contains the smallest value
K1(LIST)6(g)1(Min)
6(g)6(g)1(List)b,
1(List)c)
w
uu
uu
uTo find which of two lists contains the greatest value (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 values. If they don’t, an error (Dim
ERROR) occurs.
uu
uu
uTo calculate the mean of list values (Mean)
K1(LIST)6(g) 3(Mean) 6(g) 6(g) 1(List) <list number 1-6>
)w
17 - 3 Manipulating List Data

275
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 (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 values. If they don’t, an error (Dim
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 (Median)
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
uu
uu
uTo calculate the median of values of specified frequency (Median)
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 values. If they don’t, an error (Dim
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
Manipulating List Data 17 - 3

276
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 (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 sum of products (Prod)
K1(LIST) 6(g) 6(g) 2(Prod) 6(g) 1(List) <list number
1-6> w
Example To calculate the sum of products for the 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 (Cuml)
K1(LIST) 6(g) 6(g) 3(Cuml) 6(g) 1(List) <list number
1-6> w
Example To calculate the cumulative frequency of each value in List 1
(2,3,6,5,4)
The result is displayed in ListAns Memory.
AK1(LIST)6(g)6(g)
3(Cuml)6(g)1(List)b
w
2+3=
2+3+6=
2+3+6+5=
2+3+6+5+4=
17 - 3 Manipulating List Data

277
uu
uu
uTo calculate the percentage represented by each value (%)
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.
Example To calculate the percentage represented by each value in List 1
(2,3,6,5,4)
The result is displayed in ListAns Memory.
AK1(LIST)6(g)6(g)
4(%)6(g)1(List)b
w
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 =
uu
uu
uTo transfer list contents to Matrix Answer Memory (List →Mat)
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

278
17-4 Arithmetic Calculations Using Lists
You can perform arithmetic calculations using two lists or one list and a numeric
value.
List
Numeric Value
List
Numeric Value
+
−
×
÷=List
ListAns Memory
kk
kk
kError Messages
• A calculation involving two lists performs the operation between corresponding
cells. Because of this, a Dim ERROR occurs if the two lists do not have the same
number of values (which means they have different “dimensions”).
• An Ma 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.
K
2. Press 1(LIST) to display the List Data Manipulation Menu.
1(LIST)
3. Press 1(List) to display the “List” command and input the number of the list you
want to specify.
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Calculation results are
storedin ListAns Memory.

279
uu
uu
uTo directly input a list of values
You can also directly input a list of values using {, }, and ,.
Example 1 To input the list: 56,82,64
!{56,82,64!}
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 0 is 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) doperation in the above procedure, you could input !{e
b,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
Arithmetic Calculations Using Lists 17 - 4

280
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
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 also stores
them in ListAns Memory. You can then 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 contains the values 1, 2, 3, this function will produces three
graphs: Y = X, Y = 2X, Y = 3X.
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 and then use the list copy function to copy the values from
the table to the list.
17 - 4 Arithmetic Calculations Using Lists
P.126
P.248

281
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
–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!}.
14
Example 2 To use List 1 2 and List 2 5 to perform List 1List 2
36
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

282
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.
!Z
Press the function key (1to 6) 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).
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