STATISTICAL CALCULATIONS
27
28
3TATISTICALCALCULATIONSCANBEPERFORMEDIN34!4MODE
4HEREAREEIGHTSUBMODESWITHIN34!4MODE0RESSb 1, then
PRESSTHENUMBERKEYTHATCORRESPONDSTOYOURCHOICE
0 (SD3INGLEVARIABLESTATISTICS
1 (a+bx,INEARREGRESSION
2 (a+bx+cx
2
): Quadratic regression
3 (a
e^bx%ULEREXPONENTIALREGRESSION
4 (a+b
lnx,OGARITHMICREGRESSION
5 (a
x^b0OWERREGRESSION
6 (a+b/x): Inverse regression
7 (a
b^x'ENERALEXPONENTIALREGRESSION
4HESTATISTICALDATAINPUTSCREENAPPEARS
!FTERENTERINGSTATISTICALDATAFROMTHEINPUTSCREEN
PRESS
_
or
j
ANDCLOSETHEINPUTTABLE
9OUCANTHENCHECKSTATISTICALVALUESFROMTHE
STAT menu
(
; 8
)
ANDSPECIFYSTATISTICALVARIABLES
D
ata Entry and Correction
Data entry
%NTRYlELD
3INGLEVARIABLEDATATABLE 4WOVARIABLEDATATABLE
s !FTERENTERINGTHEDATA
PRESS
e
4HEINPUTISlNALIZEDANDTHE
CURSORMOVESTOTHENEXTLINE)FDATAWASNOTENTEREDINAN
x or y, 0 is
ENTEREDISENTEREDIN&21FREQUENCYANDTHECURSORMOVESTOTHE
NEXTLINE
s
9OUCANUSE
H
TOENTER8AND&21OR89AND&21ATONCE
s )NTHEINPUTTABLEUPTODIGITSAREDISPLAYEDFOREACHVALUE
INCLUDINGTHESIGNANDDECIMALPOINT!NYVALUESTHATEXCEEDDIGITS
INLENGTHAREDISPLAYEDINEXPONENTNOTATION
s
5PTODATAITEMSCANBEENTERED7ITHSINGLEVARIABLEDATA
ADATAITEMWITHANASSIGNEDFREQUENCYOFONEISCOUNTEDASONE
DATAITEMWHILEANITEMWITHANASSIGNEDFREQUENCYOFORHIGHER
ISSTOREDASASETOFTWODATAITEMS7ITHTWOVARIABLEDATAASETOF
DATAITEMSWITHANASSIGNEDFREQUENCYOFONEISCOUNTEDASTWODATA
ITEMSWHILEASETOFITEMSWITHANASSIGNEDFREQUENCYOFORHIGHER
is stored as a set of three data items.
s 4OEXECUTESTATISTICALCALCULATIONPRESS
_
or
j
and close the
INPUTTABLE
Data correction
Use l, r, u, or d to move the cursor and select the
desired data. Press @ u or @ dTOJUMPTHECURSORTOTHE
beginning or end of the data.
Data correction
-OVETHECURSORTOTHEDATATHATYOUWANTTOCORRECTENTERTHENUMERIC
VALUEANDPRESSe.
Data insertion
4OINSERTALINEINFRONTOFTHECURSORPOSITIONPRESS
;
T.
4HEINITIALVALUESENTEREDINTHEINSERTEDDATAAREINXANDYAND
in FRQ.
Data deletion
4ODELETETHEENTIRELINEWHERECURSORISPOSITIONEDPRESS@ y.
Notes:
s )N34!4MODEALLSTATISTICALDATAWILLBEERASEDIFTHESUBMODEIS
changed or
@
Z
ISPRESSED
s )N34!4MODEPRESS
_
TODISPLAYTHEINPUTTABLE
Statistical Calculations and Variables
4HEFOLLOWINGSTATISTICSCANBEOBTAINEDFOREACHSTATISTICALCALCULATION
REFERTOTHETABLEBELOW
Single-variable statistical calculation
Statistics of
1
,
ANDTHEVALUEOFTHENORMALPROBABILITYFUNCTION.
Linear regression calculation
Statistics of
1
,
and
4
. In addition, the estimate of
y
for a given
x
(estimate
y
´) and the estimate of
x
for a given
y
(estimate
x
´).
Quadratic regression calculation
Statistics of
1
,
and
4
!NDCOEFlCIENTS
a
,
b
,
c
INTHEQUADRATIC
regression formula (
y
=
a
bx
cx
2
&ORQUADRATICREGRESSION
CALCULATIONSNOCORRELATIONCOEFlCIENT
r
) can be obtained.)
7HENTHEREARETWO
x
|VALUESEACHVALUEWILLBEDISPLAYEDWITHhvOR
hvANDSTOREDSEPARATELYINTHE8AND9MEMORIES
9OUCANALSOSPECIFYTHESTVALUExANDTHENDVALUExSEPARATELY
Euler exponential regression, logarithmic regression,
power regression, inverse regression,
and general exponential regression calculations
Statistics of
1
,
and
4
. In addition, the estimate of
y
for a given
x
and the estimate of
x
for a given
y
. (Since the calculator converts
each formula into a linear regression formula before actual calculation
TAKESPLACEITOBTAINSALLSTATISTICSEXCEPTCOEFlCIENTS
a
and
b
, from
converted data rather than entered data.)
1
n
.UMBEROFSAMPLES
x
n
-EANOFSAMPLES
x
data
)
sx
3AMPLESTANDARDDEVIATION
x
data
)
s
x
3AMPLEVARIANCE
x
data)
Vx
0OPULATIONSTANDARDDEVIATION
x
data
)
V
x
0OPULATIONVARIANCE
x
data)
Ȉ
x
3UMOFSAMPLES
x
data
)
Ȉ
x
3UMOFSQUARESOFSAMPLES
x
data
)
xmin
-INIMUMVALUEOFSAMPLES
x
data
)
xmax
-AXIMUMVALUEOFSAMPLES
x
data
)
y
n
-EANOFSAMPLES
y
data
)
sy
3AMPLESTANDARDDEVIATION
y
data
)
s
y
3AMPLEVARIANCE
(
y
data)
Vy
0OPULATIONSTANDARDDEVIATION
y
data
)
V
y
0OPULATIONVARIANCE
(
y
data)
Ȉ
y
3UMOFSAMPLES
(
y
data
)
Ȉ
y
3UMOFSQUARESOFSAMPLES
(
y
data
)
Ȉ
x
y
3UMOFPRODUCTSOFSAMPLES
x,
y
)
Ȉ
x
y
3UMOFPRODUCTSOFSAMPLES
(
x
,
y
)
Ȉ
x
3UMOFRDPOWERSOFSAMPLES
(
x
data
)
Ȉ
x
4
3UMOFTHPOWERSOFSAMPLES
(
x
data
)
ymin
-INIMUMVALUEOFSAMPLES
(
y
data
)
ymax
-AXIMUMVALUEOFSAMPLES
(
y
data
)
Q
1
&IRSTQUARTILEOFSAMPLE
(
x
data
)
Med
-EDIANOFSAMPLE
(
x
data
)
Q
4HIRDQUARTILEOFSAMPLE
(
x
data
)
4
r
#ORRELATIONCOEFFICIENT%XCEPT1UADRATICREGRESSION
a
#OEFFICIENTOFREGRESSIONEQUATION
b
#OEFFICIENTOFREGRESSIONEQUATION
c
#OEFFICIENTOFQUADRATICREGRESSIONEQUATION
R
Coefficient of determination (Quadratic regression)
r
#OEFFICIENTOFDETERMINATION%XCEPT1UADRATICREGRESSION
STAT Menu
!FTERCLOSINGTHEINPUTTABLEYOUCANVIEWSTATISTICALVALUESVIEW
REGRESSIONCOEFlCIENTVALUESANDSPECIFYSTATISTICALVARIABLESFROMTHE
STAT menu (
; 8
).
;
8
0$ISPLAYSTATISTICALVALUES
;
8
1$ISPLAYREGRESSIONCOEFlCIENTVALUES
;
8
23PECIFYSTATISTICALVALUEVARIABLES
;
8
3:
3PECIFYSTATISTICALVALUE
Ȉ
related) variables
;
8
43PECIFYMAXMINVALUEVARIABLES
;
8
53PECIFYREGRESSIONCOEFlCIENTVARIABLES
Notes:
s ,ISTDISPLAYOFREGRESSIONCOEFlCIENTVALUESANDSPECIlCATIONOF
REGRESSIONCOEFlCIENTVARIABLESDONOTAPPEARINSINGLEVARIABLE
statistical calculation.
s
Estimated values
x
’ and
y
ARESPECIlEDWITHTHEKEYS@
V
, @
U
)FTHEREARETWO
x
VALUESYOUCANSPECIFY
x
1’ and
x
FROMTHE34!4
menu (
;
8
5TOOBTAINTHEVALUESSEPARATELY
s )NTHESTATISTICALVALUEANDREGRESSIONCOEFlCIENTVALUELISTSYOUCANNOT
RETURNTOTHEMENUBYPRESSINGN.
Statistical Calculation Formulas
29
!NERRORWILLOCCURWHEN
s The absolute value of the intermediate result or calculation result is
EQUALTOORGREATERTHAN
× 10
100
.
s 4HEDENOMINATORISZERO
s !NATTEMPTISMADETOTAKETHESQUAREROOTOFANEGATIVENUMBER
s .OSOLUTIONEXISTSINTHEQUADRATICREGRESSIONCALCULATION
Normal Probability Calculations
30
)N34!4MODETHETHREEPROBABILITYDENSITYFUNCTIONSCANBEACCESSED
UNDERTHE-!4(MENUWITHARANDOMNUMBERUSEDASANORMAL
distribution variable.
Notes:
s 0T1TAND2TWILLALWAYSTAKEPOSITIVEVALUESEVENWHENT
BECAUSETHESEFUNCTIONSFOLLOWTHESAMEPRINCIPLEUSEDWHENSOLVING
for an area.
s 6ALUESFOR0T1TAND2TAREGIVENTOSIXDECIMALPLACES
s 4HESTANDARDIZATIONCONVERSIONFORMULAISASFOLLOWS
t =
x − x
—
σx
TABLE MODE
31
9OUCANSEETHECHANGESINVALUESOFONEORTWOFUNCTIONSUSING4!",%
mode.
Setting a table
1. Press b
2
TOENTER4!",%MODE
%NTERAFUNCTION&UNCTIONANDPRESS
e
.
)FNEEDEDENTERTHENDFUNCTION&UNCTIONANDPRESS
e
.
%NTERASTARTINGVALUE8?3TARTANDPRESS
e
.
The default starting value is 0.
%NTERASTEPVALUE8?3TEP4HEDEFAULTSTEPVALUEIS
s 9OUCANUSEu and dTOMOVETHECURSORBETWEENTHESTARTING
VALUEANDSTEPVALUE
6. Press eWHENYOUlNISHENTERINGASTEPVALUE!TABLEWITHA
VARIABLE8ANDTHECORRESPONDINGVALUES!.3COLUMNAPPEARS
DISPLAYINGLINESBELOWTHESTARTINGVALUE
)FYOUENTEREDTWOFUNCTIONSTHE!.3AND!.3COLUMNSAPPEAR
9OUCANUSEu and dTOCHANGETHE8VALUEANDSEEITS
CORRESPONDINGVALUESINTABLEFORMAT
s 4HETABLEISFORDISPLAYONLYANDYOUCANNOTEDITTHETABLE
s 4HEVALUESAREDISPLAYEDUPTODIGITSINCLUDINGSIGNSANDADECIMAL
POINT
s
Press l
or rTOMOVETHECURSORTO!.3COLUMN!.3AND!.3
COLUMNSIFYOUENTEREDTWOFUNCTIONSOR8COLUMN
s
&ULLDIGITSOFTHEVALUEONTHECURSORAREDISPLAYEDONTHEBOTTOMRIGHT
Notes:
s )NAFUNCTIONONLYh8vCANBEUSEDASAVARIABLEANDOTHERVARIABLES
are all regarded as numbers (stored into the variables).
s )RRATIONALNUMBERSSUCHAS
r and π can also be entered into a starting
VALUEORASTEPVALUE9OUCANNOTENTERORANEGATIVENUMBERASA
STEPVALUE
s 9OUCANUSE7RITE6IEWEDITORWHENINPUTTINGAFUNCTION
s 4HEFOLLOWINGFEATURESARENOTUSEDIN4!",%MODECOORDINATE
CONVERSIONSCONVERSIONBETWEENDECIMALANDSEXAGESIMALNUMBERS
and angular unit conversions.
s
)TMAYTAKETIMETOMAKEATABLEORhvMAYBEDISPLAYEDDEPENDINGON
THEFUNCTIONENTEREDORCONDITIONSSPECIlEDFORTHEVARIABLE8
s 0LEASENOTETHATWHENMAKINGATABLETHEVALUESFORVARIABLE8ARE
REWRITTEN
s
Press @ Z or mode selection to return to the initial screen of the
MODEANDRETURNTOTHEDEFAULTVALUESFORTHESTARTINGVALUEANDSTEPVALUE
.
COMPLEX NUMBER CALCULATIONS
32
4OCARRYOUTADDITIONSUBTRACTIONMULTIPLICATIONANDDIVISIONUSING
COMPLEXNUMBERSPRESSb 3TOSELECT#/-0,%8MODE
2ESULTSOFCOMPLEXNUMBERCALCULATIONSAREEXPRESSEDUSINGTWO
systems:
1
@ E: Rectangular coordinate system
(The
SYMBOLAPPEARS
@ u: Polar coordinate system
(The
SYMBOLAPPEARS
Complex Number Entry
1
Rectangular coordinates
x-coordinate + y-coordinate O
or x-coordinate + O y-coordinate
Polar coordinates
r @ Q
θ
r : absolute value θ: argument
s /NSELECTINGANOTHERMODETHEIMAGINARYPARTOFANYCOMPLEXNUMBER
STOREDINTHEINDEPENDENTMEMORY-ANDTHELASTANSWERMEMORY
!.3WILLBECLEARED
s !COMPLEXNUMBEREXPRESSEDINRECTANGULARCOORDINATESWITHTHE
YVALUEEQUALTOZEROOREXPRESSEDINPOLARCOORDINATESWITHTHEANGLE
EQUALTOZEROISTREATEDASAREALNUMBER
s
&ROMTHE-!4(MENUYOUCANOBTAINTHECOMPLEXCONJUGATECONJTHE
ARGUMENTOFACOMPLEXNUMBERARGTHEREALPARTOFACOMPLEXNUMBERREAL
ANDTHEIMAGINARYPARTOFACOMPLEXNUMBERIMG
EQUATION SOLVERS
33
The results obtained by these functions may include a margin of error.
Simultaneous Linear Equations
3IMULTANEOUSLINEAREQUATIONSWITHTWOUNKNOWNS6,%ORWITHTHREE
UNKNOWNS6,%MAYBESOLVEDUSINGTHEFOLLOWINGFUNCTIONS
1
6,%b 4 0
a
1
x
b
1
y
=
c
1
a
x
b
y
=
c
a
1
b
1
a
b
D =
6,%b 4 1
a
1
x
b
1
y
c
1
z
=
d
1
a
x
b
y
c
z
=
d
a
x
b
y
c
z
=
d
a
1
b
1
c
1
a
b
c
a
b
c
D =
s )FTHEDETERMINANT$ANERROROCCURS
s )FTHEABSOLUTEVALUEOFANINTERMEDIATERESULTORCALCULATIONRESULTIS
× 10
100
or more, an error occurs.
Solving simultaneous linear equations
1. Press b 4 0 or b 4 1.
%NTERTHEVALUEFOREACHCOEFlCIENT
a
1
, etc.).
s #OEFlCIENTSCANBEENTEREDUSINGORDINARYARITHMETICOPERATIONS
s 4OCLEARTHEENTEREDCOEFlCIENTPRESSj.
s 0RESSu or dTOMOVETHECURSORUPORDOWNTHROUGHTHE
COEFlCIENTS0RESS@ u or @ dTOJUMPTOTHElRSTOR
LASTCOEFlCIENT
7HENALLCOEFlCIENTSHAVEBEENENTEREDPRESSe to solve the
EQUATION
s
7HILETHESOLUTIONISDISPLAYEDPRESSe or j to return to the
COEFlCIENTENTRYDISPLAY4OCLEARALLTHECOEFlCIENTSPRESS@ Z .
Quadratic and Cubic Equations
Quadratic (ax
2
+ bx + c = 0) or cubic (ax
3
+ bx
2
+ cx + d = 0)
EQUATIONSMAYBESOLVEDUSINGTHEFOLLOWINGFUNCTIONS
1
1UADRATICEQUATIONSOLVERb 4 2
#UBICEQUATIONSOLVERb 4 3
s
)FTHEREARETWOORMORESOLUTIONSTHOSESOLUTIONSAREALSOSHOWN
s )FCALCULABLEYOUCANALSOOBTAINTHEMINIMUMVALUEWHENAAND
THEMAXIMUMVALUEWHENAOFAQUADRATICFUNCTION
y = ax
2
+ bx
+ c) .
Solving quadratic and cubic equations
s 0RESSb 4 2 or b 4 3.
s #OEFlCIENTSFORTHESEEQUATIONSCANBEENTEREDINTHESAMEMANNERAS
THOSEFORSIMULTANEOUSLINEAREQUATIONS
s 7HENUSINGTHE15!$2!4)#EQUATIONSOLVERCONTINUEBYPRESSING
e (or dTODISPLAYTHEMINIMUMVALUEORMAXIMUMVALUE4O
RETURNTOTHESOLUTIONPRESSuWITHTHEMINIMUMVALUEORMAXIMUM
VALUEDISPLAYED
s 4ORETURNTOTHECOEFlCIENTENTRYSCREENWHENTHESOLUTIONOR
MINIMUMMAXIMUMVALUEISDISPLAYEDPRESSe or j.
s 4OCLEARALLTHECOEFlCIENTSPRESS@ Z .
MATRIX CALCULATIONS
34
9OUCANSTOREANDCALCULATEUPTOFOURMATRICES
Entering and Storing Matrices
1. Press b 5TOENTER-!42)8MODE
0RESSN 1TOBRINGUPTHEMATRIXENTRYSCREEN
s !NYMATRIXDATAREMAININGINTHEBUFFERALONGWITHANYPREVIOUSLY
ENTEREDLOADEDORCALCULATEDMATRIXDATAWILLBEDISPLAYED
$ElNETHEMATRIXDIMENSIONSUPTOFOURROWSBYFOURCOLUMNSBY
ENTERINGTHEREQUIREDDIMENSIONSUSINGTHENUMBERKEYSANDPRESSING
e.
-ATRIXDIMENSIONSROW× column)
%LEMENTlELDS
%NTRYlELD
-ATRIXENTRYSCREENEXAMPLE
%NTEREACHELEMENTINTHEMATRIXBYENTERINGAVALUEINTHEENTRYlELD
ANDPRESSINGe.
s %ACHMATRIXELEMENTCANDISPLAYUPTOSEVENDIGITSTHEDECIMAL
POINTCOUNTSASONEDIGIT)FANELEMENTEXCEEDSSEVENDIGITSIN
LENGTHITMAYBEDISPLAYEDINEXPONENTNOTATIONWITHINTHEMATRIX
s !MAXIMUMOFTHREEROWSBYTHREECOLUMNSCANBEDISPLAYEDAT
one time. Use u, d, l, and r to move the cursor
THROUGHTHEMATRIX
7HENYOUHAVEENTEREDAVALUEFOREACHELEMENTPRESSjTOEXIT
THEMATRIXENTRYSCREEN
6. Press N 3ANDSELECTAMEMORYMAT!nMAT$TOSTORETHE
NEWLYCREATEDMATRIXIN
DISTRIBUTION FUNCTIONS
4HECALCULATORHASDISTRIBUTIONFEATURESTOlNDSTATISTICALCALCULATIONS
Press b 7ANDSELECTTHETYPE./2-!,")./-).!,
0/)33/.ANDTHENSELECTTHEDESIREDDISTRIBUTIONFUNCTION
Note: Calculation results are stored in ANS memory.
Normal Distribution
Normal pdf
#ALCULATESTHEPROBABILITYDENSITYOFTHESPECIFIEDVALUEXFORTHENOR
MALDISTRIBUTIONWITHTHESPECIFIEDMEAN±ANDSTANDARDDEVIATION
ı
).
Normal cdf
#ALCULATESTHEPROBABILITYOFASPECIFIEDINTERVALSXXFORTHENORMAL
DISTRIBUTIONWITHTHESPECIFIEDMEAN±ANDSTANDARDDEVIATION
ı
).
Inverse Normal
Calculates the inverse cumulative normal distribution function for a
GIVENAREAAUNDERTHENORMALDISTRIBUTIONCURVESPECIFIEDBYMEAN±
and standard deviation (
ı
).
Binomial Distribution
Binomial pdf
#ALCULATESAPROBABILITYDENSITYATXFORTHEDISCRETEBINOMIAL
DISTRIBUTIONWITHTHESPECIlEDTRIALNUMBERNANDPROBABILITYOF
SUCCESSPONEACHTRIAL
Binomial cdf
#ALCULATESACUMULATIVEPROBABILITYATXFORTHEDISCRETEBINOMIAL
DISTRIBUTIONWITHTHESPECIlEDTRIALNUMBERNANDPROBABILITYOF
SUCCESSPONEACHTRIAL
Poisson Distribution
Poisson pdf
#ALCULATESAPROBABILITYATXFORTHE0OISSONDISTRIBUTIONWITHTHESPECI
fied mean (μ) .
Poisson cdf
#ALCULATESACUMULATIVEPROBABILITYATXFORTHE0OISSONDISTRIBUTION
WITHTHESPECIFIEDMEAN±
Find the nominal distribution
PROBABILITYDENSITYFORX
WHENTHENORMALDISTRIBUTION
of the test score averages is
WITHASTANDARDDEVIATION
of 6.
b
7
0
0
65
e
60
e
6
.ORMALPDF
x
:
65
.
ȝ
:
60
.
V
:
6_
e
ANS =
0
.
046985312
#ALCULATETHEPROBABILITYOF
RANGEXTOINTHE
ABOVESAMPLE
b
7
0
1
54
e
66
e
60
e
6
Normal cdf
x
1
:
54
.
x
:
66
.
ȝ
:
60
.
V
:
6_
e
ANS =
0
.
682689492
&INDTHEVALUEOFXFORTHE
PROBABILITYOFINTHE
ABOVESAMPLE
b
7
0
2
0
.
8
e
60
e
6
Inverse Normal
a
:
0
.
8
ȝ
:
60
.
V
:
6_
e
ANS =
65
.
0497274
&INDTHEPROBABILITYDENSITY
FORTRIALSWITHXFOR
THEBINOMIALDISTRIBUTIONWITH
SUCCESSPROBABILITYOF
b
7
1
0
7
e
15
e
0
.
3
"INOMIALPDF
x
:
7
.
n
:
15
.
p
:
0
.
3_
e
ANS =
0
.
081130033
#ALCULATETHEPROBABILITYOF
RANGEUPTOXSUCCESS
number) in the above
SAMPLE
b
7
1
1
7
e
15
e
0
.
3
Binomial cdf
x
:
7
.
n
:
15
.
p
:
0
.
3_
e
ANS =
0
.
949987459
&INDTHEPROBABILITYDENSITY
OFXFORTHEMEANOFA
0OISSONDISTRIBUTIONOF
b
7
2
0
4
e
3
.
6
0OISSONPDF
x
:
4
.
ȝ
:
3
.
6_
e
ANS =
0
.
191222339
&INDTHEPROBABILITYWITHIN
THERANGEUPTOX
b
7
2
1
4
e
3
.
6
Poisson cdf
x
:
4
.
ȝ
:
3
.
6_
e
ANS =
0
.
706438449
DRILL MODE
Math Drill: b 8 0
-ATHOPERATIONQUESTIONSWITHPOSITIVEINTEGERSANDAREDISPLAYED
RANDOMLY)TISPOSSIBLETOSELECTTHENUMBEROFQUESTIONSANDOPERATOR
TYPE
-ULTIPLICATION4ABLE
× Table): b 8 1
1UESTIONSFROMEACHROWOFTHEMULTIPLICATIONTABLETOARE
DISPLAYEDSERIALLYORRANDOMLY
4OEXIT$2),,MODEPRESSb and select another mode.
Using Math Drill and × Table
1. Press b 8 0 for Math Drill or b 8 1 for × Tabl e.
Math Drill: Use u and dTOSELECTTHENUMBEROFQUESTIONS
50, or 100).
× Table : Use u and dTOSELECTAROWINTHEMULTIPLICATION
TABLETO
Math Drill: Use l and rTOSELECTTHEOPERATORTYPEFOR
QUESTIONS
+, −, ×, ÷, or +−×÷).
× Table : Use l and rTOSELECTTHEORDERTYPEh3ERIALvOR
h2ANDOMv
4. Press e to start.
7HENUSING-ATH$RILLOR
×
4ABLERANDOMORDERONLYQUESTIONSARE
RANDOMLYSELECTEDANDWILLNOTREPEATEXCEPTBYCHANCE
%NTERYOURANSWER)FYOUMAKEAMISTAKEPRESSj or N to clear
ANYENTEREDNUMBERSANDENTERYOURANSWERAGAIN
6. Press e.
s )FTHEANSWERISCORRECTh
vAPPEARSANDTHENEXTQUESTIONIS
DISPLAYED
s )FTHEANSWERISWRONGh
vAPPEARSANDTHESAMEQUESTIONIS
DISPLAYED4HISWILLBECOUNTEDASANINCORRECTANSWER
s )FYOUPRESSeWITHOUTENTERINGANANSWERTHECORRECTANSWER
ISDISPLAYEDANDTHENTHENEXTQUESTIONISDISPLAYED4HISWILLBE
COUNTEDASANINCORRECTANSWER
#ONTINUEANSWERINGTHESERIESOFQUESTIONSBYENTERINGTHEANSWER
ANDPRESSINGe.
!FTERYOUlNISHPRESSeANDTHENUMBERANDPERCENTAGEOF
CORRECTANSWERSAREDISPLAYED
9. Press e to return to the initial screen for your current drill.
Ranges of Math Drill Questions
4HERANGEOFQUESTIONSFOREACHOPERATORTYPEISASFOLLOWS
+ Addition operator: “0
+vTOh+v
] Subtraction operator: “0
−vTOh−vANSWERSARE
POSITIVEINTEGERSAND
> Multiplication operator: “1
×vORh×vTOh×v
) Division operator: “0
÷vTOh÷vANSWERSAREPOSITIVE
INTEGERSFROMTOANDDIVIDENDSOFUPTOAND
DIVISORSOFUPTO
+]>) Mixed operators1UESTIONSWITHINALLTHEABOVERANGESARE
DISPLAYED
ERRORS AND CALCULATION RANGES
Errors
!NERRORWILLOCCURIFANOPERATIONEXCEEDSTHECALCULATIONRANGESORIF
AMATHEMATICALLYILLEGALOPERATIONISATTEMPTED7HENANERROROCCURS
PRESSINGl or rAUTOMATICALLYMOVESTHECURSORBACKTOTHEPLACE
INTHEEQUATIONWHERETHEERROROCCURRED%DITTHEEQUATIONORPRESSj
or @ ZTOCLEARTHEEQUATION
Error codes and error types
%22/23YNTAXERROR
s !NATTEMPTWASMADETOPERFORMANINVALIDOPERATION
%X+ & 5 =
%22/2#ALCULATIONERROR
s 4HEABSOLUTEVALUEOFANINTERMEDIATEORlNALCALCULATIONRESULTEQUALS
OREXCEEDS
100
.
s !NATTEMPTWASMADETODIVIDEBYZEROORANINTERMEDIATECALCULATION
RESULTEDINZERO
s 4HECALCULATIONRANGESWEREEXCEEDEDWHILEPERFORMINGCALCULATIONS
s ORANEGATIVENUMBERWASENTEREDASASTEPVALUEIN4!",%MODE
4HEABSOLUTEVALUEOFASTARTINGVALUEORASTEPVALUEEQUALSOR
EXCEEDS
100
IN4!",%MODE
s 7HENTHENUMBERTOBEFACTOREDINTOPRIMESISGREATERTHANAND
OTHERTHANADIGITPOSITIVEINTEGERORWHENTHERESULTOFPRIME
FACTORIZATIONISANEGATIVENUMBERDECIMALFRACTIONr
, or ʌ.
%22/2.ESTINGERROR
s 4HEAVAILABLENUMBEROFBUFFERSWASEXCEEDED4HEREAREBUFFERS
for numeric values and 64 buffers for calculation instructions).
*
BUFFERSIN#/-0,%8MODEANDBUFFERFORMATRIXVECTORDATA
%22/2$ATAOVERERROR
s $ATAITEMSEXCEEDEDIN34!4MODE
%22/2$ElNITIONERROR
s -ATRIXDElNITIONERRORORTHEATTEMPTEDENTERINGOFANINVALIDVALUE
%22/2$)-UNMATCHEDERROR
s -ATRIXVECTORDIMENSIONSINCONSISTENTWHILECALCULATING
%22/25NDElNEDERROR
s 5NDElNEDMATRIXVECTORUSEDINCALCULATION
Alert Messages
Cannot delete!
s 4HESELECTEDITEMCANNOTBEDELETEDBYPRESSINGN or @ y
INTHE7RITE6IEWEDITOR
%X* 5 r A l N
)NTHISEXAMPLEDELETETHEEXPONENTBEFOREATTEMPTINGTODELETETHE
PARENTHESES
Cannot call!
s 4HEFUNCTIONOROPERATIONSTOREDINDElNABLEMEMORY$TO$
cannot be called.
%X!NATTEMPTWASMADETORECALLASTATISTICALVARIABLEFROMWITHIN
./2-!,MODE
Buffer full!
s 4HEEQUATIONINCLUDINGANYCALCULATIONENDINGINSTRUCTIONSEXCEEDED
ITSMAXIMUMINPUTBUFFERCHARACTERSINTHE7RITE6IEWEDITOROR
CHARACTERSINTHE,INEEDITOR!NEQUATIONMAYNOTEXCEEDITS
MAXIMUMINPUTBUFFER
Calculation Ranges
36
s Within the ranges specified, this calculator is accurate to ±1
of the 10th digit of the mantissa. However, a calculation error
increases in continuous calculations due to accumulation of each
calculation error. (This is the same for
y
x
,
x
r, n!, e
x
, ln, Matrix/
Vector calculations,
3, etc., where continuous calculations are
performed internally.)
Additionally, a calculation error will accumulate and become
larger in the vicinity of inflection points and singular points of
functions.
s #ALCULATIONRANGES
±10
−
99
to ±9.999999999 × 10
99
and 0.
)FTHEABSOLUTEVALUEOFANENTRYORAlNALORINTERMEDIATERESULTOF
a calculation is less than 10
−
99
, the value is considered to be 0 in
CALCULATIONSANDINTHEDISPLAY
Display of results using r (when EXACT is selected)
#ALCULATIONRESULTSMAYBEDISPLAYEDUSINGrWHENALLOFTHEFOLLOWING
conditions are met:
s 7HENINTERMEDIATEANDlNALCALCULATIONRESULTSAREDISPLAYEDINTHE
FOLLOWINGFORM
±
a
P
b
⎯
e
±
c
P
d
⎯
f
s 7HENEACHCOEFlCIENTFALLSINTOTHEFOLLOWINGRANGES
1
≤ a << b <≤ c <
1
≤ d <≤ e <≤ f < 100
s 7HENTHENUMBEROFTERMSINTHEINTERMEDIATEANDlNALCALCULATION
RESULTSISONEORTWO
.OTE 4HERESULTOFTWOFRACTIONALTERMSTHATINCLUDErWILLBEREDUCEDTO
a common denominator.
BATTERY REPLACEMENT
Notes on Battery Replacement
)MPROPERHANDLINGOFBATTERIESCANCAUSEELECTROLYTELEAKAGEOREXPLOSION
"ESURETOOBSERVETHEFOLLOWINGHANDLINGRULES
s -AKESURETHENEWBATTERYISTHECORRECTTYPE
s 7HENINSTALLINGORIENTTHEBATTERYPROPERLYASINDICATEDINTHE
calculator.
s 4HEBATTERYISFACTORYINSTALLEDBEFORESHIPMENTANDMAYBEEXHAUSTED
BEFOREITREACHESTHESERVICELIFESTATEDINTHESPECIlCATIONS
Notes on erasure of memory contents
7HENTHEBATTERYISREPLACEDTHEMEMORYCONTENTSAREERASED
%RASURECANALSOOCCURIFTHECALCULATORISDEFECTIVEORWHENITIS
REPAIRED-AKEANOTEOFALLIMPORTANTMEMORYCONTENTSINCASE
accidental erasure occurs.
When to Replace the Battery
)FTHEDISPLAYHASPOORCONTRASTORNOTHINGAPPEARSONTHEDISPLAYWHEN
jISPRESSEDINDIMLIGHTINGEVENAFTERADJUSTINGTHEDISPLAYCONTRAST
ITISTIMETOREPLACETHEBATTERY
Cautions
s !NEXHAUSTEDBATTERYLEFTINTHECALCULATORMAYLEAKANDDAMAGETHE
calculator.
s &LUIDFROMALEAKINGBATTERYACCIDENTALLYENTERINGANEYECOULD
RESULTINSERIOUSINJURY3HOULDTHISOCCURWASHWITHCLEANWATERAND
immediately consult a doctor.
s 3HOULDmUIDFROMALEAKINGBATTERYCOMEINCONTACTWITHYOURSKINOR
CLOTHESIMMEDIATELYWASHWITHCLEANWATER
s )FTHEPRODUCTISNOTTOBEUSEDFORSOMETIMETOAVOIDDAMAGETOTHE
UNITFROMALEAKINGBATTERYREMOVEITANDSTOREINASAFEPLACE
s $ONOTLEAVEANEXHAUSTEDBATTERYINSIDETHEPRODUCT
s +EEPBATTERIESOUTOFTHEREACHOFCHILDREN
s %XPLOSIONRISKMAYBECAUSEDBYINCORRECTHANDLING
s $ONOTTHROWBATTERIESINTOAlREASTHEYMAYEXPLODE
Replacement Procedure
4URNTHEPOWEROFFBYPRESSING@ o.
2EMOVETWOSCREWS&IG
,IFTTHEBATTERYCOVERTOREMOVE
2EMOVETHEUSEDBATTERYBYPRYINGITOUTWITH
ABALLPOINTPENOROTHERSIMILARPOINTEDDEVICE
&IG
)NSTALLONENEWBATTERY-AKESURETHEh
+vSIDE
ISFACINGUP
2EPLACETHECOVERANDSCREWS
0RESSTHE2%3%4SWITCHONTHEBACKWITHTHE
TIPOFABALLPOINTPENORSIMILAROBJECT
!DJUSTTHEDISPLAYCONTRAST3EEh!DJUSTINGTHE
DISPLAYCONTRASTv!NDTHENPRESSj.
s -AKESURETHATTHEDISPLAYAPPEARSASSHOWN
BELOW)FTHEDISPLAYDOESNOTAPPEARASSHOWN
REMOVETHEBATTERYREINSTALLITANDCHECKTHE
DISPLAYONCEAGAIN
Modifying a stored matrix
4OLOADASTOREDMATRIXINTOTHEMATRIXENTRYSCREENPRESSN
2THENSELECTTHEMEMORYMAT!nMAT$THATYOUWISHTO
modify.
s ,OADINGNEWDATAINTOTHESCREENWILLAUTOMATICALLYREPLACEANY
DATATHATMAYALREADYEXISTTHERE
-ODIFYTHEVALUESOFELEMENTSINTHEMATRIXANDPRESSe after
each one.
s )FYOUWISHTOMODIFYTHENUMBEROFROWSORCOLUMNSlRSTPRESS
j N 19OUCANTHENENTERNEWVALUESFORTHEMATRIX
dimensions.
7HENYOUHAVElNISHEDMAKINGCHANGESPRESSjTOEXITTHE
MATRIXENTRYSCREEN
4. Press N 3ANDSELECTAMEMORYMAT!nMAT$TOSTORETHE
NEWLYCREATEDMATRIXIN
Using Matrices in Calculations
-ATRICESSTOREDINMEMORIESMAT!nMAT$CANBEUSEDINARITHMETIC
CALCULATIONSWITHTHEEXCEPTIONOFDIVISIONBETWEENMATRICESAND
calculations that use
x
, x
, and x
−
1
9OUCANALSOUSETHEFOLLOWING
MATRIXSPECIlCFUNCTIONSTHATAREAVAILABLEINTHE-!4(MENU
det matrix name Returns the determinant of a
SQUAREMATRIX
trans matrix name
2ETURNSTHEMATRIXWITHTHE
COLUMNSTRANSPOSEDTOROWSAND
THEROWSTRANSPOSEDTOCOLUMNS
identity value
2ETURNSTHEIDENTITYMATRIXWITH
SPECIlEDVALUEOFROWSANDCOLUMNS
dim (matrix name, row, column) 2ETURNSAMATRIXWITHDIMENSIONS
CHANGEDASSPECIlED
lLLvalue, row, column)
&ILLSEACHELEMENTWITHASPECIlED
value.
RAND?MATrow, column)
2ETURNSARANDOMMATRIXWITH
SPECIlEDVALUESOFROWSANDCOLUMNS
ref(matrix name) 4RANSFORMTOROWECHELONFORM
rref(matrix name) 4RANSFORMTOREDUCEDROWECHELON
form.
Notes:
s 7HENTHEMATRIXENTRYSCREENISDISPLAYEDYOUCANNOTPERFORM
MATRIXCALCULATIONSBECAUSETHE-!4(MENUISNOTAVAILABLE
s )FTHECALCULATIONRESULTISAMATRIXITWILLBEDISPLAYEDINTHEMATRIX
ENTRYSCREENNOTETHATTHISREPLACESANYEXISTINGDATAINTHEBUFFER
4OSTORETHECALCULATIONRESULTlRSTPRESSjTOEXITTHEMATRIX
entry screen. Press N 3ANDSELECTAMEMORYMAT!nMAT$
TOSTORETHENEWLYCREATEDMATRIXIN
s 7HENTHECALCULATIONRESULTSAREINMATRIXFORMPRESSINGNEITHER
l nor rWILLBRINGYOUBACKTOTHEORIGINALEXPRESSION
VECTOR CALCULATIONS
35
9OUCANSTOREANDCALCULATEUPTOFOURVECTORSOFTWOORTHREE
DIMENSIONIN6%#4/2MODE
Entering and Storing Vectors
"EFOREPERFORMINGVECTORCALCULATIONSAVECTORMUSTBECREATED
&OLLOWTHESTEPSBELOWTOENTERANDSTOREVECTORS
1. Press b 6TOENTER6%#4/2MODE
0RESSN 1TOBRINGUPTHEVECTORENTRYSCREEN
s
!NYVECTORDATAREMAININGINTHEBUFFERALONGWITHANYPREVIOUSLY
ENTEREDLOADEDORCALCULATEDVECTORDATAWILLBEDISPLAYED
$ElNETHEVECTORDIMENSIONSDIMENSIONSORDIMENSIONSBY
USINGTHENUMBERKEYSANDPRESSINGe.
4. Enter each element in the vector by entering a value in the entry
lELDANDPRESSINGe.
s %ACHVECTORELEMENTCANDISPLAYUPTOSEVENDIGITSTHEDECIMAL
POINTCOUNTSASONEDIGIT
)FANELEMENTEXCEEDSSEVENDIGITSINLENGTHITMAYBEDISPLAYED
INEXPONENTNOTATIONWITHINTHEVECTOR
7HENYOUHAVElNISHEDENTERINGAVALUEFOREACHELEMENTPRESS
jTOEXITTHEVECTORENTRYSCREEN
6. Press N 3ANDSELECTAMEMORYVECT!nVECT$TOSTORETHE
NEWLYCREATEDVECTORIN
Modifying a stored vector
4OLOADASTOREDVECTORINTOTHEVECTORENTRYSCREENPRESSN
2THENSELECTTHEMEMORYVECT!nVECT$THATYOUWISHTO
modify.
s ,OADINGNEWDATAINTOTHESCREENWILLAUTOMATICALLYREPLACEANY
DATATHATMAYALREADYEXISTINTHEVECTORENTRYSCREEN
-ODIFYTHEVALUESOFELEMENTSINTHEVECTORANDPRESSe after
each one.
s )FYOUWISHTOMODIFYTHENUMBEROFDIMENSIONSlRSTPRESS
j N 19OUCANTHENENTERNEWVALUESFORTHEVECTOR
dimensions.
7HENYOUHAVElNISHEDMAKINGCHANGESPRESSjTOEXITTHE
vector entry screen.
4. Press N 3ANDSELECTAMEMORYVECT!nVECT$TOSTORETHE
NEWLYCREATEDVECTORIN
Using Vectors in Calculations
VECTORSSTOREDINMEMORIESVECT!nVECT$CANBEUSEDINARITHMETIC
CALCULATIONSWITHTHEEXCEPTIONOFDIVISIONBETWEENVECTORS9OUCAN
ALSOUSETHEFOLLOWINGVECTORSPECIlCFUNCTIONSTHATAREAVAILABLEINTHE
MATH menu.
DotPro(vector name, vector name)
2ETURNSTHEDOTPRODUCT
CrossPro(vector name, vector name) 2ETURNSTHECROSSPRODUCT
Angl(vector name, vector name)
Returns the angle.
Unit(vector name)
Returns the unit vector.
Notes:
s 9OUCANUSEhABSvFUNCTIONABSvector name) for the absolute value.
s 7HENMULTIPLYINGVECTORSTHECROSSPRODUCTISCALCULATED
s 7HENTHEVECTORENTRYSCREENISDISPLAYEDPRESSj and then you
PERFORMVECTORCALCULATIONS
s )FTHECALCULATIONRESULTISAVECTORITWILLBEDISPLAYEDINTHEVECTOR
entry screen.
4OSTORETHECALCULATIONRESULTlRSTPRESSjTOEXITTHEVECTOR
entry screen. Press N 3ANDSELECTAMEMORYVECT!nVECT$
TOSTORETHENEWLYCREATEDVECTORIN
s 7HENTHECALCULATIONRESULTSAREINVECTORFORMPRESSINGNEITHER
l nor rWILLBRINGYOUBACKTOTHEORIGINALEXPRESSION
Automatic Power Off Function
4HISCALCULATORWILLTURNITSELFOFFTOSAVEBATTERYPOWERIFNOKEYIS
PRESSEDFORAPPROXIMATELYMINUTES
SPECIFICATIONS
$ISPLAY
96
×DOTMATRIXLIQUIDCRYSTALDISPLAY
$ISPLAYOFCALCULATIONRESULTS
Mantissa: 10 digits
%XPONENTDIGITS
Internal calculations: -ANTISSASOFUPTODIGITS
0ENDINGOPERATIONS 64 calculations 10 numeric values
NUMERICVALUESIN#/-0,%8MODEAND
NUMERICVALUEFOR-ATRIX6ECTORDATA
0OWERSOURCE "UILTINSOLARCELLS
6x$#"ACKUPBATTERY
!LKALINEBATTERY,2OREQUIVALENT
× 1)
/PERATINGTIME
(varies according to use
and other factors)
!PPROXHOURSWHENCONTINUOUSLY
DISPLAYINGAT#&USINGTHE
ALKALINEBATTERYONLY
/PERATINGTEMPERATURE #n#&n&
%XTERNALDIMENSIONS
MM7
× 166 mm (D) × 15 mm (H)
v7
×v$×v(
7EIGHT !PPROXGLBINCLUDINGBATTERY
Accessories:
Battery
×INSTALLEDOPERATIONMANUAL
CALCULATIONEXAMPLESANDHARDCASE
FOR MORE INFORMATION
ABOUT SCIENTIFIC CALCULATORS
6ISITOUR7EBSITE
HTTPSHARPWORLDCOMCALCULATOR
Fig. 1
&IG
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