Page 1

Stat/Math
Calculator
Owner’s
Manual
(fifi
HEWLETT
PACKARD
Page 2

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Page 5

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Page 7

HP-21S
Stat/Math
Calculator
Owner’s
Manual
HEWLETT
(bfl]
Edition3June
Reorder
PACKARD
Number
1990
00021-90025
Page 8

Notice
For
warranty
and
151.
This
manual
are
subjecttochange
no
warrantyofany
limited
particular
or
for
incidentalorconsequential
furnishing,
herein.
o
Hewlett-Packard
adaptation,ortranslationofthis
written
the
copyright
The
programs
are
reserved.
without
prohibited.
and
to,
the
purpose.
regulatory
and
any
implied
examples
kind
Hewlett-Packard
information
without
notice.
with
regardtothis
warrantiesofmerchantability
performance,oruseofthis
Co.
1989.
All
permissionofHewlett-Packard
laws.
that
Reproduction,
prior
written
control
your
adaptation,ortranslationofthose
permissionofHewlett-Packard
for
this
calculator,
contained
herein
are
Hewlett-Packard
manual,
Co.
shall
notbeliable
damagesinconnection
manualorthe
rights
reserved.
Reproduction,
manualisprohibited
Company,
calculator
are
exceptasallowed
copyrighted
see
provided
Company
including,
and
fitness
for
with
examples
without
and
Co.isalso
pages
“as
is”
and
makes
but
not
for
a
any
errors
the
contained
prior
under
all
rights
programs
148
Corvallis
1000
Corvallis,
Division
N.E.
Printing
Edition
Edition
Edition
1
2
3
Circle
OR
97330, U.S.A.
History
Blvd.
March
July
June
1989
1990
1989
Mfg.
Mfg.
Mfg.
No.
00021-90026
No.
00021-90042
No.
00021-90043
Page 9

Welcome
Your
HP-21S
engineering
products
offer
service.
and
for50years.
expertisetosupport
to
reflects
the
manufacturing
Hewlett-Packard
Hewlett-Packard
Our
calculators
This
pollutants
variations
Both
caseofuse.Weadded
the
calculator.
Advanced
long
CMOS
toberetained
The
microprocessor
computations,
Extensive
adverse
and
data
are
madetoexcel
calculatorisdesignedtowithstand
(smog,
thatitmay
the
calculator
materials
keyboard
(low-power)
research
effectsofstatic
lossincalculators.
ozone),
life
indefinitely
using15digits
the
superior
its
that
use
HP-21S
quality
have
stands
(see
inside
Quality
andtobe
temperature
encounterineveryday
and
its
manual
many
and
permanent,
andapositive
electronics
and
has
been
has
createdadesign
electricity,apotential
have
examplestohighlight
feeltothe
andaliquid-crystal
the
batteriestolast
optimized
internally
and
attentiontodetail
distinguished
behind
back
easytouse.
the
extremes,
been
molded
for
for
that
this
cover)
drops,
and
work
life.
designed
key
lettering
keys.
fast
and
precise
has
minimized
causeofmalfunctions
in
Hewlett-Packard
calculator
and
worldwide
vibrations,
humidity
and
the
varied
display
a long
reliable
results.
tested
uses
provide
allow
time.
the
—we
for
of
a
data
Page 10

Features
Probability
m
Normal
m
Student’stdistribution.
distribution
distribution.
mFdistribution.
m)?(Chi-square)
Six
built-in
m
Two
m
Linear
m
m
Binomial
m
Time
One
Factorial,
Essential
Polar
Keystroke
Large
Ten
Accurate
Detachable
programs.
One
sample
sample
regression
Chi-square
distribution.
valueofmoney.
and
two
variable
combinations,
scientific
/rectangular
programming,.
12-character
data
registers
math,
quick
statistics.
test
statistics.
test.
functions.
conversions.
display.
and99program
12-digits
reference
functions
and
distribution.
test
statistics.
statistics
with
permutations.
lines.
witha1
0:499
guide.
inverses.
linear
regression.
exponent
range.
Page 11

Contents
1
10
10
10
12
12
12
13
14
14
15
15
15
16
17
17
18
19
20
20
21
Getting
On,
Simple
Understanding
Cursor
Clearing
Annunciators
Shift
INPUT
SWAP
Alpha
Introducing
Display
Specifying
Places
Displaying
Scientific
Interchanging
Full
RangeofNumbers
Messages
Started
Off,
and
Display
Arithmetic
the
the Calculator
Keys
Key
Key
Keys
the
FormatofNumbers
the
(FIX)
the
and
Precisionofa
Contrast
Calculations
Display
Math
NumberofDisplayed
Full
Engineering
the
Number
and
Keyboard
Functions
PrecisionofNumbers
Notation
Period
and
Comma
(SHOW)
Decimal
(ALL)
Contents
5
Page 12

2
3
22
22
22
24
25
25
26
29
29
30
31
31
32
33
33
33
34
35
37
39
Arithmetic
Chain
Operator
Using
Reusing
Exchanging
Using
Numeric
General
Reciprocal
Percent
Percent
Percent
Pi
(7)
Trigonometric
Changing
Trigonometric
Angle
Coordinate
PartsofNumbers
and
Calculations
Priority
Parentheses
the
Previous
Two
Storage
Functions
and
Logarithmic
Functions
Change
the
and
Hour
Conversions
Storage
and
Pending
Result
Numbers
Registers
Modes
Trigonometric
Functions
Conversions
(SWAP)
Functions
and
Functions
Registers
Operations
(LAST)
Mode
4
6
Contents
40
40
40
40
41
42
43
44
44
45
Probability
Probability
Factorial
Combinations
Random
Distributions
Normal
InverseofUpper
Distribution
Student’stUpper
InverseofUpper
t
Distribution
Number
Upper
and
Distributions
and
Permutations
and
Seed
Tail
Probability
Tail
Probability—Normal
Tail
Probability
Tail
Probability—
Student’s
Page 13

46
47
48
49
50
53
53
54
55
55
56
56
56
56
57
59
61
63
65
69
69
71
F
Distribution
InverseofUpper
Upper
Tail
Distribution
InverseofUpper
Distribution
HowtoConvert
Statistical
Clearing
SummaryofStatistical
Entering
Correcting
Mean,
Linear
Weighted
Built-in
One
Statistical
Statistical
One-Variable
Two-Variable
Correcting
Correcting
Standard
Regression
Sample
Population
Interval
Example:
Example:
Upper
Tail
Probability—Chi-Square
(x?)
Tail
(x?)
From
Calculations
Data
Calculations
Data
Statistics
Statistics
Statistical
One-Variable
Two-Variable
Mean
Library
Statistics
Mean—TestofHypothesis/Confidence
Estimate
Data
Deviations,
and
Estimation
(1-StAt)
Population
Population
Tail
Probability
Probability—F
Distribution
Probability—Chi-Square
Upper
Tail
and
Weighted
Mean
Data
Data
and
Summation
Standard
Standard
Deviation
Deviation
Statistics
Known
Unknown
74
74
75
77
79
80
Population
Example:
Example:
Example:
of
MeansofTwo
Example:
Two
Sample
Proportion
Confidence
Interval
TestofHypothesis
TestonPaired
Differences
Populations
Calculating
Test
Sample
Statistics
(2-StAt)
Estimate
Size
(Paired
t)
Contents
7
Page 14

84
84
88
90
90
93
95
98
99
99
103
104
105
106
108
111
113
115
116
116
118
119
Difference
of
Hypothesis/Confidence
Example:
and
Example:
and
Difference
Example:
Example:
Linear
Data
Between
Population
Unknown
Population
Known
Between
Difference
Difference
Regression
Entry
Population
Population
Test
Statistics
Standard
Standard
Non-Zero
Zero
TestofHypothesis/Confidence
Example:
Example:
Example:
Given
Chi-Square
Example:
of
Fit)
Example:
of
Fit)
Binomial
Time
ValueofMoney
Example:
Example:
Example:
Example:
Example:
of
Non-Uniform
Slope
EstimatedyasaMean
EstimatedyasaParticular
x
Test
(CHI-2)
Single
Classification
With
Unequal
Single
With
Equal
Distribution
Expected
Classification
Expected
(bin)
(FinAnCE)
Student
Home
Savings
Compound
Net
Loan
Mortgage
Account
Present
Cash
Interest/Discount
Value
Flows
Means—Test
Interval
Deviations
Deviations
Proportions
(Lr-StAt)
Interval
(Including
Values
(Including
Values
(NPV)
Estimation
Equal
Unequal
Estimation
Value,
Given
Value,
Goodness
Goodness
Case
Tables
x
7
8
Contents
122
124
126
127
128
129
Programming
Creating
Positioning
Running
Programs
Program
Entering
Programs
Boundaries
Programs
the
Program
(LBL
Pointer
and
RTN)
Page 15

129
130
130
131
131
132
133
134
138
138
139
141 Sample
143
143
144
144
144
145
145
146
147
148
149
151
Starting
Starting
Stopping
Clearing
Editing
Stepping
Sample
Programs
Programs
Programs
Programs
Programs
Through
Program:
Subroutines
Branching
Branching
Conditional
and
Conditionals
(GTO)
Instructions—Decisions
Program:
Data
Available
Program
Nonprogrammable
Support,
Calculator
Batteries,
Support
AnswerstoCommon
Environmental
Changing
Testing
The
Limited
If
Calculator
Self-Test
One-Year
the
Calculator
Regulatory
Limits
the
Batteries
Information
With
XEQ
With
GTO
Programs
Pythagorean
Standard
DeviationofGrouped
Memory
Functions
and
Questions
Operation
Warranty
Requires
Service
and
Theorem
Service
R/S
and
Control
152
154
Messages
Index
Contents
9
Page 16

Getting
On,
Off,
Started
and
Display
Contrast
|
Since
the
information
itself
off
three
battery
possible
To
change
Simple
|
To
turnonyour
turn
the
()
(GFF)).
the
calculator
you’ve
approximately10minutes
alkaline
symbol
(page
the
batteries
(==1)inthe
145).
display
Arithmetic
||Ifyou
makeatyping
(¢]toerase
HP-21S,
calculator
has
continuous
stored.Toconserve
last
contrast,
off,
after
approximately
display,
hold
Calculations
mistake
the
incorrect
press
press
[®],
memory,
you
replace
down
digits.
(also
labeled
then
turningitoff
energy,
one
while
the
stop
using
year.Ifyou
the
batteriesassoon
and
press
enteringanumber,
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(written
calculator
it.
as
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not
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calculator’s
see
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or
[].
To
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turns
low-
as
press
10
1:
Getting
Started
Page 17

Arithmetic
arithmetic
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11
Page 18

Negative
Calculate
Numbers.
-75
<+ 3.
Enter
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number
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Keys:
75
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Calculate
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and
Page 19

Clearing
Keys
()(CLPRGM]
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To
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programs
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13
Page 20

Annunciator
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The
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34).
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Page 21

SWAP
Key
m
The
divisionorsubtraction.
m
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indicates
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Thex-and
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TheA,B,C,D,E,andFlabelstothe
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Getting
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Started
one
15
Page 22

Keys:
Display:
Description:
89.25
3.57
(=)
2.36
Two-Number
numbers
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9.4472
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the
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17
29 29
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to
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1:
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Page 23

Specifying
Places
(FIX)
To
enter
the
specify
the
appear
Number
the
of
Displayed
numberofdecimal
places,
numberofdigits(0through9)that
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press(][FIX],
you
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Keys:
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[x]
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Description:
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Getting
Started
17
Page 24

Scientific
and
Engineering
Notation
Sign
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Press
Enter
point.
point,
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18
1:
Getting
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Started
Sign
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exponent
Powerof10
(multiplesof3)
Page 25

To
1.
2.
specify
Press
Enter
the
engineering
[¢q])(ENG].
the
first
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notation,
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display
an
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2.
3.Ifthe
4.
Calculate
Keys:
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8
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Numbers
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you
the
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15
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the
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19
Page 26

Full
Precision
To
temporarily
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(SHOW].
ofaNumber (SHOW)
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(«q)(SHOW
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The
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the
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20
1:
Getting
Started
Page 27

Messages
The
HP-21S
informs
from
and
the
their
youifyou
display,
meanings.
displays
messages
attemptanincorrect
press
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about
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[¢].
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152
foralistofmessages
1:
Getting
Started
21
Page 28

2
Arithmetic
Chain
Chain
each
operator
Keys:
750
360
Operator
Some
example,9+12=+3has
Calculations
calculationsdoa
operation.
priority
[x]12(2]
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Priority
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HP-21S
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Display:
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25.0000
and
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Storage
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Pending
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9+
12
expressions
Calculate
or
9+—1:;2—
750x12+360.
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Registers
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is
Completes
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annunciatorisoff.
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Description:
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PEND
on.
the
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different
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ways.
of
For
22
2:
Arithmetic
and
Storage
Registers
Page 29

The
HP-21S
(»*]
(exponentiation)
uses
the
following
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Highest
priority
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(=]
The
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Thus,
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12
3
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3
5
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6
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the
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Display:
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6.
7.0000
1,372.0000
5.0000
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1,617.0000
1,623.0000
|
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2:
Arithmetic
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23
Page 30

Using
Use
they
be
25+
You
Parentheses
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can
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9
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by
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Now
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85
&
12
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done
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85-12
the
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Vv
(169-8)
30.0000
85
85.0000
73.0000
0.4110
169
8.9000
2.9833
1.2260
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Evaluates
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calculation.
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73.
24
2:
Arithmetic
and
Storage
Registers
Page 31

Reusing
the
When
you
storedinthe
display,
following
Previous
startanew
LAST
press
[\q)
two
calculations:
Result
calculation,acopyofthe
register.Torecall
[LAST].
0.0821x(18+273.1)
2+
0.0821x(18+273.1)
For
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(LAST)
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273.1
2
=
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Exchanging
Pressing
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numbersto75
Display:
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2.5439
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[(1)[SWAP]
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44.
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Displays
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For
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numbers
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you
2:
Arithmetic
and
Storage
Registers
25
Page 32

Keys:
Display:
Description:
44(]75
[1][SWAP
B
8+
435
(1][SWAP
(=]
Whenafunction
Pressing
[¢q)[SWAP]
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returns
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(][DEG]
10
15
(«Q)(>P]
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You
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75
44.0000
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5
4.0000
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two
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the
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[q][SWAP]
Using
26
2:
Storage
Registers
RegistersRythroughRyare
accessed
statistics
summation
Arithmetic
using
functions,R4throughR,are
data.
and
Storage
and
(RCL].
Registers
usedtostore
When
you
usedtostore
numbers.
are
using
They
the
are
Page 33

n
to
the
n
displayedinthe
The
following
n(nisaninteger0through9)copies
designated
n
copies
keystrokes
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contents ofR,to
current
with
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(27.1+35.6)x1.0823
full12digit
the
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calculate
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the
numberinthe
precision.
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number
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Keys:
271
35.6
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To
Clearing
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all
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The
an
2:
Arithmetic
and
Storage
Registers
27
Page 34

The
following
Keys
[STO)[+]
(STO)E)
(STOJ(x]
(STO)(:]
keystrokes
n
n
n
n
New
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old
number+displayed
old
number-displayed
old
numberxdisplayed
old
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use
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1.097x35.6671=?
in
Register
n
number
number
number
number
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(RCL]
1
=
0
[+]
Display:
1.0970
1
25.6671
28.1568
1.0970
1
10.0000
35.6671
39.1268
Description:
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1.097inR,,
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first
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calculation.
contents
replace
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second
answer.
Ry,
of
2:
28
Arithmetic
and
Storage
Registers
Page 35

3
Numeric
HP-21S
number
functions
acted
m
Functions
example,
m
Functions
For
6
example,4(INPUT]5[*][%CHG]
between4and5.The
1+
3 2
between4and
m
Polar/rectangular
return
two
General
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with
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calculates
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and
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either
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function):
argument
the
arguments
arguments
3
[»][%6CHG]
coordinate
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actonthe
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use
numberinthe
rootof6.
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calculates
canbeexpressions.
also
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conversions
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Functions
(an
the
the
percent
For
the
percent
arguments
argumentisa
display.
For
arguments.
change
example,
change
and
3:
Numeric
Functions
29
Page 36

Key(s)
Description
Square
root.
Keys:
45
Calculate
45
(x]
=
105
()
3.7
[*/~)(«1)(10*]
Reciprocal
(¢)(x?)
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x1073”7,
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Natural
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Display:
6.7082
3.1623E-5
0.0002
6.3096E
antilogarithm.
logarithm.
-9
Description:
V
45.
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antilogarithmof-3.7.
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base
base
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10
10
3:
Press
display.
Numeric
Functions
(I
30
to
calculate
Calculate/5+
the
reciprocalofthe
1/,.
numberinthe
Page 37

Keys:
Display:
Description:
3
=
The
exponentiation
positive
numbers.
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=
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keys
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4.
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usedtofindapercent,
the
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and1+
add
or
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m
m
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by
function
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100.
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the
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last
the
that
3:
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operator
displayed
interprets
percent
of the
Functions
you
number
the
entered
31
Page 38

Example.
Find
27%of85.3.
Keys:
85.3
(x]27(\1](%]
(=)
Find
the
number
200
(=]25[v][%]
=
Percent
To
calculate
Change
the
(expressedasa
Example.
Calculate
Keys:
291.7
316.8
[*][%CHG]
Calculate
the
Display:
0.2700
23.0310
that1s25%
50.0000
150.0000
percent
change
percentageofn,)
the
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8.6047
percent
change
Description:
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Calculates
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change
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Description:
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calculation.
and
316.8.
n;.
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12
65
32
[x]
5
18
[»][%CHG]
3:
Numeric
Functions
60.0000
38.3333
Calculates
Displays
between60and
and
percent
(65+18).
enters
change
n;.
Page 39

Pi
()
Pressing
displayed
12-digit
Example.
Find
the
(A=4nr).
Keys:
4
(x]
[(«q])(m]
x]
4.5
(1)
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(=)
Trigonometric
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valueisactually
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Display:
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display
inch
Description:
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square
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one
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and
press
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format,
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area
the
in
3:
Numeric
Functions
33
Page 40

Keys
(]
()
(DEG]
(RAD]
Description
Sets
Degrees
degreesina
measuredindecimal
than
degrees-minutes-seconds).
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radiansina
mode.
circle.
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circle.
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degrees
are
are
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360
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current
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tangent
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Description:
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arc
sine
arc
cosine
arc
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15
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1
60
34
3:
Numeric
Functions
0.2588
1.7321
Degrees
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mode.
sineof15°.
tangentof60°.
Page 41

=
.35
[«](ACCS]
(=)
.62
[«1](ACOS)
=
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and
2.7321
69.5127
51.6839
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3:
Numeric
Functions
number
35
Page 42

@lT@
Angleindecimal
Angle
radians
degrees
in
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hours
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Keys:
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format
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[«](>HR]
]
in
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322.2000
90.3375
25.1532
251532040000
I:-—:Jl
Hours
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format
Description:
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degrees.
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minutes,15seconds
decimal
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to25degrees,
minutes,32seconds.
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(32.04
degrees.
decimal
seconds).
T
QG
in
1.79~.
1.79r
radians
25.2589
15
seconds
to
20
to
degrees
36
3:
Numeric
Functions
Page 43

Coordinate
Conversions
L
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®S0O8e000
-
0000
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ooooo
cocooo
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from
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6
[*][>R]todisplay
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to
display
coordinates,
y.
x.
3:
Numeric
Functions
37
Page 44

Example.
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coordinates.
the
rectangular
coordinates
(10,
—15)topolar
Keys:
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(DEG]
10
15
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the
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Display:
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18.0278
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3.5000
6.0622
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Description:
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mode.
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and
displays
Displays
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r.
coordinates:
Enters
r.
Enters6,calculatesxand
y,
and
displays
Displays
y.
x.
38
3:
Numeric
Functions
Page 45

Parts
L
(«](IP)
Keys
of
Numbers
Integer
partofthe
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number.
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valueofthe
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Display:
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123456789000
123457000000
internallytothe
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number.
occursinALL
FIX,
SCI,orENG
(the
Description:
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number.
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number.
Rounds
internally.
number
without
numberofdigits
display
mode.)
full
precision
number
its
of
3:
Numeric
Functions
39
Page 46

Probability
Probability
and
Distributions
|
Factorial
Pressing
number
Combinations
The
numberofcombinationsofn
of
different
No
item
of
the
calculating
The
numberofpermutationsofn
of
different
ofnitems.Noitem
different
keystrokes
Your
permutations,
probabilities.
[*][nl]
mustbean
occurs
sameritems
orders of
calculates
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for
calculating
HP-218S
integerinthe
and
than
are
can
the
provides
and
random
the
factorialofthe
Permutations
onceinthe
not
counted
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more
sameritems
permutations:
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range0through
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taken
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separately.
[INPUT]
that
than
are
combinations,
numberstohelp
numberinthe
takenratatimeisthe
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items,
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r-value
takenratatimeisthe
canbetaken
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counted
n-value
separately.
you
253.
groupofn
and
different
these
keystrokes
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fromalarger
arrangement,
r-value
calculate
display.
number
items.
number
and
Use
these
[®][Pn,r].
The
orders
for
group
40
4:
Probability
and
Distributions
Page 47

Keys:
Display:
Description:
5
3
[](Cn,]
5
3
[*][Pn,r]
Combination
Random
To
storeaseed
number
previous
To
and
contents.
generateasequenceofnumbers
(«(a)(RAN#].
and
Number
for
press
This
5.0000
10.0000
5.0000
60.0000
Permutation
and
the
random
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first
producesapseudo-random
0<RAN#<1."
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(mo-r)r!
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’
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number
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seedisstoredinR
random
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from
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n!
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generator,
the
previously
numberinthe
Enters
Enters
calculates
the
n-value.
the
r-value;
combinations
of5objects,3atatime.
Enters
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calculates
the
n-value.
the
r-value;
permutations
of5objects,3atatime.
enterapositive
and
writes
over
the
sequenceisdisplayed.
stored
seed,
press
range
*
The
numberispartofa
This
sequence
London:
Addison
passes
Wesley,
sequenceofuniformly
the
spectral
test
1981).
(D.
Knuth,
4:
Probability
distributed
Seminumerical
and
psuedo-random
Algorithms,
Distributions
numbers.
Vol.
41
2.
Page 48

Distributions
under
that
tail
Using
HP-21S,
inverse.
under
You
valueofthe
the
are
other
chapter.
distribution
Distribution
Normal
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the
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the
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than
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probability
you
can
calculateanupper
upper
tail
probability
curvetothe
calculate
random
variableifyou
thatiscalculatedisthe
upper
functions
rightofthe
the
area
variable.
tail,
Keys
=
know
use
are:
distribution
under
Conversely,
the
conversion
Inverse
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functionsonthe
tail
correspondstothe
random
the
curveifyou
the
area
upper
(zp]
probabilityorits
area
variable
you
under
tail.Ifyou
instructionsatthe
Keys
know
can
calculate
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value.
the
curve.
are
using
These
distribution
textbooks.
determine
statistical
42
4:
Probability
Student’s
F
X
The
calculator
any
upper
tables.
t
functions
functions
tail
probability,
and
Distributions
()
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replace
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statistical
expand
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X%
tables
the
tablesbyallowing
the
selected
found
values
in
in
you
to
Page 49

Normal
Upper
To
upper
Q(z)isthe
variableZis
calculate
tail
Tail
Probability
the
area
under
the
curvetothe
probability),
probability
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enter
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thatastandard
than
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z value
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press
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random
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the
probability
Keys:
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Description:
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the
0
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upper
tail
Q(z)=0.0446
z=1.7
is
4:
Probability
and
Distributions
43
Page 50

InverseofUpper
Distribution
If
you
know
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upper
to
calculatez,enter
the
Tail
Probability—
tail
probabilityp(area
probability
and
press
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0.025?
Keys:
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label
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Display:
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the
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the
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the
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enter
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Description:
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calculator
thezvalue.
then
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1.
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t
you
of
maximum
useis299.
44
4:
Probability
and
Distributions
Page 51

7
Example.
distribution
Keys:
8
1.86
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If
you
to
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(](te].
Whatisthe
with8degreesoffreedom
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know
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upper
the
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=
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.001
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under
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then
withaStudent’s
the
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4:
Probability
and
Distributions
45
Page 52

Example.Ahypothesis
Student’stdistribution
foranupper
Keys:
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F
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with26degreesoffreedom
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Display:
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Find
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46
4:
Probability
To
calculate
store
the
denominator
value
and
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df;
the
2.
The
can
useis299.
the
area
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press
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degreesoffreedom,
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and
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wheretostore
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value
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curve,
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the
enter
the
rightofthe
To
press
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value
the
F
(1]
Page 53

Example.
freedom
to
16,
foranF
Whatisthe
(df;)
equalto3
valueof5.29?
upper
and
denominator
tail
probability
with
numerator
degreesoffreedom
degrees
(df,)
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of
Keys:
3
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If
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2
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Upper
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Display:
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want
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4:
Probability
and
Distributions
47
Page 54

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8
.05
[*][Fp]
Upper
L
1
2
Tail
with
the
numerator
degreesoffreedom
upper
tailFvalue
LeveI
aff
1
Probability—Chi-Square
To
calculate
the
degreesoffreedominR,
press
[\]
[Q(X?)].
test
requires
fora0.05
Display:
4.0000
8.0000
3.8379
of
Significance
2
the
area
the
criticalFvalue
degreesoffreedom
(df,)
equalto8.
levelofsignificance?
Description:
Stores
Stores
Calculates
Co|
under
the¥?distribution
then
enter
from
(df;)
equalto4
Whatisthe
df;.
df;.
F.
s
Distribution
curve,
the
x? value
the
F
and
(x?)
store
and
48
4:
Probability
To
store
degreesoffreedom
1.
The
calculator
and
maximum
can
useis299.
Distributions
(df,),
enter
the
value
and
numberofdegreesoffreedom
press
the
Page 55

.
Example.
are17degreesoffreedom
Keys:
17
33.41
Inverse
Distribution
If
you
calculate
(]
B%e).
The)statistic
1
[q][Q(X?)]
of
Upper
know
the
upper
x?,
store
df|
15
&3
18
(x?)
tail
the
degreesoffreedominR,
calculated
(df;).
Display:
17.0000
0.0100
.10
Tail
Probability—
probability
fromasampleis33.41
Whatisthe
.05
upper
Description:
Stores
freedom.
Calculates
probability.
Chi-Square
(area
under
then
tail
probability?
the
the
curve),
enterpand
and
there
degrees
the
upper
and
press
of
tail
want
to
4:
Probability
and
Distributions
49
Page 56

Example.Atest
value
correspondingtoan
Keys:
19
.001
How
The
probability.
curvetothe
with
some
equaltoone,
symmetric.
mirror
1
[](X3p)
to
Convert
distribution
areas
other
imageofthe
functions
The
upper
rightofthe
other
than
areaifyou
and
That
is,
sample
that
has19degreesoffreedom
upper
Display:
19.0000
43.8202
df
17|
27.59|
28.87|
30.14
31.41
From
return
tail
probability
given
upper
tail.Itis
remember
the
normal
the
portionofthe
portionofthe
.05
value.
\
X
tail
probabilityof0.001.
Description:
Stores
freedom.
Calculates
.01
33.41
34.80
Upper
values
Sometimes
easytoconvert
that
and
curvetothe
Tail
for
the
upper
correspondstothe
you
the
total
area
Student’stdistributions
curvetothe
rightofzero.
(df;).
Find
the
the
degrees
the»?value.
tail
camulative
area
under
will
needtowork
from
upper
tail
under
the
curve
are
leftofzeroisthe
x?
of
the
to
is
50
4:
Probability
and
Distributions
Page 57

Example.
the
probability
The
probability
normal
1.7,
Q(1.7),
The
variableZisastandard
thatZis
thatZis
curvetothe
and
then
less
than
1.7?
less
than
1.7isthe
leftof1.7.
subtractitfrom1(the
You
can
calculate
normal
area
total
random
under
the
areatothe
area
variable.
area=Q(1.7)
the
standard
under
the
What
right
of
curve).
is
Keys:
1.7
[¢q](Q(2)]
1(3)
Example.
the
probability
The
variableZisastandard
thatZis
Display:
0.0446
0.9554
greater
-1.2
than
normal
1.2orless
0
Description:
Calculates
area.
Subtracts
from
1.
random
than
—1.2?
1.2
upper
tail
upper
tail
variable.
area=Q(1.2)
area
What
is
4:
Probability
and
Distributions
51
Page 58

The
Since
you
desired
the
normal
can
calculate
areaisto
distributions
the
the
rightof1.2,
upper
tail
are
symmetric,
area,
plus
the
Q(1.2),
areatothe
the
areas
and
multiplyby2.
leftof—1.2.
are
the
same,
so
Keys:
1.2
[)[Qz)]
x]2(5]
Example.
so
that
0.95.
The
given
normal
(0.05=2=0.025).
of
0.025.
The
variableZisastandard
the
probability
areais0.95.
distributionissymmetric,
Display:
0.1151
0.2301
normal
thatZis
less
thanzand
N
O
The
area
not
includedis1—0.95=0.05.
halfofthis
The
desiredzcorrespondstoan
Description:
Calculates
area.
Calculates
random
greater
area=0.95
area=
N
areaisin
upper
upper
answer.
variable.
than-zis
1—’02—953
the
upper
tail
tail
probability
tail
Find
z
equal
to
=0.025=Q(1.96)
Since
the
Keys:
.025
You
52
(*](zp)
will
find
4:
Probability
other
examplesoftail
and
Display:
1.9600
Distributions
Description:
Desired
conversionsinchapter
valueofz.
6.
Page 59

Statistical
Calculations
The
for
accumulatedinregistersR4through
at
storedineach
the
Mean
and
Linear
Linear
Weighted
regression
estimate
Summation
Clearing
Clear
the
statistical
you
don’t
clear
automatically
statistical
registers,
and
[€][Z-]
one-
and
two-variable
the
lower
rightofthe
register.
statistical
standard
mean.
functionstocalculate
deviation.
statistics.
and
forecasts.
statistics:n,2x,
Statistical
registers
the
registers,
includedinthe
press
(R4
data
summation
[®](CLZ].
keys
are
statistics.
keys
Once
£x%,
Xy,
Data
through
currently
(The
usedtoenter
Summation
indicate
you
enter
the
)2,
and
Lxy.
Ry)
before
storedinR4
calculations.Toclear
displayisalso
and
Rg.
The
what
statistical
the
data,
following:
entering
throughRyis
cleared.)
register
delete
data
you
new
the
data
is
labels
data
can
use
data.
is
If
5:
Statistical
Calculations
53
Page 60

Summary
Some
functions
values
have
Keys
(=]
(]
Ew
()
of
Statistical
return
been
returned.
Arithmetic
(average)ofthe
Meanofthe
weightedbythe
Sample
deviationofthe
two
values.
Press
[4][SWAP]tosee
Description
mean
x-values.
x-values
y-values.
standard
x-values.*
Calculations
The:annunciator
(«1)[SWAP]toDisplay
Arithmetic
(average)ofthe
Sample
deviationofthe
you
entered
indicates
the
hidden
mean
standard
that
value.
y-values.
y-values
y-data.*
two
if
(](ox,0y]
y-value
()
x-value
(]3]
(«a)(m,b]
*
Sample
Population
t
The
correlation coefficientisa
how
closely
correlation,
indicates
Population
deviationofthe
Estimateofx
valueofy.
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valueofx.
Slope
calculated
standard
non-correlated
deviation
standard
and-1indicatesaperfect
the
data
deviation
fits
standard
foragiven
foragiven
(m)ofthe
line.
assumes
assumes
numberinthe
the
calculated
data.
x-values.*
dataisa
negative
samplingofa
the
data
constitutes
range—1through+1that
line.A+1
correlation.Avalue
Population
deviationofthe
you
entered
Correlation
Correlation
y-intercept
calculated
indicatesaperfect
standard
coefficient.t
coefficient.t
(b)ofthe
line.
larger,
the
entire
y-values
y-data.*
complete
population.
measures
positive
closetozero
if
set.
54
5:
Statistical
Calculations
Page 61

Keys
4
(n)
Number
of
data
Description
points
entered.
5(x)
8
Entering
Thereisno
statistical
exceed
warning
(«1][CLRG].
One-Variable
To
enterxdata
1.
2.
3.
limittothe
registers.Ifstatistical
+9.99999999999x10*°,
(OFLO).
Clear
Enter
the
numberofitems
Continue
[Z+].
The
6
(Xy)
7
(&¢*)
(3y%)
9
(Xxy)
Sumofthe
Sumofthe
Sumofthe
Sumofthe
Sumofthe
x-values.
y-values.
squaresofthe
squaresofthe
productsofthex-and
Statistical
numberofvalues
Data
remains
Statistics
for
one-variable
the
contents ofR4throughRyby
first
value
accumulated.
accumulating
n-valueisincremented
Data
data causes
the
stored
statistics,
and
press
valuesbyentering
you
HP-21S
until
[Z+].
The
with
x-values.
y-values.
y-values.
can
accumulateinthe
the
valueofa
displaysatemporary
you
press
pressing
HP-21S
the
each
entry.
register
(]
[®](CLZ].
displaysn,the
numbers
and
to
overflow
or
pressing
5:
Statistical
Calculations
55
Page 62

Two-Variable
To
enter
x,y
pairsofstatistical
1.
Clear
the
2.
Enter
the
3.
x-value
Enter
and
the
displaysn,the
4.
Continue
entry.
To
enter
data
for
x,
and
its
corresponding
Correcting
Statistics
and
data,
contentsofR,
first
x-value
throughRyby
and
press
the:annunciator
corresponding
y-value
numberofpairsofitems
entering
x,y
pairs.
calculating
the
The
weighted
weightasy.
Statistical
Weighted
pressing
(INPUT].
appearsinthe
and
The
press
Mean
[#][CLZ].
HP-21S
display.
[£+].
The
accumulated.
n-valueisincremented
mean,
enter
Data
each
displays
HP-21S
with
data
the
each
value
as
Incorrect
is
incorrect,
entries
Correcting
To
delete
and
1.
Keyinthe
2.
Press
3.
Enter
Correcting
To
delete
and
1.
Keyinthe
2.
Press
3.
Enter
canbedeleted
you
must
delete
One-Variable
reenter
[¢q)(Z-]todelete
the
reenter
[q)(Z-]todelete
the
statistical
x-valuetobe
correct
value
Two-Variable
x,y
pairsofstatistical
x-value,
correct
press
x,y
pair
using
and
reenter
data,
deleted.
the
value.
using
the
values.
using
(€](Z-].Ifeither
both
values.
Data
The
n-valueisdecreasedbyone.
[Z+].
Data
data,
and
then
keyinthe
The
n-valueisdecreasedbyone.
and
valueofanx,y
[Z+].
pair
y-value.
56
5:
Statistical
Calculations
Page 63

Mean,
Standard
Statistics
L
OsseOs
O00000
CoOo0ooo
oooaoo
ooooo
OOoooo
OoOoO0OOos
You
can
calculate
deviation
summation
you
(S,),population
statistics,n,£x,
can
also
population
summation
Deviations,
the
sample
calculate
standard
statistics
the
deviationofthe
Ly,
mean
standard
and
mean,
£y?,
and
and
Summation
(x),
sample
deviation
£x?ofx-data.
sample
standard
y-data,
Zxy.
standard
(o,),and
For
and
the
x,y
data,
deviation,
Example
1.Ayacht
captain
averagetochangeasail.
observes
of
sample
square,
Keys:
()
4.5
4
2
3.25
3.6
3.6
3.5
3.75
[2)(z.7]
(>)(5x.8y]
minutes
standard
using
(]
themasthey
required:
deviationofthe
the
formulaV£x?/n
carry
4.5,4,2,
Display:
0.0000
1.0000
2.0000
3.0000
4.0000
5.0000
4.0000
5.0000
6.0000
3.5000
0.8515
wantstodetermine
She
randomly
out
the
sail
3.25,
3.5,
times.
.
chooses
change,
3.75.
Calculate
Also,
how
longittakes
six
membersofher
and
records
the
calculate
the
Description:
Clears
statistics
Enters
first
Enters
Enters
Enters
to
Oops!
enter
Deletes
second
third
fourth
Whatifyou
3.5?
3.6
n-valuebyone.
Enters
fifth
correctly.
Enters
sixth
Calculates
Calculates
standard
on
crew,
the
number
mean
and
root
mean
registers.
value.
value.
value.
value.
meant
and
decreases
time
time.
the
mean.
the
sample
dewviation.
5:
Statistical
Calculations
57
Page 64

RCL])
7
8
4
=]
The
standard
[«1)[SWAP]
deviations
are
isasamplingofa
If
the
data
constitutes
deviations
canbecalculatedbypressing
[+2)(SWAP]todisplayo,.
the
sample
larger,
77.1250
6.0000
3.5853
calculatedby[®](Sx,Sy]
complete
the
entire
standard
deviations.
setofdata.
population,
[®][ox,0y]todisplayo,and
Displays
Displays
Calculates
square.
and
They
the
population
Tx?.
7.
the
[*][Sx,Sy]
assume
that
standard
root
the
mean
data
(]
Example
193,
182, 177,
kilograms.
heights
and
y-data).
Keys:
(]
193
182
177
185
()
(«](SWAP
[)lox,o
2.
The
and
Find
the
weights,
90
81
83
77
coach
185
centimeters
mean
then
has
four
and
population
find
the
Display:
0.0000
1.0000
2.0000
3.0000
4.0000
184.2500
82.7500
5.8041
new
playersonthe
and
weightsof90,
standard
total
weightofthe
team
with
81,
83,
and
deviationofboth
players
(sumofthe
Description:
Clears
statistics
Begins
and
Calculates
heights
Displays
entryofheights
weights.
mean
(x).
meanofweights
).
Calculates
standard
heights
population
deviation
(x).
heights
of
77
their
registers.
of
for
58
5:
Statistical
Calculations
Page 65

(«)(SWAP
6
Linear
4.7104
331.0000
Regression
Least
squares
for
estimation
throughasetofx,y
x,y
pairs.Astraight
thex-and
slope
andbis
linear
and
y-variablesofthe
the
and
y-intercept.
Estimation
regressionisa
forecasting.Itis
data.
There
line
estimates
formy=mx+b,
Displays
standard
weights
Displays
(sumofy’s).
statistical
usedtofitastraight
mustbeat
the
population
deviation
(y).
total
method
least
two
relationship
wheremis
for
weight
used
line
different
between
the
Linear
Linear
canbeusedtoestimateay-value
linear
Regression.
1.
Enter
the
2.
Press
=
(Q)[E1]
correlation
m
[«¥)[m,b]todisplaym,the
displayb,the
Estimation.
estimation
1.
Enter
the
2.
Enter
the
mToestimatexfor
Todoa
x,y-data
using
[Q)([SWAP]
coefficient.
y-intercept.
The
calculations,
x,y-data
known
using
x-valueory-value.
linear
the
(or
straight
the
the
giveny,enter
[«)(zd.
mToestimateyfor
()
Bu).
the
givenx,enter
regression
instructionsonpage
(][]
slopeofthe
line
calculatedbylinear
foragiven
instructionsonpage
calculation,
[1](SWAP))todisplayr,the
line,
x-value,orvice
the
y-value,
the
x-value,
56.
then
56.
then
then
[¢](SWAP]
regression
versa.Todo
press
press
to
5:
Statistical
Calculations
59
Page 66

Example.
concentrationofone
varying
are observed:
only
X
Y
The
rate
the
initial
|0.050
|[0.0062
of a
certain
chemical.
concentrationofthe
0.075
0.00941
chemical
When
0.10
0.0140
the
reaction
reactionisrun
chemical,
dependsonthe
0.125
0.0146
the following
initial
repeatedly,
rates
0.20
0.023
Calculate
line
fittedtothe
Keys:
(]
.05
.075
.00941
A
125
2
(«a)(m.b]
[«
[SWAP
[«Q](Zr]
Estimate
moles
.09
[«)([SWAP]
per
[](3.1]
the
slope
.0062
.014
.0146
.023
the
rateofthe
liter.
and
y-interceptofthe
data.
Also
Display:
0.0000
5.0000
0.1093
0.0014
0.9890
reaction
0.0113
calculate
when
least
the
correlation
the
concentration
squares
regression
coefficient.
Description:
Clears
statistics
Enters
x,y-data.
Displays
Displays
(:
result).
Displays
coefficient.
Calculates
forx=
slope.
y-intercept
indicates
correlation
equals
0.09.
straight
registers.
another
0.09
estimateofy
60
5:
Statistical
Calculations
Page 67

Estimate
.02
the
(N][Z1]
Weighted
To
calculate
frequencies
1.
Use
frequenciesofthe
2.
Press
concentration
Mean
the
weighted
yy,
y2,...,
¥n,
and
[*][zw].
necessary
0.1700
0.0000
meanofdata
to
enter
x-values.
x,y
for
the
points
pairs.
rate
equalto0.0200.
Calculates
fory=0.02.
Clears
annunciator.
x;, x,,
...,X,occurring
The
y-values
estimateofx
display
are
the
and
:
with
Example.Asurveyof266
54ofthem
$216.
Keys:
(]
200
205
210
216
(]
rent
Whatisthe
54
32
88
92
[zw
for
$200
average
per
Display:
0.0000
1.0000
2.0000
3.0000
4.0000
209.4436
one-bedroom
month,32for
monthly
rent?
rental
apartments
$205,88for
$210,
Description:
Clears
statistics
Begins
entryofrents
numberofapartments.
Calculates
mean.
reveals
and92for
registers.
weighted
that
and
5:
Statistical
Calculations
61
Page 68

Equations:
62
5:
Statistical
Calculations
Page 69

Built-in
Program
Library
The
built-in
be
accessedbypressing
letter
keys,AthroughF,in
pressed,
abbreviated
released.
Name
A
B
C
D
program
the
top
row
program
One
Sample
Two
Sample
Linear
Chi-Square
library
consistsofsix
[€q])(LOAD]
the
keys
assume
nameisdisplayed
Title
Test
Statistics
Test
Statistics
Regression
Test
Test
Statistic
programs
followedbyoneofthe
top
row.
(When
their
letter
values.)
until
the
Statistics
that
[$]
An
letter
Message
1-StAt
2-StAt
Lr-StAt
CHI-2
key
can
is
is
E
you’ve
can
the
(However,
use
without
F
entered
and
Lr-StAt,
calculation,
Whenaprogramisloaded,itclears
memory.
Once
the
statistics
you
Lr-StAt
calculatingastatistic,
repeat
Binomial
Time
Probability
ValueofMoney
the storage
your
tests
describedinthis
load
affecting
youdonot
correcting
data
and
your
registers
(either
use
data.
needtoreenter
the
Distribution
any
other
programs
are
left
raworsummary),
chapterinany
1-StAt,
and
Also,ifyou
mistake.
that
intact.)
you
order.
then
reload
and
makeamistake
your
data.
6:
Built-in
bin
FinAnCE
maybein
can
calculate
For
instance,
use
You
simply
Library
63
Page 70

This
table
lists
the
organizationofthe
quick
reference
guide.
symbols
programs.
usedinthe
The
diagramsinthis
flow
diagrams
chapter
that
show
the
makeupthe
The
restofthis
the
example
asaguidetofind
Symbols
Symbol
%3
»
3T
TESX,~NQAMOQT
that
in
Program
Sample
Sample
Sample
Population
Sample
Population
Population
Precision
Observed
Expected
Degreesoffreedom.
Standard
Student’strandom
Chi-square
Hypothesized
Upper
Probability.
size.
mean.
standard
proportion.
tail
chapter
describes
resembles
the
solution,
the
Flow
Description
deviation.
standard
proportion.
mean.
(1/,
widthofconfidence
value.
value.
normal
random
probability.
each
problem
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6:
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Page 76

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Page 79

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6:
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Page 80

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Page 100

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