STAT
~+
TOT
COU
UTPC
HP-28S
statistics
~
MEAN
CORR
UTPF
commands
n x m matrix called
matrix is
The
not
the
numbers),
data
statistics matrix .
data
Data
defined
current
already
statistics matrix
exist,
command
and
point
entered
points
that
Point
1
2 X
to
when
~
+. A
is
stored
The n dimension
have
N~
SDEV
COY
UTPN
deal
the
current statistics matrix.
be
a matrix
~DAT
you
begin
data
point
as
one
sets
the m dimension
been
entered
Coordinate
1 2 .
X
11
21
CU
VAR
LR
UTPT
with
statistical
stored
in
the
is created automatically, if it
entry
of
statistical
is a vector
row
in
of
the
statistics matrix.
(number
(number
X
12
X
22
as
illustrated
of rows) is
Number
STO~
MAX~
PRDEV
COMB
data
The
variable
m
coordinate
of
below:.
..
.. .
...
RCU
MIN~
PERM
collected in
current
data
statistics
~DAT.
points
values (real
The
columns)
the
number
m
X
X2m
1m
does
with
of
an
first
the
of
n
Certain
of
numbers,
the
list
tion
statistics
the
statistics matrix. User variable
the
columns
are
the
slope
of
the
linear
X
commands
first two
with
the
and
regression
n1
intercept
combine
of
which
command
command
X
n2
data
~PAR
identify
COL~.
computed
.. .
from two specified
contains a list
the
two
columns. You
The
from
last two
the
numbers
most
LR.
Dictionary
Xnm
columns
of
four
real
select
in
the
recent execu-
245
un
STAT
Because
ndry
the
The
(covariance)
ple
If
the
lation
1.
2.
3.
4.
These
data
~DAT
commands
specific statistics
commands
calculate
of
the
population. These
data
represent
statistics as follows.
Execute
data.
Execute
Execute SDEV,
population.
Execute ~-
data.
~+
commands
to
or
delete
and
~PAR
are
ordinary
to recall, view,
commands
SDEV (standard deviation),
sample
the
entire
MEAN
~+
~-
to
to
add
VAR,
DROP
allow
data
from
return a data
you to select a statistics matrix,
or
alter their contents, in
that
statistics using
commands
population,
the
mean
or
COY.
to
remove
the
matrix.
variables, you
deal
with
VAR
data
that
are described in detail below.
you
can
point
representing
data
point
to
The
result is
the
mean
data
CL~
can
addition
the
variables.
(variance),
represent a sam-
calculate
the
the
data.
the
statistics for
point
STO~
and
use
ordi-
and
the
popu-
mean
from
RCL~
to
to
COY
the
the
add
~+
~
+
adds
~DAT.
246
[X1
[[x11
one
or
Dictionary
Level 1
x
X2
•..
X12
more
Sigma Plus
xm]
...
x1m]
data
I
..
..
..
points to
the
current
Command
statistics matrix
...
STAT
For a statistics matrix
~+
in several ways:
Entering one
gument
Entering one
argument
Entering several
n
rows
of
In
each
case,
rent
statistics matrix
creates it as
does
exist,
number
doesn't
~-
data
for
~
+ is a real
data
for
~
+ is a vector
m real
the
an
n x m matrix
an
error occurs if it
of
coordinate
match
the
data
coordinate
coordinate
number
with
m columns, you
point with a single coordinate value.
number
point with multiple coordinate values.
points.
of
.
m real
The
can
coordinate
argument
enter
for
values.
~
the
argument
+ is a matrix
values.
stored
values
values are
in
~DAT.
stored
does
in
of
columns
Sigma Minus
not
each
..
added
If
~DAT
in
the
contain
data
in
as
new
does
variable
a real matrix,
point
entered
~DAT.
Level 1
x
rows
to
not
exist,
~DAT.
If
with
Command
The
The
the
cur-
~+
~DAT
or
if
~+
for
ar-
of
the
~
-
returns
corresponding
by
~+
into
matrix is
The
to
the
deleted
vector
returned
statistics matrix
a vector
to
the
of
the
coordinate
statistics matrix
.
by ~ -
m real
by
~
numbers,
values
~DAT.
can
be
+ .
in
The
edited
or
one
number
the
last
data
last
row
or replaced,
Dictionary
of
if m =
point
the
then
1,
entered
statistics
restored
247
..• STAT
N~
returns
stored
of
CL~
CL~
STO~
the
in
matrix.
clears
the
number
~DAT.
The
the
statistics matrix
of
number
Level 1
obj
Sigma N
It
data
points
of
points
Clear Sigma
It
by
purging
Store Sigma
It
Level 1
n
entered
is
equal
the
in
the
statistics matrix
to
the
number
~DAT
Command
of
Command
variable.
Command
rows
STO~
~DAT.
RCL~
RCL~
takes
returns
rectory.
(when
248
~DAT
Dictionary
To
an
object from
the
recall
doesn't
Recall Sigma
contents
the
of
statistics matrix
exist
in
the
the
the
stack
Level 1
It
variable
current
and
stores it
obj
~DAT
~DAT
from
from a
directory), execute
in
the
the
parent
variable
Command
current
di-
directory
::
D AT .
...
STAT
TOT
These
column
commands
TOT
TOT
computes
in
the
statistics matrix
real
numbers,
MEAN
of
the
MEAN
compute
current
the
sum
or
as a single real
SDEV
elementary
statistics matrix.
Total Command
• x
of
each
of
the m columns
~DAT.
The
sums
number
Mean
• x
VAR
statistics for
Level 1
are
returned
if m =
Level 1
MAX2:
the
data
of
coordinate
as a vector
1.
MIN2:
in
each
values
of
m
Command
MEAN
values
of
computed
where
of
in
m real
xi is
data
computes
points.
the
the
statistics matrix
numbers,
from
the
or
the
ith
coordinate
mean
of
each
~DAT,
as a single real
formula
mean
value
of
the m columns
and
returns
number
in a column,
if m = 1.
the
mean
and
n is
Dictionary
of
coordinate
as a vector
The
mean
the
number
is
249
...
STAT
SDEV Standard Deviation Command
Level 1
.. x
SDEV
columns
standard
a single real
from
where
data
computes
of
deviations
the
formula
xi
is
the
in this
coordinate
number
column,
VAR
VAR
computes
the m columns
turned
m =
1.
as
a vector
The
variance is
the
are
ith
coordinate
the
sample
of
the
of
sample
values
returned
if m =
and
n is
variance
current
m real
computed
11
standard
in
1.
The
value
the
deviation
the
current
as a
vector
standard
in a column,
number
of
each
statistics matrix.
of
m real
deviations
of
data
x is
numbers,
are
the
points.
of
the
computed
mean
Variance Command
Level 1
.. x
of
the
statistics matrix.
numbers,
from
1/
1
L (Xi -
1 i = l
coordinate
or
as
a single real
the
formula
X)
2
values
The
variance is re-
in
each
number
m
The
or
of
as
the
of
if
where
data
250
Xi is
in this
Dictionary
the
ith
coordinate
column, and
n is
value
the
in a column,
number
of
x is
data
the
points
mean
.
of
the
•.. STAT
MAX~
MAX~ finds
of
the
current
of
m real
MIN~
MIN~
of
the
m real
numbers,
finds
current
numbers,
the
maximum
statistics matrix.
or
as a single real
the
minimum
statistics matrix .
or
as a single real
Maximum Sigma
Level 1
• x
coordinate
The
Minimum Sigma Command
coordinate
The
value
in
maxima are
number
Level
• x
value in
minima
number
are
if m = 1.
each
returned
if m =
1
each
returned
Command
of
the m columns
as a vector
1.
of
the m columns
as a vector of
COL~
COL~
CORR
Level
2
COY
Sigma Columns Command
Level 1
LR
PREDV
•
Dictionary
251
...
STAT
COL~
stores
~PAR.
matrix
pairs
pendent
SCL~
For CORR
takes two
them
The
numbers
~DAT,
of
columns.
variable for
.
n2
designates
and
column
as
the
first two objects in
identify
and
are
nl
designates
LR,
the
COY, the
numbers,
column
used
by
or
the
dependent
order
nl
the
numbers
statistics
the
column
horizontal
variable or
of
the
and
n2' from
list
contained
in
commands
corresponding
coordinate
the
two
column
the
the
current
that
vertical
numbers
stack
in
the
work
to
for
DRW~
coordinate
and
variable
statistics
with
the
inde-
or
is
unimportant.
If
any
of
the
two-column
not
yet exist, it is automatically created
and
n2
=
2.
commands
is executed
with
default values
when
~PAR
nl
does
= 1
CORR Correlation Command
Level 1
It
correlation
CORR
the
elements
the
returns
current
of
formula
the
correlation of two
statistics matrix.
~PAR
(default 1
The
and
columns
columns
2).
The
of
coordinate
are specified
correlation
by
the
is
computed
values in
first two
from
.
where
xiII is
ordinate
nl'
xn
' is
2
data
points.
252
"
L
(XiII
I -
XIII)
(Xi"2
- X
)
i = 1
the
ith
in
the
coordinate
column
of
the
I 2
value
the
mean
Dictionary
n2'
data
value in
xn
is
the
I
in
column
1I2
column
mean
n2'
and
nl'
of
xin is
the
n is
data
the
the
ith co-
in
column
number
of
...
STAT
COY
COY
returns
columns
the
first two
computed
where
nate
xn;:
pomts.
LR
value
is
the
xil11
of
the
from
is
in
mean
the
sample
current
elements
the
formula
the
ith
coordinate
the
column
of
the
Covariance Command
Level 1
..
covariance
covariance of
statistics matrix.
in
~PAR
(default 1
value
n2' x
data
Linear Regression Command
nl
in
column
is
the
coordinate
The
columns
and
in
column
the
mean
of
n2'
and
Level
2 Level 1
..
intercept slope
are specified
2).
The
nl'
xil12 is ith coordi-
the
data
n is
the
number
values
in
covariance is
in
column
of
two
by
nl'
data
LR
computes
independent
rent
statistics matrix.
data
are
specified
The
intercept
and 1 of
the
ficients as
the
variable
the
linear
regression
data
column,
The
by
the
first two elements
and
slope
of
stack, respectively.
the
third (intercept)
~PAR.
of a dependent
where
the
the
columns
columns
of
independent
regression line are
LR
also stores
and
fourth
data
column
of
data
exist in
and
in
~PAR
(default 1
returned
these
regression coef-
(slope) items in
Dictionary
on
the
cur-
dependent
and
to levels 2
the
list
253
an
2).
in
·uSTAT
PREDV Predicted Value Command
Level 1 Level 1
x
PREDV
using
LR
computes a predicted
the
linear
regression coefficients
and
stored
in
the
variable
predicted value =
The
regression coefficients intercept
third
and
fourth
cute PREDV
of
zero is
zero.
used
UTPC
The
HP-28S provides four upper-tail probability
you
can
use to
The
upper-tail
probability
where
F(x)
items, respectively, in
without
for
UTPF
that X is
is
the
having
both
coefficients, so
UTPN
determine
probability function
greater
distribution
the
•
value from a real
~PAR:
(x x slope)
and
previously executed
statistical significance
of a random
than a number
function
predicted
most
value
number
recently
+ intercept.
slope
are
stored
the
variable
that
PREDV will always
UTPT
of
x,
X.
and
COMB
commands,
is
argument
computed
by
LR
~PAR.
LR, a default
If
you exe-
PERM
which
of
test statistics.
variable X is
equal
to 1 - F(x),
x,
with
as
the
value
return
the
The
inverses
fidence intervals.
function is a value from 0
as a percent,
example,
which
100% -
254
of
the
the
90th
the
probability
90%
= 10%.
Dictionary
distribution
The
argument
inverse function values are called percentiles . For
percentile
that
functions
through
of a distribution
the
random
are useful for constructing con-
of
an
1;
when
inverse
variable X is greater
upper-tail
the
argument
is
the
is expressed
number
probability
x for
than
x is
You
can
ability
normal
use
the
Solver to
functions. Suppose
distribution
. Let
P
M
x =
obtain
mean
the
you
wish
=
percentile/IOO
of
the
v = variance
random
·
inverses
to
distribution
variable
of
the
upper-tail
determine a percentile
..
STAT
of
prob-
the
UTPN
distribution.
for X, create
and
pr
Try a
Now
yi
(described below)
store it as
ess
SOLVR
normal
compute
elds
the
result X = 1.6449.
To
solve
1 - P =
the
program
.:,::
1 P -
the
current
to
produce
distribution
the
95th
returns
the
the
the
equation
utpn
t'1
',}
equation
Solver
with M = 0, V =
o 1
percentile:
.
95
upper-tail
(M,
~<
U T P t·j -
by
pressing I
menu
•
V,
:
X),
1:
probability
;,:.
,
SOLV I STEQ
for
normal
.
Then
Dictionary
255
·
..
STAT
UTPC
UTPC
variable
dom
returns
is
of
the
greater
UTPF
Level
3
n1
UTPF
returns
dom
variable is greater
denominator
be
positive integers .
UTPN
Upper Chi-Square Distribution Command
Level 2 Level 1 Level 1
n
the
probability
than
distribution. n
Upper Snedecor's f Distribution Command
Level
2
the
probability
degrees of
x
x,
where
Level 1
x •
than
freedom
Upper Norma. Distribution
utpc(n,
must
utpf
x,
where
•
n is
be
I
(nl'
of
the F distribution
utpc(n,
x)
that
a chi-square
the
number
a positive integer.
Level 1
utpf(n1, n2,
n2' x)
that
nl
and
n2
are
x)
of
degrees
x)
a Snedecor's F
the
numerator
.
nl
and
random
of
free-
ran-
and
n2
must
Command
Level
3 Level 2
m v
UTPN
variable
respectively,
number.
256
returns
is
Dictionary
the
greater
of
the
Level 1
probability
than
x,
where m and
normal
I
x •
utpn
(m,
distribution. v
Level 1
utpn(m,
v,
x)
that a normal
v are
the
must
v,
x)
mean
be a
random
and
variance,
non-negative
•••
STAT
UTPT
Upper Student's t Distribution
Level 2 Level 1 Level 1
n x
•
UTPT returns the probability utpt(n,
variable
dom of the distribution.
COMB
is
greater than
Level 2 Level 1
n m
x,
where n is the
n must be a positive integer.
Combinations
•
x)
that
Level
utpt(n,
x)
a Student's t
number
1
of degrees of free-
Command
random
Command
COMB returns the number of combinations of n items taken m at a
time:
m!
(n -m)!
n!
than
10
12
.
The arguments
n
C
m =
,
nand m must
be less
PERM
Level 2 Level 1
n m
PERM returns the
time:
The arguments
nand
Permutations Command
number
of permutations of n items taken m
,
P
m =
n
m must be less
•
---------
(n
Level
11!
-
than
m}!
1
at
a
12
.
10
Dictionary
257
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