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In: Business and Management

Submitted By sachinrullllz
Words 1400
Pages 6
Computational
Finance
 Fall
2012
 Daniel
Egger
 
 Handout
No.
2
 Basic
Statistics


! !


 2.1
Topics
Covered
 
 2.2
Mean
and
Median
of
a
Data
Set
 2.3
Variance
and
Standard
Deviation
of
a
Data
Set
 2.4
Covariance
and
Correlation
of
two
Data
Sets

 2.5
Standard
Units
(Z‐Scores)
and
their
use
for
Calculating
Correlation

 2.6
Slope
(Beta)
and
Y‐Intercept
(Alpha)
of
the
regression
line
of
one
stocks’s
annual
 returns
against
annual
market
return
 2.7
Calculating
the
Expected
Return,
and
Volatility,
of
a
Combination
of
Assets
 2.8
Graphing
the
Efficient
Frontier
for
Risk‐Averse,
Profit‐Maximizing
Investors
 
 2.2
Mean
and
Median
of
a
Data
Set
 
 The
Mean
is
the
average
of
a
set
of
n
known
values
X
=
 {x1 , x2 ,..., xn } .

 A
sample
mean
can
be
written:

 
 1 n x 
=

 " xi 
 ! n i=1 
 (Note
that
if
a
“sample
mean”
and
a
“population
mean”
need
to
be
distinguished,
 x 
 is
conventionally
used
for
the
sample
mean,
and
 µ 
for
the
population
mean.
This
 distinction
will
not
concern
us
in
Introductory
Computational
Finance).
 
 ! The
mean
may
be
calculated
using
the
Excel
function
AVERAGE.
 ! 
 The
Median
is
the
number
in
the
middle
of
an
ordered
set
of
values;
half
of
all
values
 are
greater,
and
half
less.
When
the
total
number
of
values
is
even,
the
median
is
the
 average

of
the
two
numbers
in
the
middle.
 
 The
median
may
be
calculated
using
the
Excel
function
MEDIAN.
 
 
 


1


!

2.3
Variance
and
Standard
Deviation
of
a
Data
Set
 
 2 The
population
Variance
of
a
data
set,
 " 
(lower
case
Greek
“sigma”
squared)

 
 1 n " 2 
=
 # (xi " x)2 
 n i=1 ! 
 Can
be
read
as
“the
average
of
the
squared
differences
from
the
mean
of
the
data
 set.”
Population
Variance
may
be
calculated
using
the
Excel
function
VARP.

 ! 
 Population
Standard
Deviation
of
a
data
set,
 " 
(lower
case
Greek
“sigma”)
 

1 n "= $ (xi # x)2 
 ! n i=1 
 Standard
deviation
is
the
square…...

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