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ccorrelation is your life . without relation no correlation exists .....
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Page
7 o
f 11
Exa
mpl
e: C
alcu
late
the
coef
ficie
nt o
f cor
rela
tion
and
inte
rpre
t its
val
ue.
Sale
s R
even
ue
Adv
ertis
ing
Expe
nditu
re
5-10
10
-15
15-2
0 20
-25
75-1
25
4 1
- -
125-
175
7 6
2 1
175-
225
1 3
4 2
225-
275
1 1
3 4
AN
S: r
= 0.
596
Exa
mpl
e: C
alcu
late
the
coef
ficie
nt o
f cor
rela
tion
and
inte
rpre
t its
val
ue.
Age
Gro
up
Sum
Ass
ured
10
,000
20
,000
30
,000
40
,000
50
,000
20
-30
4 6
3 7
1 30
-40
2 8
15
7 1
40-5
0 3
9 12
6
2 50
-60
8 4
2 -
- A
NS:
r =
-0.2
56
Exa
mpl
e:
expe
nses
from
the
data
giv
en b
elow
and
inte
rpre
t its
valu
e:
Adv
ertis
ing
Expe
nses
(Lak
hs)
10
12
15
23
20
Sale
s (La
khs)
14
17
23
25
21
AN
S: r
= +0
.865
Exa
mpl
e: S
how
that
the
coef
ficie
nt o
f cor
rela
tion
lies b
etw
een
-1 a
nd +
1.
Ans
:
Let
a
nd
Now
i.e.
Page
8 o
f 11
Sim
ilarly
usin
g w
e ge
t
Whi
ch c
oncl
udes
Prob
able
Err
or:
The
prob
able
err
or o
f the
coe
ffici
ent o
f cor
rela
tion
is o
btai
ned
as
The
coef
ficie
nt o
f cor
rela
tion
in th
e po
pula
tion
expe
cted
to b
e
Cor
rela
tion
Coe
ffic
ient
Ran
k co
rrel
atio
n m
etho
d is
appl
ied
whe
n th
e ra
nk o
rder
dat
a ar
e av
aila
ble
or
whe
n ea
ch v
aria
ble
can
be r
anke
d in
som
e or
der.
The
mea
sure
bas
ed o
n th
is
met
hod
is kn
own
as ra
nk c
orre
latio
n co
effic
ient
. Thi
s m
etho
d is
appl
ied
to th
e si
tuat
ion
in w
hich
exa
ct n
umer
ical
mea
sure
men
t are
not
ava
ilabl
e. F
or in
stan
ce,
sinc
erity
or
ho
nesty
of
ea
ch
empl
oyee
. C
oeff
icie
nt d
enot
ed b
y a
nd d
efin
ed a
s
D re
fers
to th
e di
ffere
nce
of ra
nks b
etw
een
paire
d ite
ms i
n tw
o se
ries.
[Pro
of: s
ee N
urul
Isla
m P
age
272]
Exa
mpl
e: T
wo
man
ager
s ar
e as
ked
to r
anke
d a
grou
p of
em
ploy
ee in
ord
er o
f po
tent
ial f
or e
vent
ually
bec
omin
g to
p m
anag
ers.
The
rank
ings
are
as f
ollo
ws:
Empl
oyee
A
B
C
D
E
F G
H
I
J
Ran
king
by
Man
ager
1
10
2 1
4 3
6 5
8 7
9
Ran
king
by
Man
ager
2
9 4
2 3
1 5
6 8
7 10
Com
pute
the
coef
ficie
nt o
f ran
k co
rrel
atio
n an
d co
mm
ent o
n th
e va
lue.
Page
9 o
f 11
Solu
tion:
Em
ploy
ee
A
10
9
1 B
2 4
4 C
1 2
1 D
4
3 1
E 3
1 4
F 6
5 1
G
5 6
1 H
8
8 0
I 7
7 0
J 9
10
1 N
=10
=14
Thus
we
find
that
the
re i
s a
high
deg
ree
of p
ositi
ve c
orre
latio
n in
the
ran
ks
assig
ned
by th
e tw
o m
anag
ers.
Exa
mpl
e: C
ompu
te th
e ra
nk c
orre
latio
n co
effic
ient
for t
he fo
llow
ing
data
od
2 te
sts g
iven
to c
andi
date
s for
a c
ritic
al jo
b an
d co
mm
ent o
n th
e va
lue.
Prel
imin
ary
test
92
89
87
86
83
77
71
63
53
50
Fina
l tes
t 86
83
91
77
68
85
52
82
37
57
Solu
tion:
Pr
elim
inar
y te
st
Fina
l tes
t
92
10
86
9 1
89
9 83
7
4 87
8
91
10
4 86
7
77
5 4
83
6 68
4
4 77
5
85
8 9
71
4 52
2
4 63
3
82
6 9
53
2 37
1
1 50
1
57
3 4
N=1
0
=44
Page
10
of 1
1
Thus
we
find
that
the
re i
s a
high
deg
ree
of p
ositi
ve c
orre
latio
n be
twee
n pr
elim
inar
y te
st an
d fin
al te
st
Tie
in R
anks
:
An
adju
stmen
t of t
he a
bove
form
ula
is m
ade
whe
n ra
nks a
re e
qual
Exa
mpl
e: A
n ex
amin
atio
n of
eig
ht a
pplic
ants
for
a po
st w
as ta
ken
by a
firm
. Fr
om t
he m
arks
obt
aine
d th
e ap
plic
ants
in
the
Bang
la a
nd E
nglis
h pa
pers
, C
ompu
te th
e ra
nk c
orre
latio
n co
effic
ient
:
App
lican
t A
B
C
D
E
F G
H
Mar
ks in
Ban
gla
15
20
28
12
40
60
20
80
Mar
ks in
Eng
lish
40
30
50
30
20
10
30
60
Solu
tion:
Mar
ks in
Ban
gla
Fi
nal t
est
15
2 40
6
16
20
3.5
30
4 0.
25
28
5 50
7
4 12
1
30
4 9
40
6 20
2
16
60
7 10
1
36
20
3.5
30
4 0.
25
80
8 60
8
0 N
=8
=8
1.5
Page
11
of 1
1 M
arks
20
is re
peat
ed 2
tim
es, h
ence
a
nd M
arks
30
is re
peat
ed 3
tim
es,
henc
e .
