ÿþK U R S
S T A T Y S T Y K A
L e k c j a 1
S t a t y s t y k a o p i s o w a
R O Z W I Z A N I E Z A D A N I A D O M O W E G O
w w w . e t r a p e z . p l S t r o n a 1
C z [ 1 : T E S T
P y t a n i e 1 : b
P y t a n i e 2 : c
P y t a n i e 3 : d
P y t a n i e 4 : a
P y t a n i e 5 : d
P y t a n i e 6 : d
P y t a n i e 7 : d
P y t a n i e 8 : b
P y t a n i e 9 : b
P y t a n i e 1 0 : c
w w w . e t r a p e z . p l S t r o n a 2
C z [ 2 : Z A D A N I A
Z a d a n i a n a m i a r y [r e d n i e
Z a d a n i e 1
a ) X =ð1 , 7 7
H =ð1 , 9 6
b )
X =ð 2 , 2 6
g
Z a d a n i e 2
1 2 3 4 5
x i
1 4 2 7 6
n i
X =ð 3 , 6 5
Z a d a n i e 3
a ) D =ð 1
b ) D =ð 3
Z a d a n i e 4
a ) M e =ð 1
b ) M e =ð 2
Z a d a n i e 5
Q 1 =ð 3
Q 2 =ð 4 =ð M e
(ð )ð
Q 3 =ð 5
w w w . e t r a p e z . p l S t r o n a 3
Z a d a n i e 6
X =ð 3 1 4 4 , 7 4
D =ð 2 8 8 5 , 2 5
M e =ð 2 9 5 4 , 5 5
Q 1 =ð 2 0 9 0 , 9 1
Q 3 =ð 3 8 1 8 , 1 8
Z a d a n i a n a m i a r y r o z p r o s z e n i a
Z a d a n i e 7
S =ð 5 , 1 1 2
Z a d a n i e 8
d =ð1 , 1 3
Q =ð 1 , 2 5
-ð1 , 2 5 <ð X T Y P <ð1 , 2 5
R =ð 4
Z a d a n i e 9
V S =ð 4 6 %
Z a d a n i e 1 0
Q =ð1 , 5
Z a d a n i e 1 1
d =ð1 , 6
w w w . e t r a p e z . p l S t r o n a 4
Z a d a n i a n a m i a r y a s y m e t r i i
Z a d a n i e 1 2
W S =ð -ð3 , 0 5 . O a s y m e t r i i l e w o s t r o n n e j .
Z a d a n i e 1 3
A S =ð-ð0 , 3 4 . J e s t t o n i e z b y t s i l n a a s y m e t r i a l e w o s t r o n n a .
Z a d a n i e 1 4
m 3 »ð-ð1 4 4 , 6 . J e s t t o s y m e t r i a l e w o s t r o n n a .
Z a d a n i e 1 5
A s =ð 0 , 5 3 . J e s t t o u m i a r k o w a n a a s y m e t r i a p r a w o s t r o n n a .
Z a d a n i a n a m i a r y k o n c e n t r a c j i
Z a d a n i e 1 6
a ) k =ð 0 , 3 1 . S Ba b a k o n c e n t r a c j a .
b ) k =ð 0 , 4 5 . U m i a r k o w a n a k o n c e n t r a c j a .
Z a d a n i e 1 7
a 4 =ð 2 , 1 6
a ) . M n i e j s z a k o n c e n t r a c j a , n i | w r o z k Ba d z i e n o r m a l n y m .
E K S C E S : -ð0 , 8 4
a 4 =ð1 , 8 5
b ) . M n i e j s z a k o n c e n t r a c j a , n i | w r o z k Ba d z i e n o r m a l n y m .
E K S C E S : -ð1 , 1 5
w w w . e t r a p e z . p l S t r o n a 5
Z a d a n i a r ó |n e
Z a d a n i e 1 8
X =ð 1 7 6 , 6 3
S =ð 1 1 , 6 5
D =ð 1 7 5 , 1 4
M e =ð 1 7 6 , 1 3
Q 1 =ð 1 6 8 , 3 6
Q 3 =ð 1 8 5 , 0 7
1 6 4 , 9 8 <ð X T Y P <ð1 8 8 , 2 8
V S =ð 6 , 6 %
Q =ð 8 , 4
1 6 7 , 7 3 <ð X T Y P <ð1 8 4 , 5 3
V Q =ð 4 , 7 7 %
W S =ð 1 , 4 9
A S =ð 0 , 1 3
m 3 =ð 1 4 3 , 3 7
A s =ð 0 , 0 9
k =ð 0 , 0 4
m 4 =ð 4 9 6 0 5 , 8
a 4 =ð 2 , 7
Z a d a n i e 1 9
b )
Q 1 =ð 3 1 , 1 4
Q 3 =ð 6 7 , 5 4
2 5 % n a j g o r s z y c h u c z n i ó w m i a Bo m n i e j n i | 3 2 p u n k t y .
2 5 % n a j l e p s z y c h u c z n i ó w m i a Bo w i c e j n i | 6 7 p u n k t ó w .
c )
Q =ð1 8 , 2
M e =ð 4 9 , 7 4
V Q =ð 3 6 , 5 9 %
w w w . e t r a p e z . p l S t r o n a 6
W y n i k i z m a t u r y n i e b y By z b y t n i o r o z p r o s z o n e .
d )
W S =ð-ð0 , 8
A S =ð-ð0 , 0 2
R o z k Ba d j e s t p r a w i e s y m e t r y c z n y , b i o r c p o d u w a g w s p ó Bc z y n n i k i p o z y c y j n e .
Z a d a n i e 2 0
a )
0 1 2 3 4 5 6
x i
5 6 3 9 4 4 3
n i
b )
< 0 , 2 ) < 2 , 4 ) < 4 , 6 ) < 6 , 8 )
x i
1 1 1 2 8 3
n i
c )
X =ð 2 , 5 5
Z a d a n i e 2 1
a )
0 1 2 3 4 5 6 7 8
x i
2 3 4 6 5 2 5 3 4
n i
w w w . e t r a p e z . p l S t r o n a 7
b )
< 0 , 2 ) < 2 , 4 ) < 4 , 6 ) < 6 , 8 ) < 8 , 1 0 )
x i
5 1 0 7 8 4
n i
c )
X =ð 4 , 1 8
Z a d a n i e 2 2
a ) 3 9 %
b ) 4 %
c )
Z Bo t y k a j a k z p r z e d z i a Bu 2 0 0 0 - 4 0 0 0
W a k a c y j n a p r z y g o d a z p r z e d z i a Bu 2 0 0 0 - 4 0 0 0
d )
Z Bo t y k a j a k X =ð 3 9 6 0
W a k a c y j n a p r z y g o d a X =ð 5 6 0 0
e )
Z Bo t y k a j a k V S =ð 5 5 , 0 8 %
W a k a c y j n a p r z y g o d a V S =ð 4 8 , 3 1 %
B a r d z i e j z r ó |n i c o w a n s t r u k t u r d o c h o d ó w m a f i r m a Z Bo t y k a j a k
w w w . e t r a p e z . p l S t r o n a 8
Z a d a n i e 2 3
a ) 2 3 %
b ) 5 %
c )
P l a m a z p r z e d z i a Bu 2 0 0 0 - 4 0 0 0
C z y [c i o c h z p r z e d z i a Bu 2 0 0 0 - 4 0 0 0
d )
P l a m a X =ð 3 9 8 0
C z y [c i o c h X =ð 5 5 4 0
e )
P l a m a V S »ð 6 6 , 0 9 %
C z y [c i o c h V S »ð 5 6 , 1 3 %
B a r d z i e j z r ó |n i c o w a n s t r u k t u r m a f i r m a P l a m a .
Z a d a n i e 2 4
X =ð1 , 2 8
Z a d a n i e 2 5
k =ð 0 , 4 . M a m y t u u m i a r k o w a n k o n c e n t r a c j .
Z a d a n i e 2 6
G r u p a l i c z y 4 s t u d e n t ó w .
K O N I E C
w w w . e t r a p e z . p l S t r o n a 9
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