cours sur les statistiques en arabe

1. ‫ذ‬ ‫ا‬: 1
‫ه‬ ‫ا‬ ‫ون‬ ‫ا‬ ‫ی‬ ‫ﺙ‬‫ﺍﳌﺎﺩﺓ‬‫ﺍﳌﺎﺩﺓ‬‫ﺍﳌﺎﺩﺓ‬‫ﺍﳌﺎﺩﺓ‬::::‫ﺍﻟﺮﻳﺎﺿﻴﺎﺕ‬‫ﺍﻟﺮﻳﺎﺿﻴﺎﺕ‬‫ﺍﻟﺮﻳﺎﺿﻴﺎﺕ‬‫ﺍﻟﺮﻳﺎﺿﻴﺎﺕ‬
::::
‫ﻡ‬ ‫ع‬ ‫ا‬ ‫ى‬ ‫ﻡ‬‫ك‬‫أد‬
I.‫ء‬ ‫ی‬ ‫ﺕ‬:
‫ا‬ ‫د‬ ‫ت‬ ‫د‬ ‫إ‬ ‫ة‬ ‫اه‬ ‫و‬ ‫ء‬ ‫ا‬.
‫ﺹ‬ ‫ا‬‫ح‬‫ا‬:
‫ا‬ ‫آ‬ ‫ا‬:‫ا‬ ‫ه‬"‫ا‬ ‫أو‬"‫را‬ ‫ا‬.
‫ا‬ ‫ة‬ ‫ا‬:‫و‬ ‫ا‬ ‫ه‬ ‫آ‬‫إ‬ ‫ة‬.
‫ا‬ ‫ة‬ ‫ا‬:‫ن‬ ‫ﻥ‬ ‫ه‬ ‫و‬ ‫درا‬ ‫اد‬ ‫ا‬ ‫ة‬ ‫ه‬ ‫ا‬ ‫ه‬:‫آ‬ ‫أو‬ ‫آ‬.
o‫د‬ ‫ا‬ ‫ة‬ ‫ا‬ ‫ه‬ ‫ا‬ ‫ا‬ ‫ة‬ ‫ا‬)‫ل‬ ‫ا‬–‫ض‬ ‫ا‬-‫زن‬ ‫ا‬(.....
o‫ا‬ ‫ة‬ ‫ا‬‫د‬ ‫ا‬ ‫ا‬ ‫ه‬ ‫ا‬)‫ا‬–‫م‬ ‫ا‬(......
‫آ‬‫ا‬ ‫ات‬ ‫ﻥ‬.
‫ن‬ ‫ﻥ‬ ‫ا‬ ‫ة‬ ‫ا‬:
←ix)‫دة‬(
←‫ف‬ ‫ﺹ‬)‫ت‬(iI‫ا‬ ‫آ‬ ‫د‬ ‫ا‬.
II.‫ﻡ‬ ‫إ‬ ‫ة‬ ‫ل‬ ‫ﻡ‬:
‫ل‬ ‫ﻡ‬1‫ری‬ ‫ﺕ‬ ‫ﻡ‬:‫ا‬‫ﻥ‬ ‫ا‬20‫وض‬ ‫ا‬ ‫ض‬:
9 8 10 12 10 8 15 18 16 15 12 12 10 10 9 8 15 12 8 10− − − − − − − − − − − − − − − − − − −
‫إ‬ ‫ول‬ ‫ﺝ‬ ‫ا‬ ‫ه‬ ‫ﻥ‬ ‫أن‬:
‫ه‬ ‫و‬ ‫ة‬ ‫ا‬:18 16 15 12 10 9 8− − − − − −‫ب‬ ‫ا‬ ‫ﻥ‬ ‫و‬:7 6 5 4 3 2 1; ; ; ; ; ;x x x x x x x
‫ة‬ ‫ا‬ ‫ا‬ ‫ا‬ix‫ا‬ ‫ﺹ‬ ‫ا‬ ‫ا‬ ‫د‬ ‫ه‬ix‫ب‬ ‫إ‬ ‫ﻥ‬ ‫و‬in1 i n≤ ≤
‫زواج‬ ‫ا‬( ),i ix n1 i n≤ ≤‫إ‬.
‫ة‬ ‫ا‬ix891012151618‫ع‬ ‫ا‬
‫ا‬425431120
‫ﻡ‬1:1 2 3 4 5 6 7 20N n n n n n n n= + + + + + + =
‫د‬ ‫ا‬20‫ب‬ ‫إ‬ ‫ﻥ‬ ‫و‬ ‫ا‬ ‫ﺝ‬ ‫ا‬ ‫ا‬N
‫ا‬ ‫دد‬ix‫ا‬ ‫د‬ ‫ا‬ ‫ه‬‫ب‬ ‫إ‬ ‫ز‬ ‫ا‬if‫ب‬ ‫ف‬ ‫ا‬ ‫و‬i
i
n
f
N
=
‫ا‬ ‫ا‬ix‫ب‬ ‫ز‬ ‫ا‬ ‫د‬ ‫ا‬ ‫ه‬ip‫ب‬ ‫ف‬ ‫ا‬ ‫و‬100i ip f=.
‫ﻡ‬2:
‫وي‬ ‫ت‬ ‫ا‬ ‫ع‬‫و‬ ‫ﺝ‬ ‫ا‬ ‫ا‬:
1
n
i
i
n N
=
=∑
‫وي‬ ‫ددات‬ ‫ا‬ ‫ع‬1‫ﻥ‬ ‫و‬
1
1
n
i
i
f
=
=∑
‫وي‬ ‫ا‬ ‫ا‬ ‫ع‬100‫ﻥ‬ ‫و‬
1
100
n
i
i
p
=
=∑
‫ﺭﻗﻢ‬ ‫ﺩﺭﺱ‬‫ﺭﻗﻢ‬ ‫ﺩﺭﺱ‬‫ﺭﻗﻢ‬ ‫ﺩﺭﺱ‬‫ﺭﻗﻢ‬ ‫ﺩﺭﺱ‬////4
:
‫ﻗﻠﻤﻲ‬ ‫ﻣﻮﻗﻊ‬ ... ‫اﻣﺘﺤﺎﻧﺎت‬ ‫ﻤﺗﺎرﻳﻦ‬ ‫اﻟﺪروس‬ ‫ﻣﻦ‬ ‫ﳌﺰﻳﺪ‬

2. ‫ذ‬ ‫ا‬: 2
‫ا‬ ‫ول‬ ‫ا‬ ‫و‬:
‫ة‬ ‫ا‬ix891012151618‫ع‬ ‫ا‬
‫ا‬in425431120
‫دد‬ ‫ا‬if0,20,10,250,20,150,050,051
‫ا‬ ‫ا‬ip%2010%25%20%15%5%5%100%
‫اآ‬ ‫ا‬ ‫ا‬:
‫اآ‬ ‫ا‬ ‫ا‬ix‫وي‬ ‫أو‬ ‫ﺹ‬ ‫ا‬ ‫ا‬ ‫ت‬ ‫ع‬ ‫ه‬ix‫ب‬ ‫إ‬ ‫ﻥ‬ ‫و‬iN
‫اآ‬ ‫ا‬ ‫ت‬ ‫ا‬ ‫ول‬ ‫ﺝ‬:
‫ﻥ‬ ‫ا‬ ‫ت‬ ‫ا‬:
‫ل‬ ‫ﻡ‬2
‫ده‬ ‫و‬ ‫م‬ ‫ا‬ ‫أ‬30‫ا‬ ‫ا‬ ‫ت‬ ‫ﺽ‬ ‫ا‬ ‫دة‬ ‫وض‬ ‫أ‬:
11–08–10–12–13–11–08–14–08–09–11–12-11–12–11-08–10–13–14–13–12–11–
09-12–16–14–10–11–13–12–11–11.
1.‫ن‬ ‫آ‬‫و‬ ‫ﺝ‬‫اآ‬ ‫ا‬ ‫ت‬ ‫ا‬ ‫و‬ ‫ت‬
2.‫ة‬ ‫ا‬ ‫ا‬ ‫دد‬ ‫ا‬ ‫د‬11
3.‫ة‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫د‬11
4.‫ﺽ‬ ‫ا‬ ‫ت‬ ‫و‬ ‫أ‬:‫أ‬(‫ب‬ ‫ال‬ ‫ا‬(‫ا‬ ‫ل‬ ‫ا‬
5.‫ا‬ ‫ت‬ ‫و‬ ‫أ‬:‫أ‬(‫ب‬ ‫ا‬ ‫اف‬ ‫ﻥ‬ ‫ا‬(‫ج‬ ‫ة‬ ‫ا‬(‫ازى‬ ‫ا‬ ‫اف‬ ‫ﻥ‬ ‫ا‬
6.‫ا‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫و‬ ‫أﻥ‬.
III.‫ﻡ‬ ‫آ‬ ‫إ‬ ‫ة‬ ‫ل‬ ‫ﻡ‬:
‫ل‬ ‫ﻡ‬1‫ری‬ ‫ﺕ‬ ‫ﻡ‬:
‫ت‬ ‫ا‬ ‫ى‬ ‫ك‬ ‫ا‬ ‫ع‬ ‫ا‬ ‫ل‬ ‫أ‬ ‫ا‬ ‫ول‬ ‫ا‬‫ده‬ ‫و‬ ‫ا‬80:
‫ا‬)‫ب‬cm([ [140,145[ [145,150[ [150,155[ [155,160[ [160,165
‫ا‬in1512251810
‫ا‬‫ت‬:[ [140,145,[ [145,150,.........,[ [160,165‫ة‬ ‫ا‬ ‫ف‬ ‫أﺹ‬ ‫و‬ ‫ا‬ ‫ﻥ‬.
‫ة‬ ‫ا‬ix891012151618
‫ا‬in4254311
‫ا‬ ‫ا‬ ‫ا‬‫آ‬iN461115181920
‫ا‬
0
1
2
3
4
5
6
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

3. ‫ذ‬ ‫ا‬: 3
‫ا‬ ‫ا‬:‫ت‬ ‫ا‬ ‫ﺕ‬ ‫راج‬ ‫ﻡ‬.
0
5
10
15
20
25
30
1 2 3 4 5
‫ا‬ ‫ت‬ ‫و‬:
1.‫ا‬ ‫أآ‬ ‫ة‬ ‫آ‬)‫ل‬ ‫ا‬:‫ا‬10(‫ا‬ ‫ﺹ‬ ‫أآ‬ ‫ﺹ‬ ‫آ‬ ‫و‬)‫ل‬ ‫ا‬:
‫ا‬[ [150,155.(
2.‫ا‬ ‫ا‬ ‫ل‬ ‫ا‬( ) ( )( )2 2 1 1, , ,p px n x n x n⋅⋅⋅⋅⋅‫ﺝ‬ ‫ا‬N‫ز‬ ‫ا‬ ‫ا‬ ‫د‬ ‫ا‬ ‫ه‬‫إ‬‫ب‬
m‫أو‬X‫ب‬ ‫ف‬ ‫ا‬ ‫و‬:
1 1 2 2 p px n x n x n
m
N
+ +⋅⋅⋅⋅+
=
‫ا‬ ‫ا‬ ‫ل‬ ‫ا‬( ) ( )( )2 2 1 1, , ,p pI n I n I n⋅⋅⋅⋅‫ه‬ ‫ﺝ‬ ‫ا‬N
1 1 2 2 p pn c n c n c
m
N
+ +⋅⋅⋅⋅+
=ic‫آ‬ ‫ه‬‫ل‬ ‫ا‬iI.
‫ا‬ ‫ت‬ ‫و‬:
( ) ( )( )2 2 1 1, , ,p px n x n x n⋅⋅⋅⋅⋅‫ﺝ‬ ‫ا‬ ‫إ‬N‫ا‬ ‫و‬m.
1.‫ا‬ ‫اف‬ ‫ﻥ‬ ‫ا‬:
1 1 2 2 p pn x m n x m n x m
e
N
− + − +⋅⋅⋅⋅+ −
=
2.‫ة‬ ‫ا‬:
( ) ( )
2 2
1 1 2 2 p pn x m n x m n x m
v
N
− + − +⋅⋅⋅⋅+ −
=
3.‫ازي‬ ‫ا‬ ‫اف‬ ‫ﻥ‬ ‫ا‬:vσ =
‫ﻡ‬:
‫ف‬ ‫ﺹ‬ ‫ا‬ ‫ا‬ ‫ﻥ‬ ‫آ‬ ‫إذا‬2 1, , ,pI I I⋅⋅⋅⋅⋅⋅⋅‫ض‬ ‫ﻥ‬ix‫ب‬ic‫ل‬ ‫ا‬ ‫آ‬iI‫ا‬.
‫ل‬ ‫ﻡ‬2:
‫ت‬ ‫ﺽ‬ ‫ا‬ ‫دة‬ ‫م‬ ‫ا‬ ‫أ‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫ول‬ ‫ا‬
‫ا‬ ‫ا‬[ [0,4[ [4,8[ [8,12[ [12,16[ [16,20
12421
7.‫ا‬ ‫ا‬ ‫دد‬ ‫ا‬ ‫د‬:[ [8,12
8.‫ا‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫د‬:[ [8,12
9.‫ﺽ‬ ‫ا‬ ‫ت‬ ‫و‬ ‫أ‬:‫أ‬(‫ب‬ ‫ال‬ ‫ا‬(‫ا‬ ‫ل‬ ‫ا‬
10.‫ا‬ ‫ت‬ ‫و‬ ‫أ‬:‫أ‬(‫ب‬ ‫ا‬ ‫اف‬ ‫ﻥ‬ ‫ا‬(‫ج‬ ‫ة‬ ‫ا‬(‫ازي‬ ‫ا‬ ‫اف‬ ‫ﻥ‬ ‫ا‬
11.‫أﻥ‬‫ا‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫و‬ ‫ت‬ ‫ا‬ ‫راج‬