رياضيات تخصصية 115ريض
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64 67.5 72.2 21.9 62.3 39.2 39.6 67 6.2 3.2
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73.8 45.4 80 19.1 37.8 88 83.1 26.5 35.9 25.4
55.6 24.9 46.2 63.6 52.3 53 23.2 54.2 63.8 73.9
Wא
٤١١٥ אא
אאאא
78
F١EאRW 993.03.99 MinMaxR
F2،אE5m F٣EאW
208.195
99
m
RL
אאאאאאאאאאא
אאאאאאWאאאK
(آلف لایر) الفئات حدود Fالتكرار
14 0 – 20
26 20 – 40
17 40 – 60
22 60 – 80
11 80 – 100
المجموع 90
٣Wאאא65אK
אאW
فئات األجور اليومية عدد العمال8
10
16
14
10
5
2
70 – 100 100 – 120
120 – 140
140 – 160
160 – 180
180 – 200
200 - 220
المجموع 65
٤١١٥ אא
אאאא
79
١E Kאאאא ٢E Kאאאא ٣E אאאא200219K ٤E Kאאא ٥E אאא160K
Wא
١E אאא120א ٢E אאא179 א ٣E אאאא200219٢ ٤E אאא 120 – 139
٥E אאא160אאאאWאאא48 = 14 + 16+ 10 + 8א
٤}٢Kאאא(Relative frequency)W
אאאאאאאאאאאאאאא100K
100% i
i
F
FF
א אא א א Kאא
א א א א אאאאאאאאא
אKאא
٤W א אא ٢ אא א אאאW
٤١١٥ אא
אאאא
80
Wא
%F F (آلف لایر) الفئات حدود
15.56 14 0 – 20
28.89 26 20 – 40
18.89 17 40 – 60
24.44 22 60 – 80
12.22 11 80 – 100
المجموع 90 100
٤}٣Kא(Class midpoint)W ،אאאאאאW
2ii
i
LUx
W ix:i iU:אאi iL:אאi
٥W٢אW
(آلف لایر) الفئات حدود ixمركز الفئة Fالتكرار
14 ١٠ 0 – 20
26 ٣٠ 20 – 40
17 ٥٠ 40 – 60
22 ٧٠ 60 – 80
11 ٩٠ 80 – 100
المجموع 90
٤١١٥ אא
אאאא
81
٤}٤KWאLאאאאא
אאאאאאאאאאאאאאKא
א א אא אא א א
א אא א אאאא אא א Kאאאאאאאא،א א אאא אאא א אK
אאאאא
א K א אא אאאא אאא אאאאאא
?א،א?)(?אא،?)(אאאאK
W
אאאאאאאאא א ، א אא א א אא
Kאאאא
٦Wאאאאאא٢،W
٤١١٥ אא
אאאא
82
Wאאאא
الصاعدة الفئات حدود التكرار الصاعد
0 0
14 20
40 40
57 60
79 80
90 100
אאאאW
الفئات الهابطة حدود التكرار الهابط
90 0
76 20
50 40
33 60
11 80
0 100
٦WWאאאאא
aE אאא40K bE אאאא60K cE אאא4080 K
Wא
aE אאא4050،Kאא،אאאא
٤١١٥ אא
אאאא
83
bE אאאא6057Kאאא،
cE אאא408039אאאאא40אF40אאE
אא 80F79א ،אא Eאא40אF50אאE
א80F11אאEK
5אאKW
אא Kאא אאא אא א א
Kא
Wאאא
אאא אאא אאא אאאאא אא אאא
Kאאאאאא
Kאאאאאא
٤١١٥ אא
אאאא
84
٥}١Kאאא(Histogram)W
אאאאאאא א א Kאא
KאאאKאא
٧W٢א،אאאאאW
٥}٢Kאאא(Polygon)W
אא א א א א Kאאאאאא
٨W٢א،אאאאא
W
14
27
16
23
9
0
5
10
15
20
25
30
٢٠ ٤٠ ٦٠ ٨٠ ١٠٠ More
٢٠ ٤٠ ٦٠ ٨٠ ١٠٠ More
٤١١٥ אא
אאאא
85
6אאKW
א א א א א א א א
אKאאאאאאאאאKאא
א אאאאאא
Kא א א אאאK
א א א א א
אא KאאאKEאFאאאאאאK
אאאאאאא
Kא،אאאאא א א א
14
27
16
23
9
0
5
10
15
20
25
30
٢٠ ٤٠ ٦٠ ٨٠ ١٠٠ More
Frequency
Frequency
٤١١٥ אא
אאאא
86
אK א א א א א א א א Kאאא،אאאאא
٦}١Kאא(Mode)W אאאאאKא
אאאא،אאK
אאאאWא3,5,5,5,5,9,9,7א5K אאא4,2,5,7,6,1,3Kא
אא א א אא
K ٦}٢Kא(Median)W
אאאאKאאא אא א
אא אאא אאאKאא
אאnxxxx ,.....,,, 321א
2
1nxאn
2
2
22
1nn xxאn K
~אx~Kא
٩WWאא10,8,9,6,7
٤١١٥ אא
אאאא
87
Wא א10,9,8,7,6
5n،W
83
2
6
2
15
2
1 xxxxn
א8~
١٠Wא9,10,6,2,1,7 Wא
א10,9,7,6,2,1 6n،W
5.62
1313
2
176
2
1
2
1
2
1
2
143
2
8
2
6
2
26
2
6
xxxxxx
א5.6~ x ٦}٣KאLאא(Mean)W
אאא א א א א
אWnxxxx ,.....,,, 321Wאn
xn
ii
1K
xK
٤١١٥ אא
אאאא
88
١٠Wאאאא8,10,13,9,7,11,10
Wא Wא
71.97
68
7
101179131081
n
xn
ii
71.9א
٤١١٥ אא
אאאא
89
١WWא
44 98 40 60 66 71 82 64 72 68
55 69 77 78 88 60 65 68 69 79
69 89 64 71 66 61 75 87 54 81
70 62 74 68 60 73 82 71 62 50
Wא
aE Kאאא
bE Kאאא
cE אא75K
٢W٧٠Wאאאא
فئات األجور 50‐59 60‐69 70‐79 80‐89 90‐99 100‐109 110‐119
عدد العمال 8 10 16 15 10 8 3
W
aE אא٩٠K א؟
bE אאאאאK
cE אאאאאK
٤١١٥ אא
אאאא
90
٣WWאאאאאא
7,9,6,8,9,10,6,11,8,7,9,10,9,7,6,10,8,11,9,8
Wא
aE Kאאא
bE Kאא
cE Kא
٤WאאאאאאאW
18 14 15 14 1 20 17 8
16 3 18 15 19 14 20 17
16 15 7 12 24 28 9 34
21 5 13 25 14 11 9 21
22 25 9 3 16 23 7 19
W
a( אאאאK
b( אאאאK
c( אאאאK
٤١١٥ אא
אאאא
91
אא
אא א א،א
،،١٤٠٣א J١٩٨٣K
Design and Analysis of Computer Algorithms, Addison Wesley, Reading, England, 1974.
Alfred Aho, John Hopcroft and Jeffrey Ullman
Mathematics for scientific and technical students, Addison Wesley Longman, Harlow, England, 1998.
Gwyn Davies and Gordon Hick
Computer and Intractability, A Guide to the Theory of NP-Completeness, Freeman, San Francisco, 1979.
Micheal Garey and David Johnson
Elements of Discrete Mathematics, McGraw-Hill, New York, 1977.
C. L. Lui
Theory of Linear and Integer Programming, John Wiley & Sons, Chichester, England, 1986.
Alexander Schrijver
Basic Mathematics, John Wiley & Sons, Chichester, England, 1998.
Peter Tebbutt
א،אא،אאא،٢٠٠٣
K،K
Introductory Statistics. London : Addison-Wesley Publishing Company, 1982
Hassett, Weiss
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