1
2
  -2023
..  
 
( -II)
 : 3   : 100
:               
-
1.              
       
2.             
-
3.     ,     :

10-19
20-29
30-39
40-49
50-59
60-69
70-79
80-89
90-99

11
19
21
16
10
8
6
3
1
4.           :
   
2
2
0-10 5
10-20 7
20-30 14
30-40 12
40-50 9
50-60 6
60-70 2
-
5.             X  Y   
 6  8

6
10
8
9
?
7
6.           :

25
28
35
32
31
36
29
38
34
32
43
46
49
41
36
32
31
30
33
39
-
7.             ,
           
8.            :
 : 1990 1992 1994 1996 1998
 000   : 18 21 23 27 16
3
2
  -2023
..  
 
( -II)
 : 3   : 100
:               
-
1.              
       
:   
           ,  ,   
                 
                 
   
  ,               ,  
                 
                 
  
              
  :
1.   
o            , 
      
4
2
o :           
    
2.   
o        ,         
   
o :              
   
3.   
o            ,    
     
o :            

4.   
o        ,      
   
o              
      
5.   
o          
o :            
  
6.     
o               

o :             
   
  
     ,      :
1.     
o                
  
5
2
o            
2.    
o            
o :            
   
3. -      
o                

o :          ,   
         ;       

4.      
o      ,      
o :        
5.     
o            
o :           -
  
    
               
         :
1.    
o  , ,          
       
o :    ,        
        
2.    
o             
 
o :            
       
6
2
3.     
o              
 
o :             
     
4.    
o               
 
o :             
  
5.  
o            
o :        ,    
 
6. 
  
o    
           ,
  (  )   ( 
 )   
o :           
7.  
o             

o :            ,  
       
8. 
  
o     ,         
    
o :      
     
 

               ,
,        ,    ,    
7
2
         ,        
,  ,   ,          
         , ,    
          
2.             
:     : ,   

   ,  , ,        
       ,       
         ,       
             
  
                
               , 
       
  
            :
1.        ,  , 
     
   ,      
o

:             
2.       ,  ,      
   ,      
o

:         (, 0-50, 51-75, 76-100)
3.         ,      
   ,      
o

:      (, , , )
4.       ,  ,      
   ,      
8
2
o

:2019, 2020  2021      
    
      :           ,
        
   :           
   
   :            
 
   :           
  
                
      ,          
    
         :
1.             
o

:        

  
1
30
2
28
3
35
2.           
o

:           

 
 

1
15
15
30
2
12
16
28
3
18
17
35
  
          :
9
2
:    ,     
    ()   ()     
                
 
:    .
 (  ):        .
    
 :           
 :          
 :        
  :          ,   
      
       
                  
              
 1:   
           :

  

40

35
 
25

20
 2:   
           :

 
 


30
10
40

25
10
35
10
2
 
15
10
25

10
10
20
                   
       

             
   ,        ,     
      ,          ,  
      ,  ,       
      
-
3.     ,     :

10-19
20-29
30-39
40-49
50-59
60-69
70-79
80-89
90-99

11
19
21
16
10
8
6
3
1
:,     
     ,             
  :
1. -                 
2. -                  
      
3.  -                    
  
,             
  :
 ( )
 (f)
10 - 19
11
11
2
 ( )
 (f)
20 - 29
19
30 - 39
21
40 - 49
16
50 - 59
10
60 - 69
8
70 - 79
6
80 - 89
3
90 - 99
1
 1:  ()  
       :
:
f    
X     ,       :
 1.1:   
 

(X)
 (f)

10 - 19
(10+19)/2 = 14.5
11
11 × 14.5 = 159.5
20 - 29
(20+29)/2 = 24.5
19
19 × 24.5 = 465.5
30 - 39
(30+39)/2 = 34.5
21
21 × 34.5 = 724.5
12
2
 

(X)
 (f)

40 - 49
(40+49)/2 = 44.5
16
16 × 44.5 = 712
50 - 59
(50+59)/2 = 54.5
10
10 × 54.5 = 545
60 - 69
(60+69)/2 = 64.5
8
8 × 64.5 = 516
70 - 79
(70+79)/2 = 74.5
6
6 × 74.5 = 447
80 - 89
(80+89)/2 = 84.5
3
3 × 84.5 = 253.5
90 - 99
(90+99)/2 = 94.5
1
1 × 94.5 = 94.5
 1.2:   
 1.3:   
  () 41.24 
 2:   
          ,    
  :
:
L =     
 =  (95)
CF =      
f =    
h =   (       )
13
2
 2.1:    
 , N/2   :
        47.5   
 
 (f)
  ()
10 - 19
11
11
20 - 29
19
11 + 19 = 30
30 - 39
21
30 + 21 = 51
40 - 49
16
51 + 16 = 67
50 - 59
10
67 + 10 = 77
60 - 69
8
77 + 8 = 85
70 - 79
6
85 + 6 = 91
80 - 89
3
91 + 3 = 94
90 - 99
1
94 + 1 = 95
  30 - 39      (51) 47.5     
 2.2:   
L=29.5L (30-39    )
/2=47.5
CF=30 (30-39     )
f=21 (   )
10h=10 ( )
14
2
  37.83
 3:   
             ,   
   :
:
L =     
f1 =    
f0 =     
f2 =     
h =  
  30 - 39       (21)
  :
  32.36
15
2
 :
 = 41.24
 = 37.83
 = 32.36   
4.           :
   
0-10 5
10-20 7
20-30 14
30-40 12
40-50 9
50-60 6
60-70 2
:          
     ,     ,        
 "  "  " "         :
1.   ()-           ()    
          ,         
  
2.   () -            
   ,       -        
     
               
 1:   
         :
16
2
 ( )
   ()
0 10
5
10 20
7
20 30
14
30 40
12
40 50
9
50 60
6
60 70
2
    (0-10, 10-20   )      ,    
          
 2: 
 
    ,         :
    :
 ( )
   ( )

(x)
0 10
5
(0+10)/2 = 5
10 20
7
(10+20)/2 = 15
20 30
14
(20+30)/2 = 25
30 40
12
(30+40)/2 = 35
40 50
9
(40+50)/2 = 45
50 60
6
(50+60)/2 = 55
60 70
2
(60+70)/2 = 65
 3:  ()   
          :
17
2
:
f =  (  )
x = 
∑f =   
,  f×xf    
 ( )
   ( )
 (x)
 × 
0 10
5
5
5 × 5 = 25
10 20
7
15
7 × 15 = 105
20 30
14
25
14 × 25 = 350
30 40
12
35
12 × 35 = 420
40 50
9
45
9 × 45 = 405
50 60
6
55
6 × 55 = 330
60 70
2
65
2 × 65 = 130
:
f × x:
:
 4:   
                :
18
2
 ()2  f()2   𝑥 𝑥𝑥 𝑥

( )
  
()

()
𝒙 𝒙
()2𝒙 𝒙
()2𝒙 𝒙
0 10
5
5
5 - 32.09 = -27.09
733.86
5 × 733.86 = 3669.30
10 20
7
15
15 - 32.09 = -17.09
292.06
7 × 292.06 = 2044.42
20 30
14
25
25 - 32.09 = -7.09
50.26
14 × 50.26 = 703.64
30 40
12
35
35 - 32.09 = 2.91
8.47
12 × 8.47 = 101.64
40 50
9
45
45 - 32.09 = 12.91
166.70
9 × 166.70 = 1500.30
50 60
6
55
55 - 32.09 = 22.91
524.93
6 × 524.93 = 3149.58
60 70
2
65
65 - 32.09 = 32.91
1083.50
2 × 1083.50 = 2167.00
:
 5:   (CV)   
                  :
 
 = 32.09
  = 15.57
  = 48.52%
19
2

       32.09      48.52%     
                    ,  CV
            
        ,   ,     
          !
-
5.             X  Y   
 6  8

6
2
10
4
8
9
11
?
8
7
::    
  ( r      )           
                    
 r   -1  +1   :
+1       .
-1   
0    
   -- 
     :

6
2
10
4
8
9
11
?
8
7
 1:    
X  Y     6  8     :
       , Y          :
Y     :
20
2
    ?:
  Y  5     :

6
2
10
4
8
9
11
5
8
7
 2:      
      :
:
X (X  ) = 6
Ȳ (Y  ) = 8
 (X - X
)  (Y - Ȳ)   :

6
2
10
4
8
 - 6
0
-4
4
-2
2
9
11
5
8
7
 - 8
1
3
-3
0
-1
 , (X - X
) (Y - Ȳ)  :
 - 6
0
-4
4
-2
2
 - 8
1
3
-3
0
-1
(-6)(-8)
0
-12
-12
0
-2
  (X - X
)(Y - Ȳ):
,    (X - X
 (Y - Ȳ)²:
 - 6
0
-4
4
-2
2
(-6)²
0
16
16
4
4
 - 8
1
3
-3
0
-1
(-8)²
1
9
9
0
1
 :
21
2
, r   :
  
  -0.92 ,  -1     X  Y       
     , - X    , Y       
    
      ,           
              ,    
   ,           (X)    (Y)  
  ,           
 ,             
 ,     ,              

                
,  X  Y       ,     X   Y   
       ,         
         
6.           :

25
28
35
32
31
36
29
38
34
32
43
46
49
41
36
32
31
30
33
39
:       
 ,              ,  
                  
                
           :
X   :25, 28, 35, 32, 31, 36, 29, 38, 34, 32
Y   :43, 46, 49, 41, 36, 32, 31, 30, 33, 39
1: X  Y   
22
2
     ,   , X  Y   ()    

                 
X  :
Y  :
 :        
        :
X  Y   (Y = a+bX     ) -   X    Y 
  
X  Y   (X=c+dY   ) -   Y    X  

       (X  Y     b   Y  X     d 
  )   ( a  c    )    
 2.1:X  Y  
X  Y    ,   (b)       :
:
   -   ,
𝑥  X  Y   𝑦
        :
1.      Xi−  Yi−   𝑥𝑦

𝒙
𝒚
() 𝒙
𝒚
()𝑋
2
25
43
-11
0.1
-1.1
121
23
2

𝒙
𝒚
() 𝒙
𝒚
()𝑋
2
28
46
-8
3.1
-24.8
64
35
49
-1
6.1
-6.1
1
32
41
-4
-1.9
7.6
16
31
36
-5
-6.9
34.5
25
36
32
0
-10.9
0
0
29
31
-7
-11.9
83.3
49
38
30
2
-12.9
-25.8
4
34
33
-2
-9.9
19.8
4
32
39
-4
-3.9
15.6
16
   ()     :
3.  (a)   :
 , X  Y    :
 2.2: X  Y  
Y  X    ,   (d)       :
24
2
 Yi−         :𝒚

𝒙
𝒚
() ()𝒙
𝒚
(𝒚)
𝟐
25
43
-11
0.1
-1.1
0.01
28
46
-8
3.1
-24.8
9.61
35
49
-1
6.1
-6.1
37.21
32
41
-4
-1.9
7.6
3.61
31
36
-5
-6.9
34.5
47.61
36
32
0
-10.9
0
118.81
29
31
-7
-11.9
83.3
141.61
38
30
2
-12.9
-25.8
166.41
34
33
-2
-9.9
19.8
98.01
32
39
-4
-3.9
15.6
15.21
  (d)   :
  (c)   :
 , Y  X    :
=35.524+0.0111Y
 3:  (r)   
25
2
 ,  r    ,            
      :
b  d     :

X  Y    :
=42.048+0.0237X
Y  X    :
=35.524+0.0111Y
  0.872 ,  X  Y         
     - X  , Y   ,      
-
7.             ,
           
:  :   
                
               , ,   
                 
                 
   
      :
1.            
  ,    (CPI)          
                CPI 
,          ,    
26
2
2.             
             ,    
(  )      ,        
        
3.        :     
               
,       
4.              
       ,          
  ,              
5.    :          
                    
   
6.    :        
             ,    
       ,           
    
  
      ( )        
     ,        (  )   
 ,               
   :
:
P1       
P0       
Q0       
:
     , A  B,           
  , A   10   B   20   , A   12   B   24
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2
    A  B   5-5  ,      (    5
)        
,                
 
   :
   
                    
   
:
              ,   
          ,     -
  
   
              , 
                
        
   :
:
P1       
P0       
Q1       
:
     , A  B    ,        A
 6   B  4            
    ,         
   :
           
             
28
2
:
              
   
       ,          
     
   
    ""         
              
                  
         
   :
:
L   
P   
:
  ,        -  ,  
          
   :
             
             
:
            
            
,          
               
   -      
                
 ,       
29
2
         ,    
       

                  
       ,      
                  
 ,              

8.            :
 : 1990 1992 1994 1996 1998
 000   : 18 21 23 27 16
:  
           ,        
               ()    
        ,         :
=+
:
Y   (000  ),
X   (          ),
a    (  Y-   ),
b   (       )
-- 
    :

 (000  )
1990
18
1992
21
30
2

 (000  )
1994
23
1996
27
1998
16
 1:    
     (, 1990, 1992, ),          
   ,     1990    , 1990 0   , 1992 2   ,
                  :
 (X)
 ()
0
18
2
21
4
23
6
27
8
16
 2:     
     -    ,       
            aaa  bbb    
       
a ()  b ()     :
1.  ():
:
n     ,
∑XY, X  Y     ,
∑X  Y, X  Y     ,
∑X2, X     
31
2
2.  (aaa):
 3:    
                 
 :
 (X)
 ()
 × 
²
0
18
0
0
2
21
42
4
4
23
92
16
6
27
162
36
8
16
128
64
,     :
∑X=0+2+4+6+8=20
∑Y=18+21+23+27+16=105
∑X2=0+4+16+36+64=120
n=5 ( 5   )
 4:  b   
,     b     :
  (b)   0.1
 5:    
 ,       (a)    :
32
2
 ,   (a) 20.6
 6:    
     (b=0.1b = 0.1b=0.1)   (a=20.6a = 20.6a=20.6)  , 
      :
=20.6+0.1X
          
 7:   
 Y=20.6+0.1X        0.1  ( )   20.6
      X=0X = 0X=0,   1990
 8:   ()
                 
  ,    2000         (, X=10X =
10X=10):
=20.6+0.1×10=20.6+1=21.6
  2000     21.6  

        ,              
               ,  
  ,               
    ,      ,    0.1     
                   
:             ( )      
         ,              