1
2
  -2023
.. 

: ( )
: 3     : 75
:             
-
1.    ?           
2.             ?  
-
3.          
4.             ?  
 
-
5.  ?        
2
2
6.          ?     
 
-
7.   -   -        
8.        :
  
20-30 6
30-40 15
40-50 18
50-60 25
60-70 20
70-80 12
80-90 4
3
2
  -2023
.. 

: ( )
: 3     : 75
:             
-
1.    ?           
:            
 ,          ,   
 
     , , ,       
             ,
      (JND)    
                 
     ,  
    
 ,   
  
            
,                 
       
   ??
  (JND)            50%  
    -  
        
    
4
2
   
1.   
o   
2          10   ,  
       
o    200   ,            
o -     ' 
  ,       

2.  
o 
            
 ,  
      
o          ,        
   
o    
        
3.  
o  
      ,        

o         ,          

o     ',      ,  
     

o      
  ,  , ,       , 
  ,          
          
     -        
      
                 
         -       
   

      ?
5
2
        :
1.   ( )-         -     
     
 
2.   ( )         -    
     
 
              '  
  
 ,        
    -- 
1.   
o        ,      , 
   ,      
2.       ( )
o   
      
o    2    
o   ( , 50  ) -    
o            ,     
  
o   2.3  '    
 ,       
3.       ( )
o     ,  
o       ,   3 ,      
 
o                 
o   2.2  '      ,       
4.    
o           
o             
       
6
2
       
o     ,     -    
o         
 
o ,   -   ,    
    
    
o           
     
o    --    
o             
 
o             

    
1.   
o           
2.   
o       
    
3. -     
o   , , ,            
    
1.  
o               
   
2. 
o       ,       
   
3. 
o -         -   

7
2

                

       
        
-             
  ,        '       
 , 
       , 
         
2.             ?  
:   
       ,        
                  
      ' 
           
        ,  
  
  , - 
         ,  , 
      
   
     
          -  
           -      (
    ,       ),       -
                  
       
-  ,      
  '  50%      
 ,     
 
    ?
1.   :           - 
  ,        ,   - 
        
2.  :            
    
         
   
3. :                  
 
 , " 
 ?"  " 
 ?"
8
2
4.   :  -       
      
5. :   ,          
     50%     '    
   
        
     
   
              
  -         :    , 
        
       

     
   ,    
50%       
   
              
  ' 
                
        
      
1.  :        ,    

2.   : -     ,   
 (     )    
3.  :           
 ,  
 
 
4.  :        '     
'   
     
:
         ,     
  
 
  :            
:           , 
     
     
 :         , 
   -
        
9
2
  :
       ,    
   ,      
   :      (    ) 
           
 
   
       ,       ,   -
  '  
   
    ,   -  '     
       ,            
  ,     -    ,  
    
       ,           
 
'             ,      
               
            
     

-    ,              
       ' -       
         
       
     
   -            
       :
1.  :              
      
2.    :            
(   )         
3.  :             
-       
4.    :          -
 (        )       
    ,         
  

 ,               
  -    -      ,     
   -             
10
2
         ,  ,  -   
 '   ,              
   ,             - 
    ,        
-
3.          
:         
               
,             ,    -
              
             
  , 
              
 
     
  ,            -   
 '  :     
1.  :     ,        
    
     ,   , 
           '  
, 
            ,   
             ,  
  ,   '       
o :   
 
        

   
         
      
2.  : ,      
,               
               
       ,         
  ,             
    
11
2
o : 
       ,    
           
 
     '                 
      '         -   
 ,           
   
     
      
              
      ,    
     
   :  ,  ,   
1.  :         
  ' " "
      ,         

        IQ     
   ,           
o : --           
          
  
2.  :       ,     
              
      -        
        
o : 
-          
      
 ,       
        
3.  :    " "       
               
                
  -         
o :             
             '  
      ,       
                
-   '  ,          
12
2
       
  
          ,     
   :
1.   :
o          :    
   -     
   

      
o  ,    -    : ,
              
          
 
2. - '   :
o      '        
    '          
            
              

o ,        -  ' 
 
,             '  
        
    
       
,   
           
3.   :
o                 ,
          
    
    
o       '   
    ' 
   -             
           -  
      
4.  :
o          '    
       '       

   ,          
         
 
13
2
o      '   
     
   '  ,        
5.   :
o              
             
  
o ,     '  
     
         ,     
   -     

 ,               ,  
             '   ,
           '     ,  
 ,       ,  
      ,         
               
,   
                 
               
  ,
         ,      
4.             ?  
 
:    ()          ,
             ,      
 ,
-   -      --       
           
  ?
 ,  ,           

      ' ,      
         ,     
;    -
    ,   ,     ,     
14
2
:   
        
     
      ,           ,  
  , ,              
      
 ,      
1.    : 
          
               
   ,         ,    
             
  '             , 
    100%   , -     '   
IQ               

 
2.   :      ,       
  
         -    
    ,       
 -  
            
 
3. : -    -         ,
             '    
        ,        
:    
        ,        
     
    , ,   
  
         
1.   :           
 ,            , 
             
  ,            
   
2. :            
        '         
               
          
 ,     
  
3.   :              
          ,     
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2
      ,         
IQ       ,   ,     
      ,         
  
4.  :        
          , -    
       ,        
      ,       
     
5. :   '             
  ,            
             '      
             
    
     
        '   
   ,    
              ,   
          ,      
  
       ,       

  ,            -,
    
   "  -"         
 
 ,   -   
      
 ,        
         
      
 ,          
        
  :    ?
                
    ,        ' -    
               
                 
  -        
         -       
 ,               
 ,     -       ,     ,
    -              
16
2

 ,           
 
       ,        
                
           
  
             ,  
              ,    
     ,           
 
-
5.  ?        
:  
 ,      
         ,
,             
 
                 -
     ,       ,     -
      
 ,         '   ,  

     ""  ""    ,        
 ,  
 ""  " "   
           '     
       
   
      
              
               
     16           
1.    
 ,    ,        
                 
                
    
17
2
     :
      :
1.  :              
                 
               
 ,            
   
2.  :          

   
    
,         
 
       , ,   
        '         
 
3.  :              
       '        

 ,     '          
                
     
 
    :
    '        -        
                  

              
,             ,  
   
          '    
2.    16   
        16   '   
       ,        
 (  )      
                
     -         
 ,        
16   :
        16       ,  
           :
1.   :           
18
2
2.  -:             

3.    -:    '   
 
4.   :      
5.   :          
6.    :           

7.   :         
8.   :        '     
9.    :          
 
10.     :        
         
11.   -:         
12.     :        
       
13. -   :         
   
14.   :          
  
15.   :        
16.   :           
    :
         -         
             :
  :      '         

  , " "      
 : ,             
   
19
2
      
         ,
   
       
           ,     :
      '       '   
                
  
 ,           '   , 
             16   
       
     
:      ,     
         ,    
 
/:          
   ,            , 
     -        , 
    
:              , 
                


 ,         ,      
          '   ,     
 16                 
                 
    
            ,    
 ,        ,  - ,     
       
20
2
6.          ?     
 
:        , ,   
            '     
  (    )   ,      ,  
  '            
    ,       
  '  
   
        '    ,  
 '      
   
       
        
  ,                 
  
              ' 
          (  '   
)  ,       '     
        ,     
 -     ,      -   
       ,    
    
 
  , 
        '   ,   
        ,         
 
     , ,          
     ,          ,  
   

,    
              
  ,       ,      
          
 
  
     '       
:
1.   
            10      
 ,    ,          -   
21
2
                    
      
 ,              ,  
                   , 
  ,  ,                
    '   
      ,     
     ,          
2.    (TAT)
           ( - 
  )               
            ,     
,        ,       
 ,            ,      
    , "   '   ,       
     ,"       , "    
  
        "      -  
   ,     ,      
3. -- 
                 
     -    ,      ( ,  
),        -   -,    
     
 ,           
 ,        
  '       -    ,      ,
  
 ,          -    
       
4.   
  ,                
                ,  
      ,  ""    ,    "-
"     ,              ,
  "" ,             
  
22
2
     
:
1.    :             
  
     '   
,   ,  
     
2.  : 
     
,      
               '  
               
   
3.   :   ,       
            
             
:
1. -:     ,       
      -      - 
    ,      
2.  :       -  
     ,         

  ,           ,  
    '   
3.   :   ,      
    ,            
    -   ,       

             , 
                  
    ,    '       
        ,    '      
                  
 
,         ,     
              
23
2
-
7.   -   -        
:   :   
    ,  
   ,  
     
                 
                
""          ,    
           ,   
,      
1. 
                     
   
    :
       
       
         
:
=      
:     5      
     : 20, 25,
30, 35, 40
    40 
    20 
,  : 40 - 20 = 20
  :
      
         
  :
      ,         
           ,  
24
2
   100  ,      (100 - 20 = 80),   
       
                  
     
2. 
                 
   ()   
    :
   () 
     
       (    
 )
      
:
:
Xi =   
μ=    
N =    
:      : 20, 25, 30, 35, 40
 (20 + 25 + 30 + 35 + 40) / 5 = 30 
     :
o (20 - 30) = -10
o (25 - 30) = -5
o (30 - 30) = 0
o (35 - 30) = 5
o (40 - 30) = 10
25
2
   :
o (-10)2 = 100
o (-5)2 = 25
o 02 = 0
o 52 = 25
o 102 = 100
,      :
o (100 + 25 + 0 + 25 + 100) / 5 = 50.
 ,     50 
  :
  ,       ,     
  -     ,       
  :
    ,         , 

      ,   " "     ,
    

 ,          '   
 
3.  
               
         ,         
     :
,     (  
  )
,    
:
:   ,  50   ,    :
26
2
   :
      ,        
 
 ,        
           
   :
     ()     ,    
   
        
4.   (IQR)
  (IQR)           50% ' 
 ,     
 
IQR    :
     
      (Q1)       25%  
 ,  
 (Q3)       75%  
 
IQR Q3  Q1   
:
:   :20, 25, 30, 35, 40
Q1 25 ,  Q3 35 
 , IQR = 35 - 25 = 10
IQR  :
    50% '   ,         

         
IQR  :
      
,   
27
2
           
   
   

 ,                
              :
: ,     
:          ,   
    
 :    , 
       ,  
       
  (IQR):   50% '   ,   

 ,           
 
        ,          

        '        
   
             
   ,             
8.        :
  
20-30 6
30-40 15
40-50 18
50-60 25
28
2
60-70 20
70-80 12
80-90 4
:   :
               
 ,        ()         
          ,       
          
  ,           (CL    
)         ,     
   :
 1:       
  ,   20-30, 30-40, ,         
 , 
             
     
         :
 2:      
,     ()           
, 
      :
29
2
:
f     
x      
∑(f×x)            
,     ∑(f×x)\sum     :
 ( )
  (x)
 (f)
f×x
20-30
25
6
25 × 6 = 150
30-40
35
15
35 × 15 = 525
40-50
45
18
45 × 18 = 810
50-60
55
25
55 × 25 = 1375
60-70
65
20
65 × 20 = 1300
70-80
75
12
75 × 12 = 900
80-90
85
4
85 × 4 = 340
, f×x      :
,     :
, 
     :
30
2
 ,    54 
 3:      
     ,           
,          ,    
 
        :
       :
 ( )
  (x)
 (f)
(x−)2
f×(x−)2
20-30
25
6
(-29)2 = 841
6 × 841 = 5046
30-40
35
15
(-19)2 = 361
15 × 361 = 5415
40-50
45
18
(-9)2 = 81
18 × 81 = 1458
50-60
55
25
(1)2 = 1
25 × 1 = 25
60-70
65
20
(11)2 = 121
20 × 121 = 2420
70-80
75
12
(21)2 = 441
12 × 441 = 5292
80-90
85
4
(31)2 = 961
4 × 961 = 3844
, f×(x−Mean)2      :
 4:    
    :
 :
31
2
 5:     
 ,        :
:
       13.57 
  :
1.         
2.      
3.        
4.             
5.        
              
         ,          
       , 13.57    54    -
        
     '      ,      -
             
:            ( )      
         , 
         