2.
   2022
/   

(
 

  

)
 : 3     :100
:     -    ,          
                
  -
1.              
 (   )    :


2.     -         
  - 
3.()              ?
()    ,         :
 ()
0–5
5-10
10-15
15-20
20-25
2530
  
15
17
20
18
16
14
4.(a)           -    
2.
(b)        :
   
4–6
6–8
8-10
  
6
3
1
  - 
5.(a)              :
 
1
2
3
4
5
6
7
  
10
18
30
25
12
3
2
()         ?  -     ?
6.    ,         :

36
23
27
28
28
29
30
31
33
35
 
29
18
20
22
27
21
29
27
29
28
  - 
7.     ?          -   
 
8.    ,           
:
1992
1994
1996
1998
2000
2002
44
90
?
160
270
390
2.
   2022
/   

(
 

  

)
 : 3     :100
:     -    ,          
                
  -
1.              
 (   )    :


:   
   '     
    '
 ,    
                
 ,              ,    
     -       ,    
 
          
   
               
  ,           ,  
        ,     
    
            
󷄧󼿒     
 1:   
2.
           -       
 
       
       
            -   
  ', 
           
󷷑󷷒󷷓󷷔      
 2:   
 :


          
 3:      
 
     ,        
      -

        
     ;     
    :
󷷑󷷒󷷓󷷔    ()   -
󷷑󷷒󷷓󷷔   (∩)      
        
󹶆󹶚󹶈󹶉  
2.


󷄧󼿒 1:  
  :




󷄧󼿒 2:   
     :


            

      :

,

󰇛󰇜
󰇛󰇜󰇛󰇜


󽁔󽁕󽁖 
  ,           

󷷑󷷒󷷓󷷔 ,


     
2.
󷄧󼿒   ?
          

 :
   
,
    
,
     


  ,       
󷄧󼿒 3:       
     

    ,  
       
,  
    -  
 
󽇐 
󷷑󷷒󷷓󷷔


          - 

?

     
   :

2.
󰇛󰇜
󰇛󰇜


     
󷘹󷘴󷘵󷘶󷘷󷘸 
    '         -     
  
           ,      

  
  
    
󷈷󷈸󷈹󷈺󷈻󷈼  
   
     -      
 
     
  
     :
      ?
     ?
      ?

     
   ,          :
      
- 
 
            

 
2.
󷄧󼿒  
:
1.              
2.                 -
 :


 :

         

 ,        - 

          
2.     -         
:    
          ,    - 
    ,              
   ,  
 :
󰇝󰇞
,      1, 2, 3,  4          
 
󰇝 󰇞
                
    ,  ,    ,        
   
      
1.  :   
  ,   
󰇝
󰇞󰇝
󰇞
2.     :            
 , "10       "    
3.  :       :
o   :  ,  , .
󰇝

󰇞
o -  :      ,  ,
.
󰇝
is an even number less than 10
󰇞
    
2.
  -          
1.    ( )
      

󰇝󰇞
: 8  10        
2.  
        : 
󰇝
󰇞󰇝

󰇞
3.  
           : .
󰇝
󰇞
4.  
        
  :   

󰇝

󰇞
5.   
             : .
󰇝
󰇞󰇝
󰇞
6.   
          ,     : 
.
󰇝

󰇞󰇝
󰇞
7. 
            : .
󰇝
󰇞󰇝
󰇞
8.  
       
 :     
󰇝
󰇞󰇝
󰇞
9.  
          :  
10    
   ,  .󰇝󰇞
10.  
2.
        
 :  .
󰇝
󰇞󰇝
󰇞
11.  
       :  .
󰇝
󰇞󰇝
󰇞
12.   
     -   :  , 󰇝󰇞
󰇛󰇜󰇝󰇝󰇞󰇝󰇞󰇝󰇞󰇞
13.   
       
     :  , 
󰇝󰇞󰇝󰇞
󰆒
󰇝󰇞
 
   
    
        :
  :       
:         
 :      '   
  :  ,    ,   
    

   -,            
, ,  , -, ,  ,  
 
             

      ,           
  
 ,        :    
  
,  
         
2.
  - 
3.()              ?
()    ,         :
 ()
0–5
5-10
10-15
15-20
20-25
2530
  
15
17
20
18
16
14
:󷄧󼿒(a)      
  (GM)         '     
         ,    ,  ,
 ,   
󷷑󷷒󷷓󷷔  :
  n     n  
  ,     (  
     ), 

            '   
󷷑󷷒󷷓󷷔  :


 n     
  ,     '      
  ,     
󽇐   ( )
     
 
󽆤1.       
       ,    , 
,                  
  
󽆤2.       
2.
   ,          
  
        
 
󽆤3.        
           
  
       '  
󽆤4.      
    
     
  
󽆱      ()
    ,    

󽆥1.  
   ,         
  
     
󽆥2.           
 
     ,       ,      
    ,       
󽆥3.   
    ,          
󽆥4.       

        
,       '  
  
󷄧󼿒()         
          
         
 ()
  
2.
05
15
5-10
17
10-15
20
15-20
18
20-25
16
2530
14
󹼧 1:     
        :



:
f =   
x =     
󷷑󷷒󷷓󷷔   
  :
  


  (x)
f×x
05
15
2.5
37.5
5-10
17
7.5
127.5
10-15
20
12.5
250
15-20
18
17.5
315
20-25
16
22.5
360  (10)
2530
14
27.5
385
󷷑󷷒󷷓󷷔  


󷄧󼿒 :
2.




󷷑󷷒󷷓󷷔   = 14.75 
         14.75  
󹼧 2:     
              , 50%  
  50%   
󷷑󷷒󷷓󷷔  (  )    :

󰇭

󰇮
:
=     
=  
..=      
=    
=  
󷷑󷷒󷷓󷷔 1:     


   
05
15
15
5-10
17
32
10-15
20
52
15-20
18
70
20-25
16
86
2530
14
100
󷷑󷷒󷷓󷷔 2:   
2.


50      52 ,   10-15    
 ,
  = 10–15
 = 10
 = 20
 = 32
= 5
󷷑󷷒󷷓󷷔 3:     








󷄧󼿒  = 14.5 
󷈷󷈸󷈹󷈺󷈻󷈼 
 
      :
󽆤     '          
        
󽆤  = 14.75        
󽆤 = 14.5     
  -   14.5   

       
 
󷷑󷷒󷷓󷷔 :
2.
                 
      

4.(a)           -    
(b)        :
   
4–6
6–8
8-10
  
6
3
1
:(a)   -    
 ,             (    )
                 50  
 ,    48  52    ,    , 
20  80        ,      
 
            ,   
   
     
     :
1. 
o          
o           
2.    (--  )
o   (Q1)    (Q3)     '
o    50% '    ,    

 
3.  
o       (, ,  )    

o        
4.   (SD)
o        
o       ,     
5. 
o    
2.
o      
      ,          
          
()    
       :
   
   (f)
24
4
46
6
68
3
8-10
1
 1:    (x) 
   ,     :
2–4 → (2+4)/2 = 3
4–6 → (4+6)/2 = 5
6–8 → (6+8)/2 = 7
8–10 → (8+10)/2 = 9
   : 3, 5, 7, 9
 2:  ()   
:



󰇛󰇜󰇛󰇜󰇛󰇜󰇛󰇜




 ,   5.14 
 3:     ()
           :
3 :
5 :
2.
7 :
9 :
 4:    (f)   





 5:  
:







 ,    1.35 
  
         
  ,  ,  ,  ,    
   ,       ,    
1.35 

      
         
       ,      
   
         ,    5.14 ,
 1.35    
       
   - 
  -     
2.
  - 
5.(a)              :
 
1
2
3
4
5
6
7
  
10
18
30
25
12
3
2
()         ?  -     ?
:󷄧󼿒  ():   's   
󷋇󷋈󷋉󷋊󷋋󷋌  ?
    ,    
          60-70   
,               
 -  
  
 ""    
    ,     '  
    ,     '  
    ,    
      '     
󽇐   

       '   , 
 :
      = ( ) /  
󷄧󹻘󹻙󹻚󹻛  
  (X)
   (f)
1
10
2
18
3
30
4
25
5
12
2.
6
3
7
2
󷄧󼿒 1:  

 fX    



1
10
10
2
18
36
3
30
90
4
25
100
5
12
60
6
3
18
7
2
14
    (Σf) = 100
ΣfX = 328
󷷑󷷒󷷓󷷔 = ΣfX / Σf = 328 / 100 = 3.28
󷄧󼿒 2:  
       
,     30 ,    = 3    
󷷑󷷒󷷓󷷔 = 3
󷄧󼿒 3:     
 
  :

󰇛
󰇜

   , 
      


(X − 3.28)
(X − 3.28)²
f(X − 3.28)²
2.
1
10
-2.28
5.1984
51.984
2
18
-1.28
1.6384
29.4912
3
30
-0.28
0.0784
2.352
4
25
0.72
0.5184
12.96
5
12
1.72
2.9584
35.5008
6
3
2.72
.
22.1952
7
2
.
13.8384
27.6768
Σ f(X − )² = 182.16
󷷑󷷒󷷓󷷔  = √(182.16 / 100)
󷷑󷷒󷷓󷷔 = √1.8216 ≈ 1.35
󷄧󼿒 4:    










󷄧󼿒  (  a):
󷷑󷷒󷷓󷷔      = +0.21
󷈷󷈸󷈹󷈺󷈻󷈼:
     
           ,    
   -     ,        

󷄧󼿒  ():  
      
2.
󷋇󷋈󷋉󷋊󷋋󷋌   ?
                
             
    :
󷷑󷷒󷷓󷷔  
       ,    '  
  
    :
"   6   ,   
        ?"
           
󽆤 
                
       
󷈷󷈸󷈹󷈺󷈻󷈼     
   '    
       
        
   '    
 , ,        '  

󽇐   
󷄧󷄫  
        
:   
󷄧󷄬 
          
2.
:   ,   
          
󷄧󼿒-     
    
 ,         
 
-


    
     
  


     
  
     


     
  ,  

 -  (r)  
    

     
   
  
󷋇󷋈󷋉󷋊󷋋󷋌   
󷷑󷷒󷷓󷷔-      : "      "
󷷑󷷒󷷓󷷔   : "  170  ,    65   
 "
 ?
              
󷄧󼿒 
              , 

           
 ,              
  ,          ,    ,
        
        ,    :
󷷑󷷒󷷓󷷔-        
2.
   
    ,      -   
   
6.    ,         :

36
23
27
28
28
29
30
31
33
35
 
29
18
20
22
27
21
29
27
29
28
:    -   
             ,  
X  Y  ,  
      :
1. X  Y   (X  Y   )
2. Y  X   (Y  X   )
    , -   
   

36
23
27
28
28
29
30
31
33
35

29
18
20
22
27
21
29
27
29
28
 1: X  Y       


, →

, →

 ,   :


 2:        
 :
󰇛
󰇜󰇛
󰇜
󰇛
󰇜
󰇛
󰇜
2.
  :

 
 
󰇛
󰇜󰇛
󰇜
󰇛

󰇜
󰇛

󰇜
36
29
6
4
24
36
16
23
18
-7
-7
49
49
49
27
20
-3
-5
15
9
25
28
22
-2
-3
6
4
9
28
27
-2
2
-4
4
4
29
21
-1
-4
4
1
16
30
29
0
4
0
0
16
31
27
1
2
2
1
4
33
29
3
4
12
9
16
35
28
5
3
15
25
9
    :
󰇛
󰇜󰇛
󰇜
󰇛
󰇜

󰇛
󰇜

 3:   
1. X  Y :

󰇛
󰇜󰇛
󰇜
󰇛
󰇜



:

󰇛
󰇜
󰇛󰇜

2. Y  X :

󰇛
󰇜󰇛
󰇜
󰇛
󰇜



:

󰇛
󰇜
󰇛󰇜

    
2.
1. X  Y :

2. Y  X :


      X  Y    X     , Y
 0.89  
      X, Y     Y     , X
 0.75  
 X  Y      
 : -   ,  
  

       :  X '  Y ,   Y '
 X    ,       
 ,
                
          
  - 
7.     ?          -   
 
:                  
     ,      ,   
      '     
   
 , "         ,"     ' 
        
     
   
           , 

 ₹1,000      ,     ₹1,200     
    ?        ,  
        
2.
  ',      ,    100       
      
 :
  (2020):   = 100
  (2024):   = 120
          20%    
 ,   :
󷷑󷷒󷷓󷷔                ( 
  )    
 
   ,       
              
 ,              
       ( )
 '    ,        - 
  :
  -     
   -       
  -   ( × )    
,         ,    
 
         ,    
    
       -      
1.       
                
         ,      

  :
2.


 
 
 
       ,       

󷷑󷷒󷷓󷷔 ,        '  ,    
    -      
 ,             
 
 
2.      
               
 
       - , , , ,  , ,
            
           
,     
:
        
      
     
󷷑󷷒󷷓󷷔   — 20  ,     '     
 ,   
   
  ,    -    


3.     
             - ,
        
2.
     :
     -  
       
     
 
 , ""     '         
 
        ,      

󷷑󷷒󷷓󷷔 :               

4.      
         

 :

   '     
      
    '      
 ,       '      
        
:
      -  
     -   
      
        ,      -
         
5.      
           ,  :
 
 
2.
   
      
      
 ,       

           :
󷷑󷷒󷷓󷷔"      ?"
          
6.      
  ,       
 :
         
     
       
     ,           
   -  
        :
󷷑󷷒󷷓󷷔      ,    ?
             
 
7.      
      

   ,      
 :
     ,     
2.
     ,        

            ,  
  
8.      
         
   :
  ' 
 
 
              ,
   ,     

              
             
 
 ,    ,      
    
,      
          
     ,        ,  
,            

 
󷷑󷷒󷷓󷷔 ,       ,        
,   
2.
8.   ,           
:
1992
1994
1996
1998
2000
2002
44
90
?
160
270
390
:        
                
        '       
 '    
  ,   1996     
    
 1:  
 
1992
1994
1996
1998
2000
2002

44
90
?
160
270
390

      '  ( 2  )    
 
 
 2:        
  ,  1992          :
1992 → 0
1994 → 1
1996 → 2 (  )
1998 → 3
2000 → 4
2002 → 5
 ,    :






 3:     

     :


 

 
 
  
44
46
24
-10
6
-1
90
?
?
?
?
?
?
?
?
2.
160
110
34
-4
270
120
30
390

   :

  
  


,     :
46  110 ,  64 
110  120 ,  10 
       :
46 ()
110 ()
             
 4:        
    :

󰇛󰇜

󰇛󰇜󰇛󰇜

, (1996   1992   )

   :





 :
󰇛󰇜󰇛󰇜
󰇛󰇜
󰇛󰇜
󰇛󰇜󰇛󰇜
󰇛󰇜
 :

2.

 5:  
     1996    160  
 ,   1998   
               ,     
    
  
 1996      :


             
             
  
            , 1996   
  160  ,  
        
   
"                 
 
          ,         
 "