Easy2Siksha.com
   2022
/  

(





)
 : 3   :100
 :     ,            
           

1.             
    (  )   :


2.     ,     

3.()           ?
()          :
 (.)
0–5
5–10
1015
1520
2025
2530

15
17
20
18
16
14
4.()           
Easy2Siksha.com
()        :
 
2–4
6–8
8–10

4
3
1

5.()          :

1
2
3
4
5
6
7

10
18
30
25
12
3
2
()       ?       
?
6.   ,     :
X
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
Easy2Siksha.com
   2022
/  

(





)
 : 3   :100
 :     ,            
           

1.             
    (  )   :


:          -     
  ,  -       -      
  ,  -        ,   
     -       ,     
               
               
,           ,   
        ,        
   
              
󷄧󼿒       
 1:    
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                  
 
      
       
              
  ,               
󷷑󷷒󷷓󷷔       
 2:  
 
 :


     ,       
 3:       
      ,          
       
       

     ,     

      :
󷷑󷷒󷷓󷷔    ()    
󷷑󷷒󷷓󷷔   (∩)    
         
󹶆󹶚󹶈󹶉  
Easy2Siksha.com


󷄧󼿒 1:  
   :




󷄧󼿒 2:  
 
       :


          
      :

,

󰇛󰇜
󰇛󰇜󰇛󰇜


󽁔󽁕󽁖  
  ,            
󷷑󷷒󷷓󷷔,


      
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󷄧󼿒   ?
         
 :
    ,
   ,
     
 ,       
󷄧󼿒 3:        
  ,       

     ,          ,  
        
󽇐 
󷷑󷷒󷷓󷷔


       
?
     
    :

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󰇛󰇜
󰇛󰇜


     
󷘹󷘴󷘵󷘶󷘷󷘸 
          -     
   
                  

 ,  ,     
󷈷󷈸󷈹󷈺󷈻󷈼   
               
       
       :
    ?
   ?
   ?
        
  ,            :
   
 
 
                 
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󷄧󼿒 
:
1.                  
2.            ,    
 
  :


 :

         
,           
           
2.     ,     
:  
          ,   -   
 ,                  
  ,    :
󰇝󰇞
, 1, 2, 3  4              
󰇝 󰇞
                    
 ,     ,           
  
   
1.  :       ,  
󰇝
󰇞󰇝
󰇞
2.    :         - 
    , "10       "  
 
3. :        :
o   :     ,   , .
󰇝

󰇞
o - :      ,   ,
󰇝
is an even number less than 10
󰇞
Easy2Siksha.com
  
           
1.   ( )
      
󰇝󰇞
: 8  10        
2.  
         : 
󰇝
󰇞󰇝

󰇞
3.  
         :
󰇝
󰇞
4.  
             :    

󰇝

󰇞
5.  
            :
󰇝
󰇞󰇝
󰇞
6.  
        ,      :

󰇝

󰇞󰇝
󰇞
7. 
               
: 
󰇝
󰇞󰇝
󰇞
8.  
         :    
󰇝
󰇞󰇝
󰇞
9.  
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          :   10  
     , 󰇝󰇞
10.  
         : 
󰇝
󰇞󰇝
󰇞
11.  
      : 
󰇝
󰇞󰇝
󰇞
12.  
         :  , 󰇝󰇞
󰇛󰇜󰇝󰇝󰇞󰇝󰇞󰇝󰇞󰇞
13.   
      ,        
:   , 󰇝󰇞󰇝󰇞
󰆒
󰇝󰇞
  
           :
:          
 :          
 :          
 :     ,    ,    
 

  ,            
  , , , , ,  ,  
            
      ,            
 
,         :       , 
           
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
3.()           ?
()          :
 (.)
0–5
5–10
1015
1520
2025
2530

15
17
20
18
16
14
:󷄧󼿒()    
  ()               
         ,   ,  ,  
   
󷷑󷷒󷷓󷷔:
  n     n   
    ,    (       )  , 
                  
󷷑󷷒󷷓󷷔:


 n    
   ,           
  ,    
󽇐    ()
       
󽆤1.     
          ,   , 
,                 
       
󽆤2.     
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   ,          
             
󽆤3.      
              
         
󽆤4.     
                 
󽆱    ()
    ,      
󽆥1.  
    ,           
    
󽆥2.             
       ,      ,   
       ,      
󽆥3.  
      ,           
󽆥4.       
          ,       
 
󷄧󼿒()       
           
        
 (.)

Easy2Siksha.com
05
15
510
17
1015
20
1520
18
2025
16
2530
14
󹼧 1:     
         :



:
f = 
x =    
󷷑󷷒󷷓󷷔
 
 :
  

f

(x)
f×x
05
15
2.5
37.5
510
17
7.5
127.5
1015
20
12.5
250
1520
18
17.5
315
2025
16
22.5
360
2530
14
27.5
385
󷷑󷷒󷷓󷷔    


󷄧󼿒 :
Easy2Siksha.com




󷷑󷷒󷷓󷷔   = 14.75 
         14.75  
󹼧 2:    
               , 50% 
   50%     
󷷑󷷒󷷓󷷔   ( ):

󰇭

󰇮
:
L=     
N= 
=      
f=    
h=   
󷷑󷷒󷷓󷷔 1:    

f
 
05
15
15
510
17
32
1015
20
52
1520
18
70
2025
16
86
2530
14
100
󷷑󷷒󷷓󷷔 2:    
Easy2Siksha.com


50      52 ,   10-15    
,
  = 10–15
L = 10
f = 20
CF = 32
h = 5
󷷑󷷒󷷓󷷔 3:   








󷄧󼿒  = 14.5 
󷈷󷈸󷈹󷈺󷈻󷈼 
       :
󽆤                
       
󽆤  = 14.75       
󽆤 = 14.5          14.5     
      
󷷑󷷒󷷓󷷔   :
                
      
Easy2Siksha.com
4.()           
()        :
 
2–4
6–8
8–10

4
3
1
:()   
 ,               (  
)                50 
  ,    48  52    ,     ,  20  80
       ,        
             ,     

   
      :
1.
o        
o  ,            
2.   (- )
o   (Q1)    (Q3)       
o     50%    ,        
3.  
o       (,   )    
 
o       
4.   (SD)
o         
o            ,   
5. 
o    
o      
   -   ,            
       
()    
Easy2Siksha.com
      :
 
 (f)
24
4
46
6
68
3
810
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  :
7  :
9  :
 4:  (f)   


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


 5:  
:







 ,    1.35
 
      
  ,  ,  ,      
   ,       ,     1.35 

                 
       ,           
       ,    5.14 ,  1.35
                 
  

5.()          :

1
2
3
4
5
6
7

10
18
30
25
12
3
2
()       ?       
?
:󷄧󼿒 ():  ' 
󷋇󷋈󷋉󷋊󷋋󷋌  ?
Easy2Siksha.com
    ,      
           60-70   , 
               -   


 "
"    
  

  ,      
  

  ,       
     ,    
           
󽇐 
           ,        :
     = ( ) /  
󷄧󹻘󹻙󹻚󹻛  
 (X)
 (f)
1
10
2
18
3
30
4
25
5
12
6
3
7
2
󷄧󼿒 1:   
    fX    
X
f
fX
1
10
10
2
18
36
3
30
90
4
25
100
5
12
60
Easy2Siksha.com
6
3
18
7
2
14
 (Σf) = 100
ΣfX = 328
󷷑󷷒󷷓󷷔 = ΣfX / Σf = 328 / 100 = 3.28
󷄧󼿒 2:   
         
,   30 ,   = 3  
󷷑󷷒󷷓󷷔  = 3
󷄧󼿒 3:     
      :

󰇛
󰇜

     ,       
X
f
(X − 3.28)
(X − 3.28)²
f(X − 3.28)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
7.3984
22.1952
7
2
3.72
13.8384
27.6768
Σ f(X − )² = 182.16
󷷑󷷒󷷓󷷔  = √(182.16 / 100)
󷷑󷷒󷷓󷷔  = √1.8216 ≈ 1.35
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󷄧󼿒 4:    










󷄧󼿒  ( ):
󷷑󷷒󷷓󷷔     = +0.21
󷈷󷈸󷈹󷈺󷈻󷈼:
    
      

  ,    
    ,    ,  
    
󷄧󼿒 ():  
      
󷋇󷋈󷋉󷋊󷋋󷋌   ?
                  
                 
      :
󷷑󷷒󷷓󷷔             ,     
 
    :
    6    ,         ?”
            
󽆤
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             
       
󷈷󷈸󷈹󷈺󷈻󷈼   
        
         
        
       
    , ,        
󽇐  
󷄧󷄫 
           
:   
2󰊯 
          
:   ,            
󷄧󼿒     
         ,       




     
        

      
   
    
 

     
  ,  

   (r)  
   
Easy2Siksha.com

    
  
      
   
󷋇󷋈󷋉󷋊󷋋󷋌 
󷷑󷷒󷷓󷷔    : "      "
󷷑󷷒󷷓󷷔   : "  170  ,    65    
"
 ?
            
󷄧󼿒 
              ,   
          
 ,             
          ,   ,
       
          ,    :
󷷑󷷒󷷓󷷔          
        ,        
   
Easy2Siksha.com
6.   ,     :
X
36
23
27
28
28
29
30
31
33
35

29
18
20
22
27
21
29
27
29
28
:    
              ,   X 
Y  ,         :
1. Y  X   (X  Y   )
2. X  Y   (Y  X   )
      -    
   
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:      
 :
󰇛
󰇜󰇛
󰇜
󰇛
󰇜
󰇛
󰇜
   :
X


󰇛
󰇜󰇛
󰇜
󰇛

󰇜
󰇛

󰇜
Easy2Siksha.com
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. Y  X  :

󰇛
󰇜󰇛
󰇜
󰇛
󰇜



:

󰇛
󰇜
󰇛󰇜

2. Y  X  :

󰇛
󰇜󰇛
󰇜
󰇛
󰇜



:

󰇛
󰇜
󰇛󰇜

  
1. Y  X  :

Easy2Siksha.com
2. X  Y  :


      Y, X      X      , Y
 0.89   
      Y   X       Y   
   , X   0.75   
 X  Y           : -   , 
  

       :  Y    X   ,  
X    Y     ,       ,
                  
            

7.    ?          

:                
         ,     
,                
    , "          ,"     
        
     
              ,  1,000
        ,     1,200     
     ?        ,  
       
 ,          100     
     
  :
Easy2Siksha.com
  (2020):   = 100
  (2024):  = 120
           20%    
,   :
󷷑󷷒󷷓󷷔              (   ) 
   
   - ,          
              
,                 
    ( )
     ,           
 :
     
        
   ( × )     
,         ,    
         ,  -   
   
    -       
1.     
               
        ,       
  ,  :



 
Easy2Siksha.com
            ,     
  
󷷑󷷒󷷓󷷔  ,           ,    
    -       
,             
   
2.     
                 
       , , , ,   ,
 ,            
           
,       :
        
     
     
󷷑󷷒󷷓󷷔  — 20  ,            
 ,   
       ,          
       
3.      
              , 
      
      :
    - 
         
         
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  , ""             
    
        ,      
󷷑󷷒󷷓󷷔 :                
 
4.    
            
  :
          
       
            
,            
       :
      -  
      - 
       
         ,      -  
 
5.    
             ,  :
 
 
   
       
      ,        
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       :
󷷑󷷒󷷓󷷔       ?”
            
6.    
  ,      
  :
          
     
      
               ,
    
      :
󷷑󷷒󷷓󷷔       ,     ?
                
7.       
     
  ,          
  :
     ,      
     ,         
   -        ,  
   
8.     
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         
  :
  
 
 
             
,    ,     

              
                 , 
 ,             
,               
      ,        ,  
                
󷷑󷷒󷷓󷷔,        ,        ,
  
8.   ,           
:

1992
1994
1996
1998
2000
2002

44
90
?
160
270
390
:       
 ,  ()          
           (   )
               ,
  1996      
 1:   
Easy2Siksha.com

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
?
?
?
?
?
?
?
?
160
110
34
-4
270
120
30
390
     :

    


,    :
46  110 ,  64
110  120 ,  10
       :
Easy2Siksha.com
46 ()
110 ()
             
 4:     
     :

󰇛󰇜

󰇛󰇜󰇛󰇜

, ( 1996, 1992     )
     :





 :
󰇛󰇜󰇛󰇜
󰇛󰇜
󰇛󰇜
󰇛󰇜󰇛󰇜
󰇛󰇜
 :


 5:  
     1996     160  ,  1998      
          ,        
 
 
 1996    :


                 
                
Easy2Siksha.com
       , 1996      160  ,
            
               
        ,     