Easy2Siksha.com
2024
/
(
)
: 3 :100
: ,
–
1.() :
() :
2.() ,
()
x y
–
Easy2Siksha.com
3.() :
0–10
6
10–20
5
20–30
8
30–40
15
40–50
7
50–60
6
60–70
3
() :
(CI)
0–15
8
15–30
26
30–45
30
45–60
45
60–75
20
75–90
17
90–105
4
4. ( ) :
()
10
20
30
40
50
60
70
80
90
4
6
24
46
67
86
96
99
100
–
5.(a) :
1
2
3
4
5
6
7
10
18
30
25
12
3
2
Easy2Siksha.com
(b) 0.5
42 36
6.() , x y
:
x
30
38
28
27
28
23
30
33
28
35
29
27
22
29
20
29
18
21
27
22
() :
x
25
28
35
32
31
36
29
38
34
32
43
46
49
41
36
32
31
30
33
39
Easy2Siksha.com
2024
/
(
)
: 3 :100
: ,
–
1.() :
() :
:1()
, ,
,
:
Easy2Siksha.com
:
:
,
-
--
:
0/0 ,
:
:
Easy2Siksha.com
:
:
:
:
(a)
√x ( ) √
1()
—
1:
Easy2Siksha.com
:
• 6 → → ≥0
• 5 → → (x−3)
(x−3)
2:
/ ,
:
:
:
:
:
:
Easy2Siksha.com
:
:
:
3:
0
:
4: /
:
:
•
≥0 ( )
•
(x−2)
•
x−28/11
Easy2Siksha.com
:
:
:
1:
x=1 :
→
→
2:
x=2.2 :
→
x=2
3:
Easy2Siksha.com
x=2.8 :
x=28/11
4:
x=4 :
x=3 ( )
5:
x=2
= 0
x=28/11
:
:
Easy2Siksha.com
()
:
at
:
at
2.() ,
()
x y
:(a) ,
1.
(x)
• :
,
• :
o
o ,
o ,
Easy2Siksha.com
o - x , f(x)
• :
2.
• :
,
• :
o
o ,
o ,
o - x , f(x)
• :
3.
( )
"" ""
•
:
•
:
• :
o
o
o ,
o x
• :
o ,
o ,
o
:
• → x
• → x
• → () ()
()
:
Easy2Siksha.com
1:
:
,
2:
:
3: -
(i)
(ii)
• :
• :
,
Easy2Siksha.com
4:
x y
• : ( ), ( ),
( )
• :
,
, - - ,
: - ,
,
, -
–
3.() :
0–10
6
10–20
5
20–30
8
30–40
15
40–50
7
50–60
6
60–70
3
Easy2Siksha.com
: ( )
( )
(f)
0–10
6
10–20
5
20–30
8
30–40
15
40–50
7
50–60
6
60–70
3
( )
:
•
•
:
Mean Deviation from Mean
:
• =
• =
• =
1:
(x)
Easy2Siksha.com
, :
Lower limit + Upper limit
f
(x)
0–10
6
5
10–20
5
15
20–30
8
25
30–40
15
35
40–50
7
45
50–60
6
55
60–70
3
65
2: ( )
:
:
f
x
fx
0–10
6
5
30
10–20
5
15
75
20–30
8
25
200
30–40
15
35
525
40–50
7
45
315
50–60
6
55
330
60–70
3
65
195
:
:
Easy2Siksha.com
= 33.4
3:
:
| x | ||---|--------------|5 | 28.4 |15 | 18.4 |25 | 8.4 |
35 | 1.6 |45 | 11.6 |55 | 21.6 |65 | 31.6 |
4: (f)
:
| f | x | | ||---|---|--------------|---------------|6 | 5 | 28.4 | 170.4 |5 | 15 | 18.4 | 92 |8 | 25 |
8.4 | 67.2 |15 | 35 | 1.6 | 24 |7 | 45 | 11.6 | 81.2 |6 | 55 | 21.6 | 129.6 |3 | 65 | 31.6 |
94.8 |
:
5:
Mean Deviation
Easy2Siksha.com
Mean Deviation from Mean
( )
13.18 ?
:
, 13
= 33.4 , :
20 46
— 20-40
() :
(CI)
0–15
8
15–30
26
30–45
30
45–60
45
60–75
20
75–90
17
90–105
4
: 1:
:
Easy2Siksha.com
(CI)
0–15
8
15–30
26
30–45
30
45–60
45
60–75
20
75–90
17
90–105
4
:
1. (QD)=
2. =
() ()
2:
(CF) :
(f)
(CF)
0–15
8
8
15–30
26
34
30–45
30
64
45–60
45
109
60–75
20
129
75–90
17
146
90–105
4
150
3:
•
•
, 37.5 , 112.5
4:
• : CF 37.5 30-45 ( 30 CF 34 ,
45 CF 64 )
Easy2Siksha.com
• : 112.5 60-75 ( 60 CF 109 , 75
CF 129 )
5:
:
:
•
• =
•
•
• =
(i)
• = 30–45
•
•
•
•
• = 37.5
(ii)
• = 60–75
•
•
•
•
• = 112.5
Easy2Siksha.com
6:
• (QD):
• :
Coefficient
• = 15.44
• ≈ 0.33
“ ”
•
25%
•
75%
• 50%
• 2 ,
• —
, 15.44 ,
0.33
4. ( ) :
()
10
20
30
40
50
60
70
80
90
4
6
24
46
67
86
96
99
100
Easy2Siksha.com
:
“ ()” :
()
10
20
30
40
50
60
70
80
90
4
6
24
46
67
86
96
99
100
:
• 4 10
• 6 20
• 24 30
• …
, (
)
1: →
:
0–10
4
4
10–20
6
6−4 = 2
20–30
24
24−6 = 18
30–40
46
46−24 = 22
40–50
67
67−46 = 21
50–60
86
86−67 = 19
60–70
96
96−86 = 10
70–80
99
99−96 = 3
80–90
100
100−99 = 1
:
0–10
4
10–20
2
20–30
18
30–40
22
40–50
21
Easy2Siksha.com
50–60
19
60–70
10
70–80
3
80–90
1
2:
6 :
2 ( )
( ) ( )
( ) ( )
1:
= 22 → 30–40
2: ( )
4+2 = 6, 18+22 = 40, 21+19 = 40, 10+3 = 13
= 40 → 20-30, 30-40, 40-50 50-60
3: (
)
2+18 = 20 22+21 = 43 19+10 = 29 3+1 = 4
= 43 → 30–40 40–50
4: ( )
4+2+18 = 24 22+21+19 = 62 10+3+1 = 14
= 62 → 30–40, 40–50, 50–60
Easy2Siksha.com
5: (
)
2+18+22 = 4221+19+10 = 503+1 = 4
= 50 → 40–50, 50–60, 60–70
6: ( )
18+22+21 = 6119+10+3 = 32
= 61 → 20–30, 30–40, 40–50
3:
20–30
2
30–40
5
40–50
4
50–60
2
0
= 30–40 ( )
4: ( )
:
• = 30
•
= 22
•
= 18
•
= 21
• = = 10
Easy2Siksha.com
5:
Mode
100 0-10, 10-20, 20-30,
, :
• 30-40
• 22 -
• ,
30-40 - ,
→ ≈ 38
:
38
Easy2Siksha.com
–
5.(a) :
1
2
3
4
5
6
7
10
18
30
25
12
3
2
(b) 0.5
42 36
: ()
:
(x)
(f)
1
10
2
18
3
30
4
25
5
12
6
3
7
2
1:
:
•
• :
o
o
o
o
o
o
o
.
Easy2Siksha.com
,
2:
• = 30 ( = 3 ) , = 3
3:
:
• :
o
o
o
o
o
o
o
.
,
4:
:
Mode
() : ≈ 0.14
Easy2Siksha.com
()
:
• = 0.5
• = 42
• = 36
()
1:
Mode
, :
Mode Median
2:
= 42, = 36. ,
, = 45.
3:
= 0.5 ,
, = 18.
4:
:
Easy2Siksha.com
() : = 40%
• (a) ≈ 0.14
• () = 40%
6.() , x y
:
x
30
38
28
27
28
23
30
33
28
35
29
27
22
29
20
29
18
21
27
22
() :
x
25
28
35
32
31
36
29
38
34
32
43
46
49
41
36
32
31
30
33
39
:6(a) x y
:
x
30
38
28
27
28
23
30
33
28
35
29
27
22
29
20
29
18
21
27
22
(ρ) ,
: x y →
x y →
1: x
x :
Easy2Siksha.com
23, 27, 28, 28, 28, 30, 30, 33, 35, 38
( ):
x
23
1
27
2
28
3,4,5 → = 4
30
6,7 → = 6.5
33
8
35
9
38
10
x :
x
30
6.5
38
10
28
4
27
2
28
4
23
1
30
6.5
33
8
28
4
35
9
2: y
y :
18, 20, 21, 22, 22, 27, 27, 29, 29, 29
:
18
1
20
2
21
3
22
4.5
27
6.5
29
9
:
Easy2Siksha.com
29
9
27
6.5
22
4.5
29
9
20
2
29
9
18
1
21
3
27
6.5
22
4.5
3: d = (Rx − Ry) d²
²
6.5
9
−2.5
6.25
10
6.5
3.5
12.25
4
4.5
-0.5
0.25
2
9
-7
49
4
2
2
4
1
9
−8
64
6.5
1
5.5
30.25
8
3
5
25
4
6.5
−2.5
6.25
9
4.5
4.5
20.25
4:
:
n = 10Σd² = 217.5
Easy2Siksha.com
(a):
: x y : - x
, y
6()
:
x
25
28
35
32
31
36
29
38
34
32
43
46
49
41
36
32
31
30
33
39
:
x y →x2 y y x →y x
1:
2:
:
:
Easy2Siksha.com
x y
3: y x
y x
()
y x :
y x :
()
:
x y (
)
:
Easy2Siksha.com
x → y
y → x
() , (−0.36)
— !
(a) :
() :
7.
:
2
10
4
12
4
5
4
8
5
10
7
15
10
12
12
10
15
15
15
10
Easy2Siksha.com
: 1:
:
:
•
( )
•
( )
, = , =
2:
2
10
4
12
20
40
24
48
4
5
4
8
20
20
32
32
5
10
7
15
50
70
75
105
10
12
12
10
120
144
100
120
15
15
15
10
225
225
150
150
435
499
381
455
3:
• :
, .
• :
, .
4:
Easy2Siksha.com
' = 117.1
,
17.1%
5:
:
?
• :
• :
• :
:
:
( )
6:
Easy2Siksha.com
:
( )
• ():
• ():
• ():
:
• = 117.1
•
8. :
( )
1990
76.6
1991
78.7
1992
?
1993
77.7
1994
78.7
Easy2Siksha.com
1995
?
1996
80.6
:
,
- 1992 1995 -
( )
1990
76.6
1991
78.7
1992
?
1993
77.7
1994
78.7
1995
?
1996
80.6
?
1992,
1991 1993 , 1995, 1994 1996 , -
:
-
-
:
, :
Missing Value
Previous Year Value Next Year Value
Easy2Siksha.com
1: 1992
:
• 1991 = 78.7
• 1993 = 77.7
1992
:
1992 = 78.2
2: 1995
:
• 1994 = 78.7
• 1996 = 80.6
:
1995 = 79.65
Easy2Siksha.com
( )
1990
76.6
1991
78.7
1992
78.2
1993
77.7
1994
78.7
1995
79.65
1996
80.6
( )
-
:
• 1991 78.7
• 1993 77.7
1992
:
• 1994 78.7
• 1996 80.6
1995
:
✔
✔ -
✔ ( 1 )
✔
, :
•
Easy2Siksha.com
•
•
,
:
:
• 1990 → 76.6
• 1991 → 78.7 ()
• 1992 → 78.2 ( )
• 1993 → 77.7 ()
• 1994 → 78.7 ()
• 1995 → 79.65 ()
• 1996 → 80.6 ()
:
1990 -
1993
1996
-
-
1992 78.2 1995 79.65
1990 1996 -
1992 = 78.2
1995 = 79.65
Easy2Siksha.com
“
, ”
