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  • 332022558. 1 ( )

    1

    3 8 10 18 20 30 31 50 51 60 ( ) 2 10 8 12 18 ( ) 2 9 19 30.5 50.5 ( ) 9 19 30.5 50.5 60.5

    ( ) 7 10 11.5 20 10 ( ) 2 + 9

    2 14 24.75 40.5 30.25

    ( ) 2 12 20 32 50

    ( ) 250

    1250

    2050

    3250

    5050

    ( )

    250

    1050

    850

    1250

    1850

    4 24 40 64 100

    4 20 16 24 36

    2

    1 10 11 20 21 30 31 40 41 50 ( ) 4 6 10 12 8 ( ) 0.5 10.5 20.5 30.5 40.5 ( ) 10.5 20.5 30.5 40.5 50.5

    ( ) 10 10 10 10 10 ( ) 5.5 15.5 25.5 35.5 45.5 ( ) 4 10 20 32 40

    ( 0.1 0.25 0.5 0.8 1 ( ) 0.1 0.15 0.25 0.3 0.2

    10 25 50 80 100

    10 15 25 30 20

    1

    2 8 10 20 22 30 34 50 54 60 ( ) 1 11 8 22 8 ( ) ( )

    ( ) ( ) ( )

    ( )

    ( )

    2 3 8 9 14 15 20 21 26 27 32

    ( ) 4 6 10 12 8 ( ) ( )

    ( ) ( ) ( )

    ( ( )

  • 332022558. 2 1.1

    1( )12, 22, 31, 8, 19, 28

    =

    =12 + 22 + 31 + 8 + 19 + 28

    6 =1206 = 20

    2( )2, 2, 2, 2, 2, 3, 3, 5, 7, 17

    =

    =5(2) + 2(3) + 1(5) + 1(7) + 1(17)

    10

    =4510 = 4.5 .

    3()

    ( )112, 131, 126, 131, 141, 122, 128, 131, 110, 125

    131 () = +

    = +

    112 131 126 131 141

    = 19 0 5 0 10 = 14

    122 128 131 110 125

    = 9 3 0 21 6 = 39

    = +

    = 131 +

    (14) + (39)10

    = 131 + (5.3) = 125.7 .

    11. ( ) 35, 56, 22, 18, 48, 31( + 1) 2. ( )

    ( + 1)17, 17, 17, 22, 22, 33, 33, 15, 27, 27 3. ()( )172,135,146,150, 150, 150, 165, 142, 150, 150 ( + 1) = . .) = +

    = +

    = = 14

    = = 39

  • 332022558. 3 333202

    3.1)

    A 5 2 6 12 18 3 4 8 9 13 10 80 8

    B 20 12 8 23 7 5 70 14

    C 14 5 11 10 4 40 10

    D 3 5 17 12 13 10 6 60 10

    E 11 12 7 10 5 12 13 7 70 10

    F 2 9 5 12 10 16 15 11 8 80 10

    G 2 7 18 11 5 10 6 19 21 9 99 11

    H 12 13 8 9 10 20 6 72 12

    3.2) =

    40 + 604 + 6 = 10 .

    3.3) , , =

    80 + 70 + 40 + 6010 + 5 + 4 + 6 = 10 .

    3.4)

    =80 + 70 + 40 + 60 + 70 + 80 + 99 + 72

    10 + 5 + 4 + 6 + 7 + 8 + 9 + 6

    = 10.38 . 3.5) 2 =

    40 + 2(4)4 =

    484 = 12 .

    3.6) 2

    =2(20) + 2(12) + 2(8) + 2(23) + 2(7)

    5

    =2(20 + 12 + 8 + 23 + 7)

    5

    =2(70)5 = 2

    (14) = 28 .

    3.7) 1711 1318 =

    60 + (11 17) + (18 13)6 =

    596 = 9.83 .

    3.8) 11 242

    = 99 + (24 11) 2 5

    9 2

    =1057 = 15 .

    3. 33202 (Bonus+3) 3.1)

    A 8 2 4 10 18 13 6 9 5 15

    B 4 16 28 17 5 6

    C 13 15 21 11

    D 2 16 18 12 22 10 4

    E 10 14 6 8 17 12 17

    F 5 4 22 7 15 16

    G 8 5 12 20 5 11 3 14 12 10

    H 14 25 5 16 10

    3.2) = . . .. 3.3) , , = . . . . .. 3.4) = . . . .. 3.5) 25 = . . .. 3.6) 3 = . . .. 3.7) 414135 = . . .. 3.8) 2147125 = . . ..

  • 332022558. 4 2

    5.1

    1, 3, 5, 5, 5, 7, 7, 9, 9, 15 = 5

    5.2

    2, 3, 7, 10, 10, 10, 15, 20, 23, 23, 23, 30, 30, 35

    5.3

    3, 5, 5, 5, 9, 9, 9, 13, 13, 13

    1

    3(Median)

    610, 2, 5, 8, 15, 19, 22, 13, 30

    1Rank 1 2 3 4 5 6 7 8 9

    x 2 5 8 10 13 15 19 22 30

    2(RankMed. )

    RankMed. = n+12

    =9+1

    2= 5

    3513 13Ans.

    5.( + 1)

    5.1

    20,33, 33, 25, 25, 17, 17, 6, 6, 25

    5.2

    23,33, 18, 22, 22, 22, 23, 20, 17, 17, 23, 31

    5.3

    7,7, 3, 3, 3, 8, 8, 8, 10, 10,11,11

    5.4

    7,7, 3, 3, 3, 8, 8, 8, 10, 10, 22, 22, 22, 4,4,1,1 6.15, 4, 2, 12, 18, 9, 22, 25, 30(Bonus + 1)

    Rank 1 2 3 4 5 6 7 8 9

    x

  • 332022558. 5

    715,12, 5, 18, 25, 19, 22, 23, 30, 40

    1Rank 1 2 3 4 5 6 7 8 9 10 x 5 12 15 18 19 22 23 25 30 40

    2(RankMed. )

    RankMed. = n+12

    =10+1

    2= 5.5

    35.5

    Med. =x5 + x6

    2=

    19 + 22

    2= 20.5Ans.

    4(G.M. )G.M. = x x x . x

    82, 2, 2, 3, 3, 5, 8

    G.M. = x1x2x3 . xnn

    G.M.= (2)(2)(2)(3)(3)(5)(8)

    = 2880 = 3.12Ans.

    5

    H. M.= n

    fx

    93, 3, 3, 3, 2, 2, 2, 7, 5, 5

    H. M. = n

    fx=

    1043 +

    32 +

    17 +

    25

    H.M. = 10

    4(70) + 3(105) + 30 + 2(42)210

    =2100709 = 2.96Ans.

    7. (Bonus + 1)31,42, 25, 18, 35, 20, 29, 13, 38, 40

    Rank 1 2 3 4 5 6 7 8 9 10

    x

    8.6, 6, 4, 10, 12, 16, 4,4(Bonus + 1)

    9.(Bonus + 1)5, 2, 3, 3, 2, 5, 2, 3, 5, 5

  • 332022558. 6 10AB

    200. 100./. C300. 60./. D200. 40./.

    =

    v =s

    t t =

    s

    v

    H. M.=s + s + ssv +

    sv +

    sv

    H.M. =200 + 300 + 200200100 +

    30060 +

    20040

    =700

    2 + 5 + 5 =70012

    H.M. = 70012 = 58.33..Ans.

    1.1GroupData

    1Ex11

    =

    =

    =103040 = 25.75 .

    10.AB450. 90./. C240. 80./.

    D120. 60./.(Bonus + 1)

    11. (Bonus + 2)

    = =

    1 10 11 20 21 30 31 40 41 50 (f) 5 7 15 8 5

    (f) 1-10 5 5.5 27.511-20 7 15.5 108.521-30 15 25.5 382.531-40 8 35.5 28441-50 5 45.5 227.5

    N=40 1030

    1-10 11-20 21-30 31-40 41-50

    (f) 3 8 12 6 11

  • 332022558. 7 2( )

    12

    1-10 11-20 21-30 31-40 41-50 5 7 15 8 5

    = + 11 + 2

    L(L=20.5)(i=10)

    ( =15-7=8)

    ( =15-8=7) Mode = 20.5 + 10 = 25.8Ans..

    Mode =20.5 + 30.5

    2 = 25.5

    12. ( + 2) 1-10 11-20 21-30 31-40 41-50

    3 8 12 6 11

    = + 11 + 2

    = . . = . .

    = . = ..

    = ..

  • 332022558. 8

    1-10 11-20 21-30 31-40 41-50 ( ) 2 18 20 5 5

    1334.5 1 10 11-20 21-30 31-40 41-50 5 5 6 4

    = + 11 + 2

    4 34.5 = 30.5 + 10

    ( 6)( 6) + ( 4)

    34.5 30.5 = 10( 6)

    ( 6) + ( 4)

    4 = 10( 6)

    ( 6) + ( 4)

    4(2 10) = 10( 6)

    8 40 = 10 60

    2 = 20 = 10 .

    3( )14

    1)

    . =2=

    40

    2= 20

    2) . 4(31 40) ( ) = 30.5( ) = 10 = 16, = 20 3) .

    . = + 2

    . = 30.5 + 10402 1620 = 32.5 .

    13. 18.5 ( + 2)

    5 10 11 15 16 20 21 25 26 30 2 3 4 5

    14. ( + 2)

    1-10 11-20 21-30 31-40 41-50 ( ) 3 7 6 20 4

    1-10 11-20 21-30 31-40 41-50 (f) 3 7 6 20 4

    3 10 16 36 40

  • 332022558. 9 15.

    35.5

    1) . =2=

    35 +

    2

    2) . = 35.53( ) = 30.5( ) = 45.5 30.5 = 15 = 5 + 15 = 20 =

    3) 35.5 = 30.5 + 1535+2

    20

    35.5 30.5 = 1535 +

    2 20

    5 = 1535 +

    2 20

    5 = 1535 +

    2 20

    = 335 + 40

    2

    2 = 3( 5)

    2 = 3 15 = 15

    15.

    38( + 2)

    1-15 16-30 31-45 46-60 61-75 ( ) 5 15 10 5 6-15 16-25 26-35 36-45 46-55

    ( ) 2 8 5 5

  • 332022558. 10 162

    1615

    2810

    2

    = = 1 + 2

    1 + 2

    =6(15) + 8(10)

    6 + 8 =90 + 80

    14 = 12.143 .

    173

    1 28

    21624

    31440

    30

    1

    =

    = 1 + 2 + 3

    1 + 2 + 3

    30 =(28) + 16(24) + 14(40)

    + 16 + 14

    30 =(28) + 384 + 560

    + 30

    30( + 30) = (28) + 944

    30 + 900 = 28 + 944

    2 = 44 = 22 .

    16.2

    1520

    2159

    2( + 1)

    17.3

    1 20

    21225

    31814

    19.04

    1( + 2)

  • 332022558. 11 18

    3 12212

    281

    213.6

    316

    314.2

    3

    =

    = + +

    + +

    2

    13.6 =22(12) + 8

    22 + 8

    (13.6)(30) = 264 + 8

    408 = 264 + 8

    8 = 408 264 = 144 = 18

    3

    14.2 =22(12) + 8(18) + (16)

    22 + 8 +

    14.2(30 + ) = 264 + 144 + 16

    426 + 14.2 = 408 + 16

    1.8 = 18 = 10 .

    18.

    3 1108

    2612

    6.875

    34

    36.9

    3( + 2)

  • 332022558. 12 19. .2550

    2320

    . . 255125

    2550625

    (1)2551(2)255146 24

    (1)2550

    2550 = 23

    2551 = + 20 = 25 2551 = 25( + 20)

    2550652 25( + 20) 23 = 652

    25 + 500 23 = 652

    2 = 152 = 76

    2550 76 2551 = 76 + 20 = 96 .

    (2) = 1 + 2

    1 + 2

    255196462450

    25 =46(24) + 50

    96

    25(96) = 1104 50

    2400 = 1104 + 50

    =129650 = 25.92 .

    19. . .2551

    262550

    20. . 2550

    252550

    580(1)2550(2)2550

    530 ( + 2)

  • 332022558. 13 2031

    35

    25

    ,

    = + +

    31 = 25 + 35+

    31( + ) = 25 + 35

    31 + 31 = 25 + 35

    31 25 = 35 31

    6 = 4 =64 =

    32

    : = 3: 2 .

    21366, 74, 84 3

    21.53

    2.5

    3

    1 = 1

    2 = 2 = 1 1.5 = 1.5

    3 = 3 = 1 2.5 = 2.5

    = + +

    + +

    = 1(66) + 1.5(74) + 2.5(84)

    1 + 1.5 + 2.5

    =66 + 111 + 210

    5 =3875 = 77.4 .

    20. 11.2

    12

    10

    ( + 2)

    21.375, 45, 6022

    3 2

    358.5 ( + 2)

  • 332022558. 14 2241

    530

    38.8

    =

    = = 41

    55 30 = 150

    1+2 = 1 + 2

    1 + 2

    38.8 =41 + 150

    + 5

    38.8( + 5) = 41 + 150

    38.8 + 194 = 41 + 150

    41 38.8 = 194 150

    2.2 = 44 = 20 + 520 + 5 = 25 .

    23200 165

    15020

    200 200 165 = 33000.

    2020 150 = 3000.

    = 200 20 = 180 = 33000 3000 = 30000.

    = 30000180 = 166.67. .

    22. 100 160

    25175

    ( + 2)

    23. 25.5

    2215

    27( + 2)