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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)