8/12/2019 14. Statistics

1/32

LGO@VMKQLGR

R A J Q O H G X @J O B P^ -E

LGXMALGX@FV

7

VXGX@VX@FV

@OXRJHQFX@JO@o figss @], wa mgva stuh`ah gbjut tma prasaotgt`jo je c`vao hgtg `o tma ejrl je uocrjupah us waii gs crjupah

eraquaofy h`str`but`jos. Sa mgva gisj stuh`ah mjw tj raprasaot tma stgt`st`fgi hgtg `o tma ejrl je vgr`jus crgpms

sufm gs bgr crgpms, m`stjcrgls goh eraquaofy pjiycjos. @o ghh`t`jo, wa mgva stuh`ah tma lagsura je faotrgitaohaof`as sufm gs lago, lah`go goh ljha je uocrjupah hgtg.

@o tm`s fmgptar, wa smgii h`sfuss gbjut lago, lah`go goh ljha je crjupah hgtg. Sa smgii gisj h`sfuss tma fjofapt

je fuluigt`va eraquaofy, fuluigt`va eraquaofy h`str`but`jo goh fuluigt`va eraquaofy furva (jc`va).

LAGO JE QOCRJQ^AH HGXGSa kojw tmgt tma lago je jbsarvgt`jos `s tma sul je tma vgiuas je gii tma jbsarvgt`jos h`v`hah by tma tjtgi oulba

je jbsarvgt`jos `.a., `e x7,x2,x6,, xogra o jbsarvgt`jos, tmao

lago,o

xxxxx o

.....627 jro

x

x

o

77

7

, wmara

o

x77

7haojtas tma sul x7 + x2 x6+ + xo.

H`raft latmjh Vmjrt-fut latmjh jr Gssulah-lago latmjh Vtap-hav`gt`jo latmjh. LAGO JE CRJQ^AH HGXG H`raft latmjh

@e x7,x2,x6,, xogra o jbsarvgt`jos w`tm raspaft`va eraquaof`as e 7,e 2,e 6,..,e otmao lago, )(x hae`oah by

o

oo

eeee

xexexexex

....

.....

627

662277 jr

o

o

e

xe

x

77

7

77

77

, wmara

o

oeeeee77

6277 ..... .

Xj e`oh lago je crjupah Hgtg

Xma ejiijw`oc staps smjuih ba ejiijwah `o e`oh`oc tma gr`tmlat`f lago je crjupah hgtg by h`raft latmjh.

VXA^-74 E`oh tma figss lgrk (x`) je agfm figss us`oc, 2

i`li`l `tQppar`tijwar

x`

VXA^-24 Fgifuigta ex`ejr agfm `

VXA^-64 Qsa tma ejrluig 4 lago,

o

o

e

xe

x

77

7

77

77

,

VMJRXFQXLAXMJHJRGVVQLAHLAGOLAXMJH@o tm`s fgsa, tj fgifuigta tma lago, wa ejiijw tma ejiijw`oc staps 4

VXA^-74 E`oh tma figss lgrk (x`) je agfm figss us`oc

2

i`li`l `tQppar`tijwarx

`

VXA^-24 Fmjjsa g su`tgbia vgiua je x``o tma l`hhia gs tma gssulah lago goh haojta `t by g.

VXA^-64 E`oh h`< x` g ejr agfm `

VXA^-84 E`oh e h`ejr agfm `

VXA^-14 E`oh o < 7e

8/12/2019 14. Statistics

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LGO@VMKQLGR

R A J Q O H G X @J O B P^ -E

LGXMALGX@FV

2

VXA^-54 Fgifuigta tma lago, )(x by us`oc tma ejrluigO

hegx

`` .

VXA^-HAU@GX@JOLAXMJHVjlat`las, tma vgiuas je x goh e gra sj igrca tmgt tma fgifuigt`jo je lago by gssulah lago latmjh bafjlas qu`ta

`ofjovao`aot. @o tm`s fgsa, wa ejiijw tma ejiijw`oc staps4

VXA^-74 E`oh tma figss lgrk (x`) je agfm figss us`oc,2

i`li`l `tQppar`tijwarx`

VXA^-24 Fmjjsa g su`tgbia vgiua je x``o tma l`hhia gs tma gssulah lago goh haojta `t by g.

VXA^-64 E`oh m < (uppar i`l`t ijwar i`l`t) ejr agfm figss.

VXA^-84 E`ohm

gxu ``

ejr agfm figss.

VXA^-14 E`oh eu`ejr agfm `.

VXA^-54 Fgifuigta, tma lago by us`oc tma ejrluig

O

uegx

``m, wmara `eO

Ax.7 E`oh tma lago je tma ejiijw`oc hgtg 4

Vji. Sa lgy prapgra tma tgbia gs c`vao baijw 4

Lago, 8.278>

=15

7

7

o

`

`

o

`

``

e

xe

x

Ax.2 Xma ejiijw`oc h`str`but`jo smjws tma hg`iy pjfkat giijwgofa je fm`ihrao je g ijfgi`ty. Xma lago pjfkat giijwgofa`s Rs. 7=. E`oh tma l`ss`oc eraquaofy e.

Figss @otarvgi >-= =-75 75-28 28-62 62-8>

Eraquaofy 5 3 7> = 0

Figss @otarvgi Eraquaofy (e) Figss lgrk (x`) ex`

>-=

=-75

75-28

28-6262-8>

5

3

7>

=0

8

72

2>

2=65

28

=8

2>>

228628

8>`e =15`xe

Hg`iy pjfkat giijwgofa (`o Rs.) 77-76 76-71 71-73 73-70 70-27 27-26 26-21

Oulbar je fm`ihrao 3 5 0 76 e 1 8

8/12/2019 14. Statistics

3/32

LGO@VMKQLGR

R A J Q O H G X @J O B P^ -E

LGXMALGX@FV

6

Vji. Sa lgy prapgra tma tgbia gs c`vao baijw 4

Hg`iy pjfkat

giijwgofa

Oulbar je

Fm`ihrao (e)

Figss lgrk (x`) ex`

77-76

76-71

71-7373-70

70-27

27-26

26-21

3

5

076

e

1

8

72

78

757=

2>

22

28

=8

=8

788268

2>e

77>

05

ee 88 exe `` 2>312

Lago,e

e

e

xe

xo

`

`

o

`

``

88

2>312

7

7

C`vao, lago < 7=

2>2>3127=30288

2>3127=

eee

e

e

Ax.6 E`oh tma l`ss`oc eraquaof`as e7 goh e2 o tma tgbia c`vao baijw, t `s ba`oc c`vao tmgt tma lago je tma c`vao

eraquaofy h`str`but`jo s 1>.

Vji. Sa lgy prapgra tma tgbia gs c`vao baijw 4

Figss Oulbar je (e) Figss lgrk (x`) ex`

>-2>

2>-8>

8>-5>

5>-=>

=>-7>>

73

e7

62

e2

70

7>

6>

1>

3>

0>

73>

6>e7

75>>

3>e2

737>

275= eee 27 3>6>68=> eexe ``

Lago,27

277

5=

3>6>68=>

ee

ee

e

xe

x`

o

`

``

Figss >-2> 2>-8> 8>-5> 5>-=> =>-7>> Xjtgi

Eraquaofy 73 e7 62 e2 70 72>

8/12/2019 14. Statistics

4/32

LGO@VMKQLGR

R A J Q O H G X @J O B P^ -E

LGXMALGX@FV

8

C`vao, lago < 1>

2727

27

27 3>6>68=>1>1>68>>5=

3>6>68=>1> eeee

ee

ee

2>e7 2>e2< => e7 e2< 8 (`)

Goh

275= eee` 72> < 5= + e7+e2 \72>[ 7 e e7+ e2< 12 (``)

Ghh`oc (7) goh (2), wa cat 2e7< 15 e7< 2= e2< 28Maofa, ejiijw`oc l`ss`oc eraquaof`as e7 goh e2 gra 2= goh 28 raspaft`vaiy.

Ax.8 Xma ejiijw`oc tgbia c`vas tma lgrks sfjrah by 7>> stuhaots o g figss tast 4

Vji. Sa lgy prapgra tma tgbia w`tm gssulah lago, g < 61 gs c`vao baijw 4

Lrks Oj.je stuhaots (e) Figss lgrk (x`) h`< x` g < x` 61 eh`

>-7>

7>-2>

2>-6>

6>-8>

8>-1>

1>-5>

72

7=

23

2>

73

5

1

71

21

6> < g

81

11

6>

2>

7>

>

7>

2>

65>

65>

23>

>

73>

72>

O < 7>> 3>>``he

Lago, 2=3617>>

)3>>(61

O

hegx

``

Ax.1 Xm`rty wjlao wara axgl`oah `o g mjsp`tgi by g hjftjr goh tma oulbar je magrt bagts par l`outa, wara rafjrhah

goh sullgr`zah gs ejiijws. E`oh tma lago magrt bagts par l`outa ejr tmasa wjlao, by us`oc gssulah.

Lgrk >-7> 7>-2> 2>-6> 6>-8> 8>-1> 1>-5>

Oj. je Vtuhaots 72 2= 23 2> 73 5

Oj. je magrt bagts

par l`outa 51-5= 5=-37 37-38 38-33 33-=> =>-=6 =6-=5

Eraquaofy 2 8 6 = 3 8 2

8/12/2019 14. Statistics

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LGO@VMKQLGR

R A J Q O H G X @J O B P^ -E

LGXMALGX@FV

1

Vji. Sa lgy prapgra tma tgbia w`tm gssulah lago, g < 61 gs c`vao baijw 4

Lago, 0.311

2

1.316>

72

1.31

O

he

gx ``

Ax.5 E`oh tma lago je tma ejiijw`oc h`str`but`jo by stap-hav`gt`jo latmjh 4

Vji. Sa lgy prapgra tma tgbia w`tm gssulah lago g < 72> gs c`vao baijw 4

Lago, 2.7721

157

1

602>

7>>

2>)60(72>

m

O

uegx

``

Oj. je magrt bagts

par l`outa

Oj.je wjlao (e) Figss lgrk (x`) h`< x` g

< x` 31.1

eh`

51-5=

5=-37

37-38

38-33

33-=>

=>-=6

=6-=5

2

8

6

=

3

8

2

55.1

50.1

32.1

31.1 < g

3=.1

=7.1

=8.1

0

5

6

>

6

5

0

7=

28

0

27

28

7=

O < 6> 72``he

Figss 1>-3> 3>-0> 0>-77> 77>-76> 76>-71> 71>-73>

Eraquaofy 7= 72 76 23 = 22

Figss Eraquaofy (e) Figss lgrk (x`) 2>

72>

```

x

m

gxu

eu`1>-3>

3>-0>

0>-77>

77>-76>

76>-71>

71>-73>

7=

72

76

23

=

22

5>

=>

7>>

72> < g

78>

75>

6

2

7

>

7

2

18

28

76

>

=

88

O < 7>> 60``ue

8/12/2019 14. Statistics

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LGO@VMKQLGR

R A J Q O H G X @J O B P^ -E

LGXMALGX@FV

5

Ax.3 E`oh tma lago lgrks erjl tma ejiijw`oc hgtg 4

Vji. Sa lgy prapgra tma tgbia gs c`vao baijw 4

Lago, 87.8==1

878>

O

xex

``

Ax.= E`oh tma lago lgrks je stuhaots erjl tma ghdj`o`oc eraquaofy h`str`but`jo tgbia.

Lgrks Oj. je Vtuhaots

Gbjva > =>

Gbjva 7> 33

Gbjva 2> 32

Gbjva 6> 51

Gbjva 8> 11

Gbjva 1> 86

Gbjva 5> 26

Gbjva 3> 75

Gbjva => 7>

Gbjva 0> =

Gbjva 7>> >

Lgrks

Baijw

7>

Baijw

2>

Baijw

6>

Baijw

8>

Baijw

1>

Baijw

5>

Baijw

3>

Baijw

=>

Baijw

0>

Ba

7

Oj. je Vtuhaots 1 0 73 20 81 5> 3> 3= =6 z

Lgrks Oj. je stuhaots Figss @otarvgi e Figss lgrk

(x`)

ex`

Baijw 7>

Baijw 2>

Baijw 6>

Baijw 8>

Baijw 1>

Baijw 5>

Baijw 3>

Baijw =>

Baijw 0>

Baijw 7>>

1

0

73

20

81

5>

3>

3=

=6

=1

>-7>

7>-2>

2>-6>

6>-8>

8>-1>

1>-5>

5>-3>

3>-=>

=>-0>

0>-7>>

1

8

0

72

75

71

7>

=

1

2

1

71

21

61

81

11

51

31

=1

01

21

5>

221

82>

32>

=21

51>

5>>

821

70>

O < =1 878>`xe

8/12/2019 14. Statistics

7/32

LGO@VMKQLGR

R A J Q O H G X @J O B P^ -E

LGXMALGX@FV

3

Vji. Sa lgy prapgra tma tgbia gs c`vao baijw 4

Lago, 7.17721.17=>

8>0>

O

xex

``(gpprjx)

Ax.0 E`oh tma gr`tmlat`f lago je tma ejiijw`oc eraquaofy h`str`but`jo.

Vji. Xma c`vao sar`as s `o `ofius`va ejrl. Sa lgy prapgra tma tgbia `o axfius`va ejrl w tm gssulah lago g < 82 gs

c`vao baijw 4

Lgrks Oj. je stuhaots Figss @otarvgi e Figss lgrk (x`) ex`

Gbjva >

Gbjva 7>

Gbjva 2>Gbjva 6>

Gbjva 8>

Gbjva 1>

Gbjva 5>

Gbjva 3>

Gbjva =>

Gbjva 0>

Gbjva 7>>

=>

33

3251

11

86

26

75

7>

=

>

>-7>

7>-2>

2>-6>6>-8>

8>-1>

1>-5>

5>-3>

3>-=>

=>-0>

0>-7>>

7>>-77>

6

1

37>

72

2>

3

5

2

=

>

1

71

2161

81

11

51

31

=1

01

7>1

71

31

73161>

18>

77>>

811

81>

73>

35>

>

O < =>

8>0>``xe

Figss 21-20 6>-28 61-60 8>-88 81-80 1>-18 11-10

Eraquaofy 78 22 75 5 1 6 8

Figss Eraquaofy (e) Figss lgrk (x`) h`< x` g < x` 31.1 eu`

28.1-20.1

20.1-68.1

68.1-60.1

60.1-88.1

88.1-80.1

80.1-18.1

18.1-10.1

78

22

75

5

1

6

8

23

62

63

82 < g

83

12

13

71

7>

1

>

1

7>

71

27>

22>

=>

>

21

6>

5>

O < 3> 601``he

8/12/2019 14. Statistics

8/32

LGO@VMKQLGR

R A J Q O H G X @J O B P^ -E

LGXMALGX@FV

=

Lago, 65.653>

2181

3>

601208>

3>

)601(82

O

hegx `

`(gpprjx)

LAH@GO JE G CRJQ^AH HGXGLAH@GO4 @t `s g lagsura je faotrgi taohaofy wm`fm c`vas tma vgiua je tma l`hhia ljst jbsarvgt`jo `o tma hgtg. @o

g crjupah hgtg, `t `s ojt pjss`bia tj e`oh tma l`hhia jbsarvgt`jo by ijjk`oc gt tma fuluigt`va eraquaof`as gs tmal`hhia jbsarvgt`jo w`ii ba sjla vgiua `o g figss `otarvgi. @t `s, tmaraejra, oafassgry tj e`oh tma vgiua `os`ha g figsstmgt h`v`has tma wmjia h`str`but`jo otj twj mgivas.

LAH@GOFIGVV4 Xma figss wmjsa fuluigt`va eraquaofy `s cragtar tmgo2

O`s fgiiah tma lah`go figss.

Xj fgifuigta tma lah`go je g crjupah hgtg, wa ejiijw tma ejiijw`oc staps 4VXA^-74 ^rapgra tma fuluigt`va eraquaofy tgbia fjrraspjoh`oc tj tma c`vao eraquaofy h`str`but`jo goh jbtg`o

`eO .

VXA^-24 E`oh2

O

VXA^-64 Ijjk gt tma fuluigt`va eraquaofy dust cragtar tmgo

2

Ogoh e`oh tma fjrraspjoh`oc figss (Lah`go figss)

VXA^-84 Qsa tma ejrluig Lah`go, me

FO

L

2

Smara < Ijwar i`l`t je lah`go figss.E < Eraquaofy je tma lah`go figss.F < Fuluigt`va eraquaofy je tma figss prafah`oc tma lah`go figss.m < V`za je tma lah`go figss.

`eO Ax.7>. E`oh tma lah`go je tma ejiijw`oc eraquaofy h`str`but`jo 4

Vji. Gt e`rst wa prapgra g fuluigt`va eraquaofy h`str`but`jo tgbia gs c`vao baijw 4

Mara, O < 7>>

2

O< 1>

Xma fuluigt`va eraquaofy dust cragtar tmgo 1> `s 58 goh tma fjrraspjoh`oc figss `s 2>-6>.

Vj, tma lah`go figss `s 2>-6>.

< 2>, O < 7>>, F < 2=, e < 65 goh m < 7>

Lgrks >-7> 7>-2> 2>-6> 6>-8> 8>-1> XjtgiOj. je Vtuhaots = 2> 65 28 72 7>>

Lgrks Oulbar je stuhaots (e) Fuluigt`va eraquaofy

>-7>

7>-2>

2>-6>

6>-8>

8>-1>

=

2>

65

28

72

=

2=

58

==

7>>

O < 7>>

8/12/2019 14. Statistics

9/32

LGO@VMKQLGR

R A J Q O H G X @J O B P^ -E

LGXMALGX@FV

0

Xmaraejra, lah`go me

FO

2

7.650

261

0

117=>

0

11

2>65

7>22

2>7>65

2=1>

2>

Ax.77 G i`ea `osurgofa gcaot ejuoh tma ejiijw`oc hgtg ejr h`str`but jo je gcas je 7>> pji`fy mjihars. Fgifuigta tma lah`g

gca, `e pji`f`as gra c`vao joiy tj parsjos mgv`oc gca 7= yagrs jowgrhs but iass tmgo 5> yagrs.

Gca

(`o yagrs)

Baijw

2>

Baijw

21

Baijw

6>

Baijw

61

Baijw

8>

Baijw

81

Baijw

1>

Baijw

11

Baijw

5>

Oj. je pji`fy

mjihars

2 5 28 81 3= =0 02 0= 7>>

Vji. Erjl tma c`vao tgbia wa fgo e`oh tma eraquaofy goh fuluigt`va eraquaofy gs c`vao baijw 4

Mara, O < 7>>

2

O< 1>

Xma fuluigt`va eraquaofy dust cragtar tmgo 1> `s 3= goh tma fjrraspjoh`oc figss `s 61-8>.

Vj, tma lah`go figss `s 51-8>.

< 2>, O < 7>>, F < 81, e < 66 goh m < 1

Xmaraejra, lah`go me

FO

2

35.6166

77=>

66

217711

66

11611

66

811>61

Maofa, tma lah`go gca `s 61.35 yagrs.

Gca (`o yagrs) Oulbar je stuhaots (e) Fuluigt`va eraquaofy

71-2>

2>-21

21-6>

6>-61

61-8>

8>-81

81-1>

1>-11

11-5>

2

8

7=

27

66

77

6

5

2

25

28

81

3=

=0

02

0=

7>>

O < 7>>

8/12/2019 14. Statistics

10/32

LGO@VMKQLGR

R A J Q O H G X @J O B P^ -E

LGXMALGX@FV

7>

Ax.72 Xma iaoctm je 8> iagvas je g pigot gra lagsurah fjrraft tj tma oagrast l`ii`latar, goh tma hgtg jbtg`oah s

raprasaotah `o tma ejiijw`oc tgbia. E`oh tma lah`go iaoctm je tma iagvas.

Iaoctm

(`o ll) 77=-725 723-761 765-788 781-716 718-752 756-737 732-7=>

Oj. je iagvas 6 1 0 72 1 8 2

Vji. Xma c`vao sar`as `s `o `ofius`va ejrl. Sa lgy prapgra tma tgbia `o axfius`va ejrl goh prapgra tma fuluigt`va

eraquaofy tgbia gs c`vao baijw 4

Mara, O < 8>

2

O< 2>

Xma fuluigt`va eraquaofy dust cragtar tmgo 2> `s 20 goh tma fjrraspjoh`oc figss `s 788.1-716.1

Vj, tma lah`go figss `s 788.1-716.1

< 788.1, O < 8>, F < 73, e < 72 goh m < 0

Xmaraejra, lah`gome

FO

2

31.78521.21.78872

061.7880

72

)732>(1.788

Maofa, lah`go iaoctm je iagvas `s 785.31 ll.

Ax.76 Fgifuigta tma l`ss`oc eraquaofy g erjl tma ejiijw`oc h`str`but`jo, t `s ba`oc c`vao tmgt tma lah`go je tma

h`str`but`jo s 28.

Vji. Gt e`rst wa prapgra g fuluigt`va eraquaofy h`str`but`jo tgbia gs c`vao baijw 4

Gca (`o yagrs) >-7> 7>-2> 2>-6> 6>-8> 8>-1> Xjtgi

Oj. je parsjos (e) 1 21 g 7= 3 11+g

Fuluigt`va eraquaofy 1 6> 6>+g 8=+g 11+g

Iaoctm (`o ll) Oulbar je iagvas (e) Fuluigt`va eraquaofy

773.1-725.1

725.1-761.1

761.1-788.1

788.1-716.1

716.1-752.1

752.1-737.1737.1-7=>.1

6

1

0

72

1

82

6

=

73

20

68

6=8>

O < 8>

Gca (`o ll) >-7> 7>-2> 2>-6> 6>-8> 8>-1>

Oj. je parsjos 1 21 g 7= 3

8/12/2019 14. Statistics

11/32

LGO@VMKQLGR

R A J Q O H G X @J O B P^ -E

LGXMALGX@FV

77

V`ofa tma lah`go `s 28, tmaraejra, tma lah`go figss w`ii ba 2>-6>.

Maofa, < 2>, O < 11+g, F < 6>, e < g goh m < 7>

Xmaraejra, lah`go me

FO

2

7>6>

2

11

2>28

g

g

7>2

)1(2>28

g

g

12

)1(8

g

g

8g < 1g 21 g < 21

Maofa, tma vgiua je l`ss`oc eraquaofy g `s 21.

Ax.78 Xma lah`go je tma ejiijw`oc hgtg s 121. E`oh tma vgiuas je x goh y, `e tma tjtgi eraquaofy s 7>>.

Figss @otarvgi Eraquaofy (e)

>-7>> 27>>-2>> 1

2>>-6>> x

6>>-8>> 72

8>>-1>> 73

1>>-5>> 2>

5>>-3>> y

3>>-=>> 0

=>>-0>> 3

0>>-7>>> 8

O < 7>>

8/12/2019 14. Statistics

12/32

LGO@VMKQLGR

R A J Q O H G X @J O B P^ -E

LGXMALGX@FV

72

Vji. Gt e`rst wa prapgra g fuluigt`va eraquaofy h`str`but`jo tgbia gs c`vao baijw 4

Sa mgva O < 7>>

287>>35 yxyx (`)V`ofa tma lah`go `s 121, sj, tma lah`go figss `s 1>> 5>>

< 1>>, O < 7>>, F < 65 + x, e < 2> goh m < 7>>

Xmaraejra, lah`go me

FO

2

1)78(217>>2>

651>1>>121

x

x

1 < 78 x x < 0

Gisj, putt`oc x < 0 `o (7), wa cat 0 + y < 28 y < 71Maofa, tma vgiuas je x goh y gra 0 goh 71 raspaft`vaiy.

LJHA JE G CRJQ^AH HGXGLJHA 4 Ljha `s tmgt vgiua gljoc tma jbsarvgt`jos wm`fm jffurs ljst jetao `.a., tma vgiua je tma jbsarvgt`jo

mgv`oc tma lgx`lul eraquaofy.

@o g crjupah eraquaofy h`str`but`jo, `t `s ojt pjss`bia tj hatarl`oa tma ljha by ijjk`oc gt tma eraquaofy.

LJHGIFIGVV 4 Xma figss je g eraquaofy h`str`but`jo mgv`oc lgx`lul eraquaofy `s fgiiah ljhgi figss je g

eraquaofy h`str`but`jo .

Xma ljha `s g vgiua `os`ha tma ljhgi figss goh `s fgifuigtah by us`oc tma ejrluig.

Ljha < m

eee

ee

2>7

>7

2

Smara < Ijwar i`l`t je tma ljhgi figss.m < V`za je figss `otarvgi.e7< Eraquaofy je ljhgi figss.e>< Eraquaofy je tma figss prafah`oc tma ljhgi figsse2< Eraquaofy je tma figss suffaah`oc tma ljhgi figss

Figss @otarvgi eraquaofy (e) Fuluigt`va eraquaofy

>-7>>

7>>-2>>

2>>-6>>

6>>-8>>8>>-1>>

1>>-5>>

5>>-3>>

3>>-=>>

=>>-0>>

0>>-7>>>

2

1

x

7273

2>

y

0

3

8

2

3

3+x

70+x65+x

15+x

15+x+y

51+x+y

32+x+y

35+x+y

O < 7>>

8/12/2019 14. Statistics

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LGO@VMKQLGR

R A J Q O H G X @J O B P^ -E

LGXMALGX@FV

76

Ax71 Xma ejiijw`oc hgtg c`vas tma `oejrlgt`jo jo tma jbsarvah i`eat`las (`o mjurs) je 221 aiaftr`fgi fjlpjoaots 4

Hatarl`oa tma ljhgi i`eat`las je tma fjlpjoaots.

Vji. Mara tma figss 5>-=> mgs lgx`lul eraquaofy, sj `t `s tma ljhgi figss.

12,57,2>,5> >7 eem goh 6=2e

Xmaraejra, ljha < meee

ee

2>7

>7

2

521.51521.15>2>2>

05>2>

6=12572

12575>

Maofa, tma ljhgi i`eat`las je tma fjlpjoaots `s 51.521 mjurs.

Ax.75 C`vao baijw s tma eraquaofy h`str`but`jo je tma ma`cmts je pigyars o g sfmjji.

Ma`cmts (`o fl) 75>-752 765-751 755-75= 750-737 732-738

Oj. je stuhaots 71 77= 782 723 7=

E`oh tma gvargca ma`cmt je lgx`lul oulbar je stuhaots.

Vji. Xma c`vao sar`as `s `o `ofius`va ejrl. Sa prapgra tma tgbia `o axfuis`va ejrl, gs c`vao baijw 4

Ma`cmts (`o fl) 710.1-752.1 752.1-751.1 751.1-75=.1 75=.1-737.1 737.1-738.1

Oj. je stuhaots 71 77= 782 723 7=

Sa mgva tj e`oh tma ljha je tma hgtg.

Mara, tma figss 751.1-75=.1 mgs lgx`lul eraquaofy, sj `t `s tma ljhgi figss.

Ax.73 Xma ljha je tma ejiijw`oc sar`as s 65. E`oh tma l`ss`oc eraquaofy e `o `t.

Figss >-7> 7>-2> 2>-6> 6>-8> 8>-1> 1>-5> 5>-37

Eraquaofy = 7> e 75 72 5 3

Vji. V`ofa tma ljha `s 65, sj tma ljhgi figss w`ii ba 6>-8>

eeem >7 ,75,7>,6> goh 722 e

Xmaraejra, ljha < meee

ee

2>7

>7

2

7>)2>(

)75(57>

72752

576>55

e

e

e

e

72> 5e < 75> 7>e 8e < 8> e < 7>

Maofa, tma vgiua je tma l`ss`oc eraquaofy e `s 7>.

I`eat`las (`o mjurs) >-2> 2>-8> 8>-5> 5>-=> =>-7>> 7>>-72>

Eraquaofy 7> 61 12 57 6= 20

8/12/2019 14. Statistics

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LGO@VMKQLGR

R A J Q O H G X @J O B P^ -E

LGXMALGX@FV

78

CRG^M@FGI. RA^RAVAOXGX@JO JE FQLQIGX@UA ERAWQAOFP H@VXR@BQX@JO

FQLQIGX@UAERAWQAOFP^JIPCJOFQRUA(JC@UA)Fuluigt`va eraquaofy `s je twj typas goh fjrraspjoh`oc tj tmasa, tma jc`va `s gisj je twj typas.

IAVV XMGO VAR@AV LJRA XMGO VAR@AV

IAVV XMGO VAR@AVXj fjostruft g fuluigt`va eraquaofy pjiycjo goh go jc`va, wa ejiijw tmasa staps 4

VXA^-7 4 Lgrk tma uppar figss i`l`t gijoc x-gx`s goh tma fjrraspjoh`oc fuluigt`va eraquaof`as gijoc y-

gx`s.

VXA^-2 4 ^ijt tmasa pj`ots fuffass`vaiy by i`oa saclaots. Sa cat g pjiycjo, fgiiah fuluigt`va eraquaofy

pjiycjo.

VXA^-6 4 ^ijt tmasa pj`ots fuffass`vaiy by sljjtm furvas, wa cat g furva fgiiah fuluigt`va eraquaofy

jr go jc`va.

G^^I@FGX@JO JE GO JC@UA

Jc`va fgo ba usah tj e`oh tma lah`go je g eraquaofy h`str`but`jo. Xj e`oh tma lah`go, wa ejiijw tmasa staps.

LAXMJH@

VXA^-7 4 Hrgw goyjoa je tma twj typas je eraquaof`as furvas jo tma crgpm pgpar.

VXA^-2 4 Fjlputa )(2

`eOO

goh lgrk tma fjrraspjoh`oc pj`ots jo tma y-gx`s.

VXA^-6 4 Hrgw g i`oa pgrgiiai tj x-gx`s erjl tma pj`ot lgrkah `o stap 2, futt`oc tma fuluigt`va eraquaofy

furva gt g pj`ot ^.

LAXMJH@@

VXA^-7 4 Hrgw iass tmgo typa goh ljra tmgo typa fuluigt`va eraquaofy furvas jo tma crgpm pgpar.

VXA^-2 4 Lgrk tma pj`ot je `otarsaft`oc (^) je tma twj furvas hrgw2o `o stap 7.

VXA^-6 4 Hrgw parpaoh`fuigr ^L erjl ^ jo tma x-gx`s. Xma x-fjjrh`ogta je pj`ot L c`vas tma lah`go .

Ax.7= Xma ejiijw`oc h`str`but jo c`vas tma hg`iy ofjla je 1> wjrkars je g egftjry.

Fjovart tma h`str`but`jo gbjva tj g iass tmgo typa fuluigt`va eraquaofy h`str`but`jo goh hrgw `ts jc`va.

Hg`iy `ofjla (`o Rs.) 7>>-72> 72>-78> 78>-75> 75>-7=> 7=>-2>>

Oj. je wjrkars 72 78 = 5 7>

8/12/2019 14. Statistics

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LGO@VMKQLGR

R A J Q O H G X @J O B P^ -E

LGXMALGX@FV

71

Vji. Erjl tma c`vao tgbia, wa prapgra g iass tmgo typa fuluigt`va eraquaofy h`str`but`jo tgbia, gs c`vao baijw 4

Dj`o tmasa pj`ots by g eraamgoh

furva tj cat go jc`va je iass tmgo typa.

Ax.70 Xma ejiijw`oc tgbia c`vas prjhuft`jo y`aih par maftgra je wmagt je 7>> egrls je g v`iigca.

^rjhuft`jo y`aih

(`o kc/mg) 1>-11 11-5> 5>-51 51-3> 3>-31 31-=>

Oj. je egrls 2 = 72 28 6= 75

Fmgoca tma h`str`but`jo tj ljra tmgo typa h`str`but`jo goh hrgw `ts jc`va.

Vji. Erjl tma c`vao tgbia, wa lgy prapgra ljra tmgo typa fuluigt`va eraquaofy h`str`but`jo tgbia, gs c`vao baijw 4

^rjhuft`jo ljra tmgo (`o kc/mg) 1> 11 5> 51 3> 31

Fuluigt`va eraquaofy 7>> 0= 0> 3= 18 75

Ojw, pijt tma pj`ots (1>, 7>>), (11,0=), (5>,0>), (51,3=), (3>,18) goh (31,75)

Dj`o tmasa pj`ots by g eraamgoh furva tj cat go jc`va je ljra tmgo typa.

@ofjla iass tmgo (`o Rs) 72> 78> 75> 7=> 2>>

Fuluigt`va eraquaofy 72 25 68 8> 1>

8/12/2019 14. Statistics

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LGO@VMKQLGR

R A J Q O H G X @J O B P^ -E

LGXMALGX@FV

75

Ax.2> Xma goougi prje ts agroah by 6> smjps je g smjpp`oc fjlpiax `o g ijfgi`ty c`vas r`sa tj tma ejiijw`oc h`str`but`jo

^rje`t (`o igkms Rs.) Oj. je smjps (eraquaofy)

Ljra tmgo jr aqugi tj 1

Ljra tmgo jr aqugi tj 7>

Ljra tmgo jr aqugi tj 71

Ljra tmgo jr aqugi tj 2>Ljra tmgo jr aqugi tj 21

Ljra tmgo jr aqugi tj 6>

Ljra tmgo jr aqugi tj 61

6>

2=

75

787>

3

6

Hrgw bjtm jc`vas ejr tma hgtg gbjva. Maofa, jbtg`o tma lah`go prje`t.

Vji. Sa mgva g ljra tmgo typa fuluigt`va eraquaofy h`str`but`jo tgbia. Sa lgy gisj prapgra g iass tmgo typa

fuluigt`va eraquaofy h`str`but`jo tgbia erjl tma c`vao hgtg, gs c`vao baijw 4

Ljra tmgo typa Iass tmgo typa

Ojw, pijt tma pj`ots G(1,6>), B(7>,2=), F(71,75), H(2>,78), A(21,7>), E(6>,3) goh C(61,6) ejr tma ljra tmgo typa

fuluigt`va eraquaofy goh tma pj`ots ^(7>,2), W(71,78), R(2>,75), V(21,2>), X(6>,26), Q(61,23) goh U(8>,6>) ejr

tma iass tmao typa fuluigt`va eraquaofy tgbia.

Dj`o tmasa pj`ots by g eraamgoh tj cat jc`vas ejr ljra tmgo typa goh iass tmgo typa.

Xma tjw jc`vas `otarsaft agfm jtmar gt pj`ot (73.1, 71).

Maofa, tma lah`go prje`t `s Rs. 73.1 igkms.

^rje`t ljra tmgo

(Rs. `o igkms)

Oj. je smjps

1 6>

7> 2=

71 75

2> 78

21 7>

6> 3

61 6

^rje`t iass tmgo

(Rs. `o igkms)

Oj. je smjps

7> 2

71 78

2> 77

21 2>

6> 26

61 23

8> 6>

8/12/2019 14. Statistics

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LGO@VMKQLGR

R A J Q O H G X @J O B P^ -E

LGXMALGX@FV

73

Ax.27 Xma ejiijw`oc hgtg c`vas tma oejrlgt`jo jo lgrks je 3> stuhaots `o g par`jh`fgi tast 4

Lgrks Iass tmgo

7>

Iass tmgo

2>

Iass tmgo

6>

Iass tmgo

8>

Iass tmgo

1>

Oj. je stuhaots 6 77 2= 8= 3>

Hrgw g fuluigt`va eraquaofy furva ejr tma gbjva hgtg goh e`oh tma lah`go.

Vji. Sa mgva g iass tmgo fuluigt`va eraquaofy tgbia. Sa lgrk tma uppar figss i`l`ts gijoc tma x-gx`s goh tma

fjrraspjoh`oc fuluigt`va eraquaofy (oj. je stuhaots) gijoc tma y-gx`s. Ojw, pijt tma pj`ots (7>,6), (2>,77),

(6>,2=), (8>,8=) goh (1>,3>). Dj`o tmasa pj`ots by g eraamgoh furva tj cat go jc`va je iass tmgo typa.

Mara, O < 3>

612

Xgka g pj`ot G(>,61) jo tma y-gx`s goh hrgw G^x-gx`s, laat`oc tma furva gt ^.

Hrgw ^L x-gx`s, `otarsaft`oc tma x-gx`s, gt L.

Xmao, JL < 66.

Maofa, tma lah`go lgrks `s 66.

8/12/2019 14. Statistics

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LGO@VMKQLGR

R A J Q O H G X @J O B P^ -E

LGXMALGX@FV

7=

A]ARF@VA 7 (EJR VFMJJI/BJGRH A]GLV)

JBDAFX@UA XP^A WQAVX@JOV

FMJJVAXMAFJRRAFXJOA

7. Sm`fm je tma ejiijw`oc `s g lagsura je faotrgi taohaofy :

(G) Eraquaofy (B) Fuluigt`va eraquaofy

(F) Lago (H) Figss i`l`t

2. Figss lgrk je g figss `s jbtg`oah by us`oc

(G) Figss lgrk (B)2

7[uppar i`l`t ijwar i`l`t\

(F)2

7[uppar i`l`t + ijwar i`l`t\ (H)

2

7[uppar i`l`t + ijwar i`l`t\ 7

6. Xma vgiua je

o

`

`x

7

`s

(G)2

x (B) 2 x (F) o x (H)

o

x

8. Xma lago je tma ejiijw`oc hgtg 72, 22, 62,o2`s

(G)5

)72)(7( oo (B)

5

)72)(7( ooo (F)

5

)72)(7( ooo (H)

5

)72)(7( ooo

1. Xma lago je ejiijw`oc h`str`but`jo s

(G) 7=.1> (B) 7=.1> (F) 7=.71 (H) 7=.215. Xma lago je ejiijw`oc hgtg `s 7=.31 tmao tma vgiua je p `s

(G) 27 (B) 2>.5 (F) 2> (H) 22

3. Xj e`oh lago, wa usa tma ejrluig.

(G)

o

`

`xe7

(B)

o

`

`xeO7

(F)

o

`

`xeO 7

7 (H)

o

`

``

O

xe

7

=. Sm`fm je tma ejiijw`oc fgo ojt ba hatarl`oah crgpm`fgiiy

(G) Lago (B) Lah`go (F) Ljha (H) Vtgohgrh hav`gt`jo0. @e tma lah`go je tma ejiijw`oc hgtg `s 8> tmao tma vgiua je p `s

(G) 3 (B) = (F) 0 (H) 3.5

x` 7> 72 71 21

e 2 6 3 =

x` 7> 71 p 21 6>

e 1 7> 3 = 2

Figss >- 7> 7>-6> 6>-5> 5>-=> =>-0>

Eraquaofy 1 71 6> p 2

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LGO@VMKQLGR

R A J Q O H G X @J O B P^ -E

LGXMALGX@FV

70

7>. Sm`fm je tma ejiijw`oc s trua:

(G) Ljha < 2lah`go Lago (B) Ljha < 6lah`go + 2Lago

(F) Ljha < 6lah`go 2Lago (H) Ojoa je tmasa

77. Ljha `s

(G) Ljst eraquaot vgiua (B) Iagst eraquaot vgiua

(F) L`hhia ljst vgiua (H) Ojoa je tmasa

72. Sm`fm je tma ejiijw`oc s trua

(G) Ljha < 2lah`go + Lago (B) Lah`go < Ljha +2

6[Lago Lah`go\

(F) Lago < Ljha +2

6[Lah`go Ljha\ (H) Lah`go < Ljha +

2

6[Lago +Lah`go\

76. @o tma ejrluig ejr ljha je g crjupah hgtg, ljha < meee

ee

2>7

>7

2 , wmara sylbjis mgva tma`r usugi

lago`oc e>raprasaots 4

(G) Eraquaofy je ljhgi figss

(B) Eraquaofy je lah`go figss

(F) Eraquaofy je tma figss prafah`oc tma ljhgi figss

(H) Eraquaofy je figss suffaah`oc tma ljhgi figss

78. Lah`go je g c`vao eraquaofy h`str`but`jo s ejuoh w`tm tma maip je g (G) Bgr crgpm (B) Jc`va (F) M`stjcrgl (H) Ojoa je tmasa

71. Xma lagsura je faotrgi taohaofy wm`fm s c`vao by tma x-fjjrh`ogta je tma pj`ot je `otarsaft`jo je tma ljra tmgo

jc`va goh iass tmgo jc`va `s

(G) Lago (B) Lah`go (F) Ljha (H) Ojoa je tmasa

Wua. 7 2 6 8 1 5 3 = 0 7>

Gos. F F F G B F F G B F

Wua. 77 72 76 78 71

Gos. G F F B B

JBDAFX@UA A]ARF@VAGOVSAR KAP

8/12/2019 14. Statistics

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LGO@VMKQLGR

R A J Q O H G X @J O B P^ -E

LGXMALGX@FV

2>

A]ARF@VA 2 (EJR VFMJJI/BJGRH A]GLV)

VQBDAFX@UA XP^A WQAVX@JOV

(G) LAGOJEG CRJQ^AHHGXG

7. E`oh tma lago je tma ejiijw`oc hgtg 4

(g)

(b)

2. E`oh tma lago je tma ejiijw`oc h`str`but`jo 4

(g)

(b) (`)

(``)

(```)

6. (g) Xma gr`tmlat`f lago je tma ejiijw`oc eraquaofy h`str`but`jo s 21.21. Hatarl`oa tma vgiua je p 4

(b) Xma gr`tmlat`f lago je tma ejiijw`oc eraquaofy h`str`but`jo s 83. Hatarl`oa tma vgiua je p 4

8. E`oh tma vgiua je e, tma l`ss`oc eraquaofy, `e tma lago je tma ejiijw`oc h`str`but`jo s 53.

1. (g) E`oh tma l`ss`oc eraquaof`as e7gohe2`e tma eraquaofy h`str`but`jo `s 52.= goh tma sul je gii eraquaofy `s 1>

Figss @otarvgi >-5 5-72 72-7= 7=-28 28-6>

Eraquaofy 5 = 7> 0 3

Oulbar je ^igot >-2 2-8 8-5 5-= =-7> 7>-72 72-78

Oulbar je mjusa 7 2 7 1 5 2 6

Figss @otarvgi >-7> 7>-2> 2>-6> 6>-8> 8>-1>

Eraquaofy 6 1 0 1 6

Figss @otarvgi >-7> 7>-2> 2>-6> 6>-8> 8>-1>

Eraquaofy 72 75 5 3 0

Figss @otarvgi 7>>-72> 72>-78> 78>-75> 75>-7=> 7=>-2>>

Eraquaofy 72 78 = 5 7>

Figss @otarvgi >-7>> 7>>-2>> 2>>-6>> 6>>-8>> 8>>-1>>

Eraquaofy 5 0 71 72 =

Figss >-7> 7>-2> 2>-6> 6>-8> 8>-1>

Eraquaofy 3 = p 71 8

Figss @otarvgi >-2> 2>-8> 8>-5> 5>-=> =>-7>>

Eraquaofy = 71 2> p 1

Figss @otarvgi 21-61 61-81 81-11 11-51 51-31 31-=1 =1-0=

Eraquaofy 7> 5 8 e 8 72 25

Figss >-2> 2>-8> 8>-5> 5>-=> =>-7>> 7>>-72> Xjtgi

Eraquaofy 1 e7 7> e2 3 = 1>

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LGO@VMKQLGR

R A J Q O H G X @J O B P^ -E

LGXMALGX@FV

27

(b) E`oh tma l`ss`oc eraquaof`as e7 goh e2`o tma ejiijw`oc hgtg `e tma lago `s25

0755 goh tma sul je tma

jbsarvgt`jo s 12.

(f) Xma lago je ejiijw`oc eraquaofy tgbia `s 16. But tma eraquaofy e7goh e2`o tma figssas 2>-8> goh 5>-=> gr

5. (g) E`oh tma lago je tma ejiijw`oc hgtg, by us`oc tma gssulah lago latmjh.

(b)

3. G figss tagfmar mgs tma ejiijw`oc gbsaotaa rafjrh je 8> stuhaots je g figss ejr tma wmjia tarl. E`oh tma lago

oulbar je hgys g stuhaot wgs gbsaot.

=. (g) E`oh tma gr`tmlat`f lago je tma ejiijw`oc eraquaofy h`str`but`jo by us`oc stap hav`gt`jo latmjh 4

(b) Xma ejiijw`oc tgbia c`vas tma i`targfy rgta (`o parfaotgca) je 61 f`t`as. E`oh tma lago i`targfy rgta.

(f) Xma h`str`but`jo smjw tma oulbar je w`fkats tgkao by bjwiars `o joa hgy fr`fkat lgtfmas. E`oh tma lago

0. (g) Xma ejiijw`oc tgbia c`vas tma h`str`but`jo je axpaoh`turas je h`eearaot egl`i`as jo ahufgt`jo. E`oh tma

lago axpaoh`tura jo ahufgt`jo je g egl`iy.

Figss 78>-71> 71>-75> 75>-73> 73>-7=> 7=>-70> 70>-2>>

Eraquaofy 3 e7 2> e2 3 =

Gca (`o yagrs) >-2> 2>-8> 8>-5> 5>-=> =>-7>> Xjtgi

Oj. je pajpia 71 e7 27 e2 73 7>>

Figss @otarvgi >-7> 7>-2> 2>-6> 6>-8> 8>-1>

Eraquaofy 3 = 72 76 7>

Lgrks >-7>> 7>>-2>> 2>>-6>> 6>>-8>> 8>>-1>> 1>>-5>>

Oj. je stuhaots 2 = 72 2> 1 6

Oj. je hgys >-5 5-7> 7>-78 78-2> 2>-2= 2=-6= 6=-8>

Oj. je stuhaots 77 7> 3 8 8 6 7

Figss 8-= =-72 72-75 75-2> 2>-28 28-2= 2=-62 62-65

Oj. je stuhaots 2 72 71 21 7= 72 76 6

I`targfy rgta (`o %) 81-11 11-51 51-31 31-=1 =1-01

Oj. je f`t`as 6 7> 77 = 6

Oj. je w`fkats 2>-5> 5>-7>> 7>>-71> 71>-21> 21>-61> 61>-81>

Oj. je bjwiars 3 1 75 72 2 6

Axpaoh`tura

(`o Rs.)

7>>>-71>> 71>>-2>>> 2>>>-21>> 21>>-6>>> 6>>>-61>> 61>>-8>>> 8>>>-81>> 81>>-1>>>

Oj. je egl`i`as 28 7> 66 2= 6> 22 75 3

8/12/2019 14. Statistics

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LGO@VMKQLGR

R A J Q O H G X @J O B P^ -E

LGXMALGX@FV

22

(b) (`) Xj e`oh tma fjofaotrgt`jo je VJ2`o tma g`r (`o par l`ii`jo), tma hgtg wgs fjiiaftah ejr 6> ijfgi`t`as `o g

fartg`o f`ty goh `s prasaotah baijw 4

E`oh tma lago fjofaotrgt`jo je VJ2`o tma g`r.

(``) Xma ejiijw`oc tgbia smjws tmgt tma hg`iy axpaoh`tura jo ejjh je 21 mjusa mjihs `o g ijfgi`t`as. E`oh tma

lago hg`iy axpaoh`tura jo ejjh by g su`tgbia latmjh.

7>. (g) E`oh tma lago lgrks erjl tma ejiijw`oc hgtg 4

(b) Fjlputa tma lago ejr tma ejiijw`oc hgtg 4

77. (g) E`oh tma gvargca lgrks je stuhaot erjl tma ejiijw`oc hgtg 4

Fjofaotrgt`jo je

VJ2(`o ppl.)

>.>>->.>8 >.>8->.>= >.>=->.72 >.72->.75 >.75->.>2> >.2>->.28

Eraquaofy 8 0 0 2 8 2

Hg`iy axpaoh`tura

(`o Rs.)

7>>-71> 71>-2>> 2>>-21> 21>-6>> 6>>-61>

Oj. je mjusa mjihs 8 1 72 2 2

Lgrks Baijw

7>

Baijw

2>

Baijw

6>

Baijw

8>

Baijw

1>

Baijw

5>

Oj. je stuhaots 8 7> 7= 2= 8> 3>

Lgrks Iass tmgo

7>

Iass tmgo

6>

Iass tmgo

1>

Iass tmgo

3>

Iass tmgo

0>

Iass tmgo

77>

Iass tmgo

76>

Iass tmgo

71>

Oj. je stuhaots > 7> 21 86 51 =3 05 7>>

Lgrks Oj. je Vtuhaots

Gbjva > =>

Gbjva 7> 33

Gbjva 2> 32

Gbjva 6> 51

Gbjva 8> 11

Gbjva 1> 86

Gbjva 5> 26

Gbjva 3> 75

Gbjva => 7>

Gbjva 0> =

Gbjva 7>> >

8/12/2019 14. Statistics

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R A J Q O H G X @J O B P^ -E

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26

(b) E`oh tma lago wgca je tma ejiijw`oc hgtg 4

72. (g) @o g ratg`i lgrkat, eru`t vaohjrs saii`oc lgocjas kapt `o pgfk`oc bjxas. Xmasa bjxas fjotg`oah vgry`oc

oulbar je lgocjas. Xma ejiijw`oc wgs tma h`str`but`jo je lgocjas gffjrh`oc tj tma oulbar je bjxas.

E`oh tma lago oulbar je lgocjas kapt `o g pjfkat bjx.

(b) Xma ejiijw`oc hgtg smjws tmgt tma gca h`str`but`jo je pgt`aots je lgigr`g `o g v`iigca hur`oc g pgrt`fuigr

ljotm. E`oh tma gvargca gca je tma pgt`aots.

(B) LAH@GOJEG CRJQ^AHHGXG

7. E`oh tma lah`go ejr tma ejiijw`oc eraquaofy h`str`but`jo 4

(g)

(b) (`)

(``)

(f) 7>> suroglas wara rgohjliy p`fkat up erjl g ijfgi taiapmjoa h`raftiy goh tma eraquaofy h`str`but`jo je

tma oulbar je iattars `o tma Aoci`sm gipmgbats `o tma suroglas wgs jbtg`oah gs ejiijws 4

E`oh tma lah`go oulbar je iattars `o tma suroglas. E`oh tma lago oulbar je iattars `o tma suroglas.

2. (g) E`oh tma lah`go erjl tma ejiijw`oc hgtg 4

Sgcas (`o Rs.) Oj. je Sjrkars

> goh gbjva 72>

2> goh gbjva 7>=

8> goh gbjva 0>5> goh gbjva 31

=> goh gbjva 1>

7>> goh gbjva 28

72> goh gbjva 0

78> goh gbjva >

Oj. je lgocjas 1>-12 16-11 15-1= 10-57 52-58

Oj. je bjxas 71 77> 761 771 21

Gca (`o yagrs) 1-78 71-28 21-68 61-88 81-18 11-58

Oj. je fgsas 5 77 27 26 78 1

Figss @otarvgi >-7> 7>-2> 2>-6> 6>-8> 8>-1> 1>-5>

Eraquaofy 5 0 78 2 70 7>

Figss @otarvgi 21-61 61-81 81-11 11-51 51-31

Eraquaofy 2> 21 1 3 8

Figss @otarvgi >-= =-75 75-28 28-62 62-8> 8>-8=

Eraquaofy = 7> 75 28 71 3

Oj. je iattars 7-8 8-3 3-7> 7>-76 76-75 75-70

Oj. je Vuroglas 5 6> 8> 75 8 8

Figss crjups 77>-72> 72>-76> 76>-78> 78>-71> 71>-75> 75>-73> 73>-7=> 7=>-70> 70>-2>>

Eraquaofy 5 21 8= 32 775 5> 6= 22 6

8/12/2019 14. Statistics

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(b) (`) Xma ejiijw`oc h`str`but`jo c`vas tma wa`cmts je 6> stuhaots je g figss. E`oh tma lah`go wa`cmt je

tma stuhaot

(``) E`oh tma lah`go je tma ejiijw`oc eraquaofy h`str`but`jo 4

(f) Xma ejiijw`oc tgbia c`vas tma h`str`but`jo je tma i`ea t`la je 8>> oajo iglps 4

E`oh tma lah`go i`ea t`la je g iglp.

6. (g) G i`ea `osurgofa gcaot ejuoh tma ejiijw`oc hgtg ejr h`str`but`jo je gcas je 7>> pji`fy mjihars. Fgifuigta

tma lah`go gca, `e pji`f`as gra joiy c`vao tj parsjos mgv`oc gca 7= yagrs jowgrhs but iass tmgo 5> yagrs.

(b) G survay racgrh`oc tma ma`cmts (`o fl) je 17 c`ris je figss ] je g sfmjji wgs fjohuftah goh tma hgtg

jbtg`oah ejiijws 4

E`oh tma lah`go ma`cmt.

8. (g) Xma ejiijw`oc tgbia c`vas tma lgrks jbtg`oah by 1> stuhaots o g figss tast 4

E`oh tma lah`go.

(b) Xma ejiijw`oc tgbia c`vas tma pjpuigt`jo je lgias `o h`eearaot gca crjups 4

E`oh tma`r lah`go gca.

Sa`cmt (`o kc) 8>-81 81-1> 1>-11 11-5> 5>-51 51-3> 3>-31

Oj. je stuhaots 2 6 = 5 5 6 2

Lgrks >-7>> 7>>-2>> 2>>-6>> 6>>-8>> 8>>-1>> 1>>-5>> 5>>-3>> 3>>-=>> =>>-0>> 0>>-7>>>

Eraquaofy 2 1 0 72 73 2> 71 0 3 8

I`ea X`la

(`o mjurs)

71>>-2>>> 2>>>-21>> 21>>-6>>> 6>>>-61>> 61>>-8>>> 8>>>-81>> 81>>-1>>>

Oj. je iglps 78 15 5> =5 38 52 8=

Gca `o yagrs Baijw

2>

Baijw

21

Baijw

6>

Baijw

61

Baijw

8>

Baijw

81

Baijw

1>

Baijw

11

Baijw

5>

Oj. je pji`fy

mjihars

2 5 28 81 3= =0 02 0= 7>>

Ma`cmts (`o fl) Iass tmgo

78>

Iass tmgo

781

Iass tmgo

71>

Iass tmgo

711

Iass tmgo

75>

Iass tmgo

751

Oj. je c`ris 8 77 20 8> 85 17

Lgrks 77-71 75-2> 27-21 25-6> 67-61 65-8> 87-81 85-1>

Oj. je Vtuhaots 2 6 5 3 78 72 8 2

Gca crjup

(`o yagrs)

1-78 71-28 21-68 61-88 81-18 11-58 51-38

Oj. je lgias 883 6>3 230 22> 713 07 60

8/12/2019 14. Statistics

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1. (g) Xma ejiijw`oc tgbia c`vas tma h`str`but`jo je @W je 7>> stuhaots. E`oh tma lah`go @W.

(b) Xma iaoctm je 3> iagvas je g pigot gra lagsurah fjrraft tj tma oagrast l`ii`latar goh tma hgtg jbtg`oah `s

raprasaotah `o tma ejiijw`oc tgbia 4

E`oh tma lah`go iaoctm je tma iagvas.

5. Fgifuigta tma l`ss`oc eraquaofy e erjl tma ejiijw`oc h`str`but`jo, t ba`oc c`vao tmgt tma lah`go je tma h`str`but`jo

`s 28.

3. (g) @e tma lah`go je tma ejiijw`oc eraquaofy h`str`but`jo s 2=.1, e`oh tma l`ss`oc eraquaof`as.

(b) @e tma lah`go je tma ejiijw`oc eraquaofy h`str`but`jo s 62.1, e`oh tma vgiuas je e7goh e2.

(f) (`) Go `ofjlpiata h`str`but`jo s c`vao baijw 4

@e lah`go vgiua `s 85 goh tma tjtgi oulbar je `tals `s 26>.

)( E`oh tma l`ss`oc eraquaof`as e7goh e2.

)( E`oh tma gr`tmlat`f lago (GL) je tma fjlpiatah h`str`but`jo.(``) Xma lah`go je tma ejiijw`oc hgtg `s 2>.31 E`oh tma l`ss`oc eraquaof`as x goh y, `e tma tjtgi

eraquaofy `s 7>>

@W 31-=8 =1-08 01-7>8 7>1-778 771-728 721-768 761-788

Eraquaofy = 77 25 67 7= 8 2

Ugr`gbia 7>-2> 2>-6> 6>-8> 8>-1> 1>-5> 5>-3> 3>-=>

Eraquaofy 72 6> e7 51 e2 21 7=

Figss `otarvgi >-1 1-7> 7>-71 71-2> 2>-21 21-6> 6>-61 61-8>

Eraquaofy 3 7> x 76 y 7> 78 0

Figss >-7> 7>-2> 2>-6> 6>-8> 8>-1>

Eraquaofy 1 21 e 7= 3

Figss `otarvgi >-7> 7>-2> 2>-6> 6>-8> 8>-1> 1>-5> Xjtgi

Eraquaofy 1 e7 2> 71 e2 1 5>

Figss `otarvgi >-7> 7>-2> 2>-6> 6>-8> 8>-1> 1>-5> 5>-3> Xjtgi

Eraquaofy e7 1 0 72 e2 6 2 8>

Iaoctm

(`o ll)

77=-725 723-761 765-788 781-716 718-752 756-737 732-7=>

Oj. je iagva 7> = 76 22 3 5 8

8/12/2019 14. Statistics

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(F) LAH@GOJEG CRJQ^AHHGXG

7. (g) Fgifuigta tma ljha ejr tma ejiijw`oc eraquaofy h`str`but`jo.

(b) G stuhaot ojtah tma oulbar je fgrs pgss`oc tmrjucm spjt jo g rjgh ejr 7>> par`jhs agfm je 6 l`outas goh

sullgr`zah `t `o tma tgbia c`vao baijw. E`oh tma ljha je tma hgtg .

2. (g) Xma c`vao h`str`but`jo smjws tma oulbar je ruos sfjrah by sjla tjp bgtslao je tma wjrih `o joa hgy

`otarogt`jogi fr`fkat lgtfmas 4Ruos

Vfjrah

6>>>-8>>> 8>>>-1>>> 1>>>-5>>> 5>>>-3>>> 3>>>-=>>> =>>>-0>>> 0>>>-7>>>> 7>>>>-77>>>

Oj. jebgtslgo

8 7= 0 3 5 6 7 7

E`oh tma ljha je tma hgtg.

(b) (`) Xma ejiijw`oc tgbias c`vas tma gcas je tma pgt`aots ghl`ttah `o g mjsp`tgi hur`oc g yagr.

E`oh tma ljha goh tma lago je tma hgtg

(``) Xma ejiijw`oc hgtg c`vas tma h`str`but`jo je tjtgi ljotmiy mjusa mjih axpaoh`tura je 2>> egl`i`as

je g v`iigca. E`oh tma ljhgi ljotmiy axpaoh`tura je tma egl`i`as. Gisj, e`oh tma lago ljotmiy

axpaoh`tura

(f) (`) Xma ejiijw`oc h`str`but`jo c`vas tma stgta-w`sa tagfmar stuhaot rgt`j `o m`cmar safjohgry sfmjjis j

@oh`g. E`oh tma ljha goh lago je tm`s hgtg. @otarprat twj lagsuras.

(``) Xma ejiijw`oc tgbia smjws tma lgrks jbtg`oah by 7>> stuhaots je Figss ] `o sfmjji hur`oc g

pgrt`fuigr gfghal`f sass`jo. E`oh tma ljha je tm`s h`str`but`jo

Figss >-7> 7>-2> 2>-6> 6>-8> 8>-1> 1>-5> 5>-3> 3>-=>

Eraquaofy 1 = 3 72 2= 2> 7> 7>

Oj. je fgrs >-7> 7>-2> 2>-6> 6>-8> 8>-1> 1>-5> 5>-3> 3>-=>

Eraquaofy 3 78 76 72 2> 77 71 =

Gca (`o yagrs) 1-71 71-21 21-61 61-81 81-11 11-51

Oj. je pgt`aots 5 77 27 26 78 1

Axpaoh`tura

(`o Rs.)

7>>>-71>> 71>>-2>>> 2>>>-21>> 21>>-6>>> 6>>>-61>> 61>>-8>>> 8>>>-81>> 81>>-1>>>

Oj. jeegl`i`as

28 8> 66 2= 6> 22 75 3

Oj. je stuhaots

par tagfmar

71-2> 2>-21 21-6> 6>-61 61-8> 8>-81 81-1> 1>-11

Oj. jestgta/Q.X.

6 = 0 7> 6 > > 2

Lgrks Iass tmgo

7>

Iass tmgo

2>

Iass tmgo

6>

Iass tmgo

8>

Iass tmgo

1>

Iass tmgo

5>

Iass tmgo

3>

Iass tmgo

=>

Oj. je stuhaots 3 27 68 85 55 33 02 7>>

8/12/2019 14. Statistics

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6. (g) Fjlputa tma ljha je tma ejiijw`oc hgtg 4

(b) Fjlputa tma ljha je tma ejiijw`oc hgtg 4

8. Fgifuigta tma ljha je tma ejiijw`oc hgtg 4

1. Xma ljha je tma ejiijw`oc hgtg `s =1.3 E`oh tma l`ss`oc eraquaofy `o `t.

(F) CRG^M@FGRA^RAVAOXGX@JOJEFQLQIGX@UAERAWQAOFPH@VXR@BQX@JO7. Xma ejiijw`oc h`str`but`jo c`vas tma lgrk jbtg`oah by 7>2 stuhaots je figss ].

Fjovart tma gbjva h`str`but`jo tj g iass tmgo typa fuluigt`va eraquaofy h`str`but`jo goh hrgw `ts jc`va.

2. Xma ejiijw`oc tgbia c`vas tma h`str`but`jo je @W je 5> pup`is je figss ] `o g sfmjji.

Fjovart tma gbjva h`str`but`jo tj g ljra tmgo typa fuluigt`va eraquaofy h`str`but`jo goh hrgw `ts jc`va.6. (g) Xma ejiijw`oc tgbia c`vas tma ma`cmt je traas 4

(b) Smgt `s tma vgiua je tma lah`go je tma hgtg us oc tma crgpm `o tma c`vao e`cura, je iass tmgo jc`va goh ljr

tmgo jc`va:

Hrgw bjtm jc`vas ejr tma hgtg gbjva. Maofa, jbtg`o tma lah`go je tma hgtg.

Figss @otarvgi 7-1 5-7> 77-71 75-2> 27-21 25-6> 67-61 65-8> 87-81 85-1>

Eraquaofy 6 = 76 7= 2= 2> 76 = 5 8

Vfjra =>-0> 0>-7>> 7>>-77> 77>-72> 72>-76> 76>-78> 78>-71>

Oj. je pup`i 7= 23 8= 60 72 5 75

Sgcas (@o Rs.) 17-15 13-52 56-5= 50-38 31-=> =7-=5 =3-02

Oj. je wjrkars 72 28 8> 6> 7= = 2>

V`za 81-11 11-51 51>-31 31-=1 =1-01 01-7>1 7>1-771

Eraquaofy 3 72 73 e 62 5 7>

Lgrks >-7> 7>-2> 2>-6> 6>-8> 8>-1> 1>-5>

Oj. je

stuhaots

0 7> 21 1> 1 6

@W 5>-3> 3>-=> =>-0> 0>-7>> 7>>1-77> 77>-72> 72>-76>

Oj. je pup`is 2 6 1 75 78 76 3

Ma`cmt Iass tmgo

78>

Iass tmgo

781

Iass tmgo

71>

Iass tmgo

711

Iass tmgo

75>

Iass tmgo

751

Oj. je traas 8 77 20 8> 85 1>

8/12/2019 14. Statistics

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2=

8. (g) Ejiijw`oc s tma gca h`str`but`jo je g crjup je stuhaots. Hrgw g fuluigt`va eraquaofy furva ejr tma hgtg

goh e`oh tma lah`go.

(b) G stuhaot hrgws g fuluigt`va eraquaofy furva ejr tma lgrks jbtg`oah by 8> stuhaots je g figss gs smjwo

baijw. E`oh tma lah`go lgrks jbtg`oah by tma stuhaots je tma figss.

1. Xma tgbia c`vao baijw smjws tma eraquaofy h`str`but`jo je tma sfjras jbtg`oah by 2>> fgoh`hgtas o g LFG

aotrgofa axgl`ogt`jo.

Vfjra 2>>-21> 21>-6>> 6>>-61> 61>-8>> 8>>-81> 81>-1>> 1>>-11> 11>-5>>

Oj. je

stuhaots

6> 71 81 2> 21 8> 7> 71

Hrgw fuluigt`va furva je ljra tmgo typa goh maofa e`oh lah`go.

Gca `o yagrs Oj. je stuhaots

Iass tmgo 1 65

Iass tmgo 5 3=

Iass tmgo 3 765Iass tmgo = 70>

Iass tmgo 0 21=

Iass tmgo 7> 682

Iass tmgo 77 86=

Iass tmgo 72 12>

Iass tmgo 76 1=5

Iass tmgo 78 568

Iass tmgo 71 5=8

Iass tmgo 75 3>>

8/12/2019 14. Statistics

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LGO@VMKQLGR

R A J Q O H G X @J O B P^ -E

LGXMALGX@FV

6>

A]ARF@VA 6 (EJR VFMJJI/BJGRH A]GLV)

^RAU@JQV PAGRV BJGRH WQAVX@JOV

UARPVMJRXGOVSAR XP^AWQAVX@JOV

7. Sm`fm lagsura je faotrgi taohaofy `s c`vao by tma x-fjjrh`ogta je tma pj`ot je `otarsaft`jo je tma ljra tmgo

jc`va goh iass tmgo jc`va: Haim`-2>>=

2. E`oh tma lah`go figss je tma ejiijw`oc hgtg 4 Gi-2>>=

6. E`oh tma figss lgrks je figssas 7>-21 goh 61-11 4 Ejra`oc-2>>=

8. Sr`ta tma lah`go figss je tma ejiijw`oc h`str`but`jo 4 Haim`-2>>0

1. Smgt `s tma ijwar i`l`t je tma ljhgi figss je tma ejiijw`oc eraquaofy h`str`but`jo: Ejra`oc-2>>0

VMJRXGOVSARXP^AWQAVX@JOV

7. Xma lago je tma ejiijw`oc eraquaofy h`str`but`jo `s 13.5 goh tma sul je jbsarvgt`jos `s 1>. E`oh tma l`ss`oc

eraquaof`as e7goh e24 Gi-2>>8

2. Xma ejiijw`oc tgbia c`vas tma h`str`but`jo je axpaoh`tura je h`eearaot egl`i`as jo ahufgt`jo. E`oh tma lagoaxpaoh`tura jo ahufgt`jo je g egl`iy 4 Haim`-2>>8F

Axpaoh`tura (`o Rs.) Oulbar je egl`i`as

7>>>-71>> 28

71>>-2>>> 8>

2>>>-21>> 66

21>>-6>>> 2=

6>>>-61>> 6>

61>>-8>>> 22

8>>>-81>> 75

81>>-1>>> 3

6. E`oh tma lago je tma ejiijw`oc h`str`but`jo 4 Haim`-2>>1

Lgrks Jbtg`oah >-7> 7>-2> 2>-6> 6>-8> 8>-1> 1>-5>

Eraquaofy = 7> 72 22 6> 7=

Figssas >-7> 7>-2> 2>-6> 6>-8> 8>-1> 1>-5> 5>-3>

Eraquaofy 8 8 = 7> 72 = 8

Gca (`o yagrs) >-7> 7>-2> 2>-6> 6>-8> 8>-1> 1>-5>

Oulbar je pgt`aots 75 76 5 77 23 7=

Figss >-2> 2>-8> 8>-5> 5>-=> =>-7>> 7>>-72>

Eraquaofy 3 e7 72 e2 = 1

Figss 8-= =-72 72-75 75-2> 2>-28 28-2= 2=-62 62-65

Oulbar je stuhaots 2 72 71 21 7= 72 76 6

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67

8. @e tma lago je tma ejiijw`oc hgtg `s 7=.31 e`oh tma vgiua je p 4 Gi-2>>1

1. Xma Gr`tmlat`f Lago je tma ejiijw`oc eraquaofy h`str`but`jo s 1>. E`oh tma vgiua je p 4 Haim`-2>>5

5. @e tma lago je tma ejiijw`oc s 1>, e`oh tma vgiua je e74 Haim`-2>>5

3. Xma lago je tma ejiijw`oc eraquaofy h`str`but`jo s 52.=. E`oh tma l`ss`oc eraquaofy x. Haim`-2>>3

IJOCGOVSARXP^AWQAVX@JOV

7. G survary racgrh`oc tma ma`cmts (`o fl) je 1> c`ris je figss x je g sfmjji wgs fjohuftah goh tma ejiijw`oc hgtg

wgs jbtg`oah 4 Haim`-2>>=

E`oh tma lago, lah`go goh ljha je tma gbjva hgtg.

2. E`oh tma lago, ljha goh lah`go je tma ejiijw`oc hgtg. Gi-2>>=

6. E`oh tma lago, lah`go goh ljha je tma ejiijw`oc hgtg. Ejra`co-2>>=

Figss Eraquaofy

>-1> 2

1>-7>> 6

7>>-71> 1

71>-2>> 5

2>>-21> 1

21>-6>> 6

6>>-61> 7

8. Xma ejiijw`oc tgbia c`vas tma hg`iy `ofjla je 1> wjrkars je g egftjry 4 Haim`-2>>0

x` 7> 71 p 21 6>

e 1 7> 3 = 2

Figss >-2> 2>-8> 8>-5> 5>-=> =>-7>>Eraquaofy 73 p 62 28 70

Figss >-2> 2>-8> 8>-5> 5>-=> =>-7>>

Eraquaofy 73 2= 62 e7 70

Figss >-2> 2>-8> 8>-5> 5>-=> =>-7>> 7>>-72>

Eraquaofy 1 = x 72 3 =

Ma`cmt `o fl 72>-76> 76>-78> 78>-71> 71>-75> 75>-73> Xjtgi

Oulbar je c`ris 2 = 72 2> = 1>

Figss >-7> 7>-2> 2>-6> 6>-8> 8>-1> 1>-5> 5>-3>

Eraquaofy 1 7> 7= 6> 2> 72 1

Hg`iy ofjla

(`o Rs.)

7>>-72> 72>-78> 78>-75> 75>-7=> 7=>-2>>

Oulbar je wjrkars 72 78 = 5 7>

8/12/2019 14. Statistics

32/32

LGO@VMKQLGR

R A J Q O H G X @J O B P^ -E

LGXMALGX@FV

62

VXGX@VX@FV A]ARF@VA (])-FBVAGOVSAR KAP

E`oh tma lago, ljha goh lah`go je tma gbjva hgtg.

1. Hur`oc tma lah`fgi fmafk-up je 61 stuhaots je g figss tma`r wa`cmts wara rafjrhah gs ejiijws 4 Gi-2>>0

Sa`cmt (`o kc) Oulbar je stuhaots

6=-8> 68>-82 2

82-88 8

88-85 1

85-8= 78

8=-1> 8

1>-12 6

Hrgw g iass tmgo typa goh g ljra tmgo typa jc`va erjl tma c`vao hgtg. Maofa jbtg`o tma lah`go wa`cmt erjl tma

crgpm.

5. E`oh tma ljha, lah`go goh lago ejr tma ejiijw`oc hgtg 4 Ejra`co-2>>0

Lgrks jbtg`oah Oulbar je stuhaots

21-61 3

61-81 67

81-1> 66

1>-11 73

11-51 77

51-31 7

UARPVMJRX GOVSAR XP^AWQAVX@JO

7. Lah`go 2.6>-8> 6. 73.1 goh 81 8. 6>-8> 1. 8>

VMJRX GOVSAR XP^AWQAVX@JO

7. e7 < =, e2< 7> 2.Rs. 2552.1 6. 70.02 8. p < 2> 1.p < 2= 5.e7< 28 3. 7>

IJOC GOVSAR XP^AWQAVX@JO

7. lago < 71>.21 ; Lah`go < 717.1 ; Ljha < 718. 2.lago < 61.35 ; Lah`go < 61.55 ; Ljha < 61.88

6. lago < 10.0 ; Lah`go < 57.5 ; Ljha < 51. 8.lago < 781.2> ; Lah`go < 76=.13 ; Ljha < 721

1. 82.2 kc 5.lago < 80.3 ; Lah`go < 8=.1 ; Ljha < 85.7