6th kept . session 2022 Tuesday 1 bachir Data - Data ✓ Data eiondary that primary collected data from field of enquiry has already been funds cleaning data ) ninntinihed : tinutiny of then it en ) hort is . bite stored . . : volution Data Enumeration complete 1) 21 sampling a) Haken : : pop representation no - Interview whole from verification , method , ornestionnaire methods 11 polluted myself : Method → → pop → true . ) casual gien questions risk verification long . time of not getting MMM g) " Direct if a observation locality Representation 4 tent npeuifir newspapers ' / poor : form Mtm rich is by → → ↓ get paragraphs lost in paragraphs yourself Tabular 2) 1 table stub lfyrorvl prowl Form ☒: caption title MITT : 1 6 bonne " 9 / Footnote " 45 random numbers } } Body / hraph Diagrammatic 31 a) line Table Value of during Plots Diagram 1 enports 1995 → in India 2005 in buses £ value Year 11749 1995 10895 1996 12452 19h7 : 53688 2005 Source : b 0 g 0 I 1995 1 1996 I . 1997 . . . I 2005 2 table hnowth of year investment No . in of 5 21 1998 2004 2007 2010 company units 1995 v01 a 47 investment total 29 8 1 948 4 3897 122 6137 8 179 18150 pram unit 2 line ÷ Diagrams b) Bar Diagram % & * 1445 1996 root years → Rile lontwmption Hates Delhi TN in Last consumption 5823 9220 WB 9532 MH 8723 5 years : a) Multiple Rural Diagram ronswmplion Urban Bar and according Items to of food 1989 Nss Data in Per person hlnswmption mural - . 1990 ( ng ) Urban Ribe 6.93 5.95 wheat f. 70 g. 84 % wheat rive ✗Wynn,, www. ' rural urban 7th peptunklh a pie henion Guitar 2 that oiualitative in nature Mango orange plum pineapple melon Total . 45 30-1 30 20.1 19 go 30 150 to -1 20.1 20.1 . . . ' . . d) than eanaeto, gr e at e r www.ive/-reqnenYbeYies-t-neqnenY-/-;qymmnlIjf Tally " Marks ↳ ears 3 1111-1 6 " 111 3 3 4 5 6 7 17 46 11 31673 15 y 111 8 2 11 5 17 3 20 41 than to equal oh ) Sulkin i b e I I I 2 ' 3 l I 4 b- Mean suppose Mean where the dataset of the is n observations note : it the in dataset number { Him is . . an . at of } nie . . . an = . Ñ n = Mᵗ%t;-aⁿ_ . [ ai [ it ( ai - a- 1=0 i :| h [ Hg : Ini E - ñ ) = ( n , - ) ñ ' th - ñ ÷ ≈ [ i :| no - nñ = ni - nai = 0 / + . . . ( an - ñ ) hwpplihe , yaku Frequency fi Ni f- Ni : i. " 2 tu n k a- : →=¥:÷ Mfi t%f2 ' . . . Aptn { ( ④ f11th ai a- - Ifi = 0 I & ( ai : a) fi - i. =L Hi - a- It ≤ e. , 1 N = , f , . the . t - a- / ta Nitz t.nu/-µ k ñ E 1=1 ti - ñ - & in Ñ ( fit ti = , . . . ) fa & Lai ñlti - { = 1<=1 (niti - ñti / i :L k Éaifi = K = ñ k Eti - i :| ñ Eti 1=1 ' = 0 i :| - Eñti 1=1 in suppose that smh i= then 44 - . fy : . verify y , n : that yn g, , } are final aebai . ad if b = are at fi constants bñ Median have I suppose { M Nii defined me as = - ' . : { Rn the dataset } then median ↑:'-) :( " I :/ if ' if u • n is odd is ) 1¥) is even percentile the it pµ of { %, %, %, " ' : the to data that is less value look Hit - atleast that such value the of percentile / than too or xp . / . equal atleast and of data is more } than Meps step step the equal oh to value that . : 1 : Arrange order 2 : data the increasing in . calculate number of i :/Foo / ^ observations , . where n is step } : If percentile If the this pth is i the is is i neat integer not integer . integer , integer an the is then pin kid average of which denotes percentile an , net , take greater position of than i. find eat data the following : 3850 3755 4710 7990 3910 = percentile of 85ᵗʰ the 8,1W ✗ 11 = 3950 10.2 3880 3890 9050 zqzp 4325 4130 85ᵗʰ pantile is : . 9130 quartile 1 A, : lhuartill 2 Duarte'll } : : A2 A} : : : 25th percentile goth percentile 75ᵗʰ percentile ,i% , , , #tÉ I Mode Most [ : element occurring ii. 43,9 ) Mode : / " 1443,4 ] : ' [ ' [ 121314,5 ' i' in , } , ] } ] : : = Mode . I Mode Mode 1,2 = = = doesn't enist doesn't . emit . time / seconds/ Frequency class class upper boundary slow Upper von!wnw%9 "go 69.5 - -5 g- q Limit to - to - 80 - 90 - 100 110 - - limit 8 69 10 79 lb 89 14 99 109 119 g- g. g- - g- g. _ ; : . ! to g- 3 109-5-119.5 µppeÑ a • . " p qq.li 59.5 qq.jp g. 5 895 vii. t.A.tn ñ : & Niti , - E j :I ti class Mark Frequency lumnlative 8 8 10 18 59.9 frequency 69.5 79 16 5 - 34 p8 58 ^ " 119 - 5 3 66 a. ' umulati frequency " ; / I 99.559.5 1 1 795 11 99.5 I > atba ' y . y I 1 Ml A b= Yi - Yi F-HI 1 Nz - - at = , Yi : at ba , bae , Median 1 stop step me = 2 : Identify : Denote : Median dataset see = lower the of ni . of : the class boundary median dak Iast boundary upper median host the of class median the ne cumulative : the of nu poor . . frequency dad cumulative : of the fast frequency median me % . - modal Uavs : manimwm the Mo ";g . : Mode of corresponding class The frequency the ten at - . grouped data . to Then , Mo = It . to f. 1- , t.mg : : , : %;÷ At . . modal of . freq of Freq . of previous rent last class class . bnihih Definition symmetric 63 : bi Distributions : by bi unimodal 65 kill N, U} tls ← A dataset th → is said ← rh to Nz : Ng 2h - } . - h 93 : Myth = Us : Ni th → be symmetric around point a as same is ( h • h > for ' 0 frequency of if ath for frequency of a' a h - any ) symmetric a 1 Mean all are = distribution Median equal vymmetniiity to . . Mode = the ( point unimodal ) of mean ÷Ekiti = ¥7 b : bi ' g a- , , = i Ni Ni a 13 Up ng mean : ni h A A th Ng = - a M + th "!% , it Dispersion Martin in A i/ : in mark fb 61 " 59 ii, :* mean n bo I 59 ri g- % , 5 n µ lal Deviation I ' n £ ( ni i. in I - ) il = / di value = O - A of / a . ai deviation A at A absolute the is E ' - Mean gy %f where B so hit it Range na : is MP , dataset the proof . ith ordered t.E.it -4 1 : let n is n :b ' = even i. : A in observation : " base when minimum is Median of an dataset -µµµ É . ! / at % - i É/ , ' % I'm - - / A At 1%-4.1%-4 = I' ' A /% / %) - - A / At • • : / air, In , - ,, - in A / . . - A / A / is is dataset the median of min min . . . if if n %, A ≤ . A ≤ ≤ ≤ a %, Variance É/ ai - - - ñ al . I ,É / [ a) Hifi Gi ' : Ini / & . / ( :& In ai - , , - ai = 2 - - , - ñl ' - fi A) - ' raki Hi -41 - É É 1%-4 " , , • { ( ni ti - ñ ) - ' e n ai (ñ É.in/ni-Hfi- A) . - A) ' 2 t ( A) ñ - i =\ É ki i :L - iii. ti al n " ' - !q ki - oil ' 1h row hep dataset a- : { : seniors , Me 7.33 Ki £ ii. I ¥ , / ai 9,20} 1,3 4,7 , - - ñ / Me / g. g- : = = 28.66 28 dataset new s É /ai - { : ñ / = i" 1 % / ai i. I - Mel = 1,314,7 , 9,10 } { only both the the are the mean for even terms same . . as between lice midterms no . of i. In Ki a- I % & [ • ! Éai É , = : , In É , ' ai eñ mini - i , añ - in n = - ' ' - late , : a- .tn ] E. it . ' 2 I Éi , ai - ri ' Hiiiii ✗ N N , I N Frequency fi , N2 62 : : du tu • , < ' Mi → Ni , Ni ' ' ' Nt - bi terms Ny inn - - _ An _ fn terms .fi ,;É ÷ prem 2 - / " ti ↳ a- = Eti . i. / k in ÷ & . ti E i. , 1- { i" i :| ' ri - aifi " iñtñ / fi , = ¥ % / . " - Yi - ai Énitieñ i :\ ' .É,ti ] " µg÷f • ÷ { " " ti a ' - Lai • a- , . = 1- E. ti 2 h . qq.fi El - a- Deviation standard variation boyfriend of 1) let Yi y , , = : : In § , ( ai , 8a- Properties variance $ : ya at . . : . a ,b yn bni : constants are for that such all i : hi . . n - ri / 2 Variant of y JJ : b " " flu { ignite { ily is variance the of variant ↑ of . gig - n - , . . an } iy.IE?lyi-y-FT--!.I. yi:!nI.,(aebai proof : : E In : ( b' * in bni - ar É ( , bñ - ni - bñ ) at :( ) a- 1 " . his} ) If a) In b) M ' y :O % Ki , - a- : then , 1%0 ai ri = - constant it = 0 : ti-i.in ni :ñ , have I & 2 groups of observations hi My MI Mi ^ ; NIN !! ✗ , 2h , with size eat 4=10 Mj is j 1,2 : d the . hi - - ni 12 : - jih observation i 1,1 = of I . of A) Variance All * 1 11 , a- = I Mean %U _ ' ' ✗ , of the mean , the is variance 21 - - Hm ghonp ith the of dataset combined the 43 the is ii ith the of the ith , group group : , combined dataset . . where .fr - % - - - , , / N i ÷n Ñ t " • - "" " hi µ %n ) - that man ni , " Ñ a) . Mѵ,Yy imma combination , , Hy → ' ( ' ≤ ai a- ≤ Mñµ;n! ≤ ni n' = ÉÉ ÷ in j , ¥ " . .L I % . " - t :\ iii. 1%-4 . _ ( . Kiki - am , ii. ( nij - - - ) 1am -4 ' . ñ ' . , ñ / 2 ] :( -4 Éifriil %, ' it nine ÉÉ in j= , ( ✗ - ij F) 2