-------------------------- B MN NGUYN L THNG K NHM 5 HIU O TUNG NHINH VIN N TI H HO N GIO VIN HNG DN: L TH THIN HNG Nm hc: 2011 - 2012 B GIO DC V O TO TRNG I HC HOA SEN KHOA KINH T THNG MI -------------------------- B MN NGUYN L THNG K NHM 5 HIU O TUNG NHINH VIN N TI H HO N GIO VIN HNG DN: L TH THIN HNG Phn dnh ring cho Khoa: Ngy np n: ___/___/___ Ngi np n: (k v ghi r h tn) NM HC 2011 2012 B GIO DC V O TO TRNG I HC HOA SEN KHOA KINH T THNG MI CHIU CAO TRUNG BNH CA MN HC NGUYN L THNG K SINH VIN N TI H HOA SENGVHD: L TH THIN HNG Trang i TRCH YU Tt c cc bc cha m u mong mun con mnh s pht trin chiu cao v khe mnh. Ta bit chiu cao ph thuc kh nhiu vo gen di truyn. Tuynhin,ykhngphiyutquytnhhontonmcnphthuc vo nhiu yu t khc nhau. pht trin chiu cao tt nht ta cn hiu thm cc yu t no nh hng n chiu cao. Khi c iu kin thun li cho tt c cc yu t ta s pht trin c chiu cao ti u ca mnh. V vy, nhm chng ti thc hin n CHIU CAO TRUNG BNH CA SINH VIN N TI H HOA SEN nhm a ra ci nhn tng qut nhtvchiucaovccyutnhhngnchiucaocngnhtmra bin php pht trin chiu cao cng nh nng cao sc kho thanh thiu nin c th hc tp v lm vic tht hiu qu. CHIU CAO TRUNG BNH CA MN HC NGUYN L THNG K SINH VIN N TI H HOA SENGVHD: L TH THIN HNG Trang ii LI CM N Chng ti xin gi li cm n chn thnh n c L Th Thin Hng v nhng gip , gp gip chng ti hon thnh ti ny mt cch tt v hiu qu nht. NhmchngticngxingilicmnnkhoaKinhTThng Mi trng a hc Hoa Sen v to c hi cho chng ti hc tp mt mn hc c tnh ng dng cao vo thc tin v h tr tt cho kh nng tng hp, x l s liu cho chng ti. Tuy nhin do nhng hn ch v mt kin thc cng nh thi gian, nhm chngtikhngtrnhkhinhngsaist.Rtmongsnhgivgp ca c. Chng ti chn thnh cm n. Nhm thc hin n. CHIU CAO TRUNG BNH CA MN HC NGUYN L THNG K SINH VIN N TI H HOA SENGVHD: L TH THIN HNG Trang iii NHN XT .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. CHIU CAO TRUNG BNH CA MN HC NGUYN L THNG K SINH VIN N TI H HOA SENGVHD: L TH THIN HNG Trang iv DANH SCH SINH VIN STTMSSVH V TN 1101417L Ngc Bch Thy 2101534Trn Th Mui 3101471V Th Thanh Trc 4101515Phm Trnh Huyn Trn 5101433Phm Trn Thin L 6101490L Qunh Nh 7101073Nguyn Th CmVn 8101047Nguyn Th Thanh Trc 9101402Nguyn Th Nguyt Hng CHIU CAO TRUNG BNH CA MN HC NGUYN L THNG K SINH VIN N TI H HOA SENGVHD: L TH THIN HNG Trang v MC LC Contents TRCH YU .............................................................................................................................. i LI CM N ........................................................................................................................... ii NHN XT ............................................................................................................................. iii DANH SCH SINH VIN ..................................................................................................... iv MC LC .................................................................................................................................v BNG PHN CNG CNG VIC ....................................................................................... vi BNG BIU HNH NH ................................................................................................... vii A. M U...............................................................................................................................1 1.C s l thuyt ................................................................................................................. 1 2.i tng, phm vi nghin cu v phng php nghin cu ........................................ 19 3.Cu hi nghin cu ........................................................................................................ 22 4.Gi thuyt nghin cu .................................................................................................... 22 B. NI DUNG .........................................................................................................................23 2.Mt s yu t tc ng n chiu cao ca sinh vin n i hc Hoa Sen .................... 27 3.Mt s gii php nhm pht trin chiu cao ca sinh vin n Hoa Sen ........................ 29 C. KT LUN .........................................................................................................................31 TI LIU THAM KHO .........................................................................................................b PH LC................................................................................................................................... c CHIU CAO TRUNG BNH CA MN HC NGUYN L THNG K SINH VIN N TI H HOA SENGVHD: L TH THIN HNG Trang vi BNG PHN CNG CNG VIC H tnCc cng vic thc hin1.Trn Th Mui Thu thp d liu, vit bo co,tnh ton 2.L Thy Bch Thy Thu thp d liu,vit bo co,tnh ton 3.V Th Thanh Trc Thu thp d liu, tng hp s liuchnh sa bo co 4. Phm Trnh Huyn TrnThu thp d liu,tng hp s liu 5. Phm Trn Thin LThu thp d liut,ng hp s liu 6. L Qunh NhThu thp d liu,tng hp s liu 7. Nguyn Th CmVnThu thp d liu vit bo co,tnh ton 8. Nguyn Th Thanh TrcThu thp d liu vit bo co,tnh ton 9. Nguyn Th Nguyt HngThu thp d liu,tng hp s liu CHIU CAO TRUNG BNH CA MN HC NGUYN L THNG K SINH VIN N TI H HOA SENGVHD: L TH THIN HNG Trang vii BNG BIU HNH NH Hnh 1: Biu thanh ng th hin chiu cao ca sinh vin n i hc Hoa Sen ......... 24 Hnh 2: Biu th hin gi bt u ng ca sinh vin n i hc Hoa Sen ................... 28 Hnh 3: Biu th hin gen di truyn chiu cao ca sinh vin n i hc Hoa Sen ...... 29 Bng 1: Phng php thu thp thng tin ............................................................................. 6 Bng 2: Bng d liu thu thp ........................................................................................... 23 CHIU CAO TRUNG BNH CA MN HC NGUYN L THNG K SINH VIN N TI H HOA SENGVHD: L TH THIN HNG Trang 1 A. M U 1. s l thuyt HNG I. GII THIU MN H I.1.KHI NIM V H NNGTHNG K 1.Khi nim C th hiu khi nim thng k trn hai gc : -Gcllun:Thngklmtmnkhoahckinht, nghincumtlngtrongmilinhchtchvimtcht ca cc hin tng v qu trnh kinh t x hi, pht sinh trong iu kin thi gian v a im c th. -Gcnghipv:Thngkcthhiulccsliuth hin thn tin v i tng nghin cu. Mtcchtngqut,cthnhngha:Thngklmtnhnhcaton hc lin quan n vic thu thp, phn tch v trnh by cc d liu. y lmtkhoahcbaogmmththngccphngphptvicthuthp, trnhby,tmttdliunccphngphpphntchvdon,gip cc nh qun l a ra cc quyt nh. 2.hc nng ca thng k Qu trnh nghin cu thng k tri qua ba giai on c quan h cht ch v mtthitvinhau,tronggianontrclmtinthchingiai on sau. (1) Giai on iu tra thng k: bao gm ghi chp, thu thp ti liu thng k. (2) Giai on tng hp v trnh by kt qu iu tra thu thp c. (3) Giai on phn tch v d bo thng k Nh vy, thng k c hai lnh vc: CHIU CAO TRUNG BNH CA MN HC NGUYN L THNG K SINH VIN N TI H HOA SENGVHD: L TH THIN HNG Trang 2 -Thng k m t bao gm cc phng php thu thp trnh by d liuvtnhtonccctrngnhmmtitngnghin cu. -Thng k suy din bao gm cc phng php m hnh ha trn cc d liu quan st a ra cc suy din v tp hp cc n v c nghin cu. Thngkmtvthngksuydintothnhthngkngdng,cn thng k ton l lnh vc nghin cu c s l thuyt ca khoa hc thng k. I.2. KHI NIM NTHNG K 1.Tng th , n v tng th, mu Tng th thng k (hay tng th) l tp hp tt c cc i tng m ta nghin cu. cc n v (hay phn t) to thnh tng th c gi l n v tng th. Mu l mt b phn ly ra t tng th. 2.in Bin l c im ca n v tng th, c chia ra thnh hai loi: -Bin nh tnh th hin tnh cht ca n v c kha st. -Bin nh lng th hin bng cc s. 3.D liu D liu l kt qu quan st c ca cc bin, gi tr nhn c c ththayitnvnysangnvkhc.Dliucngcphnbit thnh hai loi: d liu nh tnh v nh lng. 4.Tiu thc thng k Tiu thc thng k l khi nim dng ch cc c im ca n v tng th m ta nghin cu. a.Tiu thc nh tnh l tiu thc phn nh tnh cht ca n v tng th, khng th hin trc tip bng cc con s. b.Tiu thc nh lng (cn gi l tiu thc s lng) l tiu thc c biu hin trc tip bng con s. CHIU CAO TRUNG BNH CA MN HC NGUYN L THNG K SINH VIN N TI H HOA SENGVHD: L TH THIN HNG Trang 3 Lng bin c t phn bit thnh hai loi: -Lngbinrircllngbinmccgitrcthc ca n l hu hn hoc v hn v c th m c. -Lng bin lin tc l lng in m cc gi tr c th c ca n lp kn c mt khong trn trc s. Thngthng,ccgitrcalngbinlintclccsccphn nguyn v phn thp phn, cn gi tr ca lng bin khng lin tc l cc s nguyn. Cc tiu thc nh tnh v nh lng ch c hai biu hin khng trng nhau trn mt tng th c gi l tiu thc thay phin. 5.h tiu thng k Chtiu thngkl cc trs phnnh cccim,cctnhcht c bn ca tng th thng k trong iu kin thi gian v khng gian xc nh. Ch tiu thng k c th phn bit thnh hai loi: ch tiu khi lng v ch tiu cht lng. a.h tiu khi lng l cc ch tiu biu hin s quy m ca tng th. b.h tiu cht lng l cc ch tiu biu hin tnh cht, trnh ph bin, quan h so snh trong tng th. I.3. O LNG V THNG O D LIU thchinnghincu,trongthngkngitasdngbncpbco lngtheomcthngtintngdn,lthango:nhdanh,thbc, khong v t l. 1.Thang o nh danh (hay thang o phn loi) l bc thp nht, khngthhinshnkm.Thangonycsdngcho cc d liu nh tnh, ch khc bit nhau v tn gi. 2.Thangothbcthhinshnkmcadliunhng khng bitchnh xcmchnkm.Thang o nycng c s dng cho cc d liu nh tnh. CHIU CAO TRUNG BNH CA MN HC NGUYN L THNG K SINH VIN N TI H HOA SENGVHD: L TH THIN HNG Trang 4 3.Thang o khong th hin c mc hn km gia cc gi trolng,tronggitr0chlquycmkhngc ngha.Thangokhongcxemlthangothbcc khong cch u nhau. Thang o ny c s dng cho cc d liu nh lng. 4.Thangotllloithangodngchoccdliunh lng,cycctnhchtcathangokhong,torng gi tr 0 c ngha tht s, cho php ly t l so snh gia hai gi trthuthp.ylthangobccaonhttronghthng thang o. Trnthct,vnthangokhphctpvtacthpdngthango nhtnhivicctiuthcnhlngvngcli,pdngthango nh lng cho tiu thc nh tnh. Ngay c khi d liu thu thp xong ta cng c th chuyn i d liu nh lng thnh d liu nh tnh. HNG II. THU THP V TNH Y D LIU II.1. THU THP D LIU 1.Xc nh d liu cn thu thp Qutrnhnghin cuthngkcn phic nhiu dliu.Victhu thpd liu i hi nhiu thi gian, cng sc, chi ph. Do cn phi tin hnh thu thp d liu mt cch h thng, p ng c mc tiu nghin cu trong kh nngngunnhnlc,kinhphvthigianchophp.Munvyphixc nh r nhng d liu no cn thu thp, th t u tin ca cc d liu ny. 2.Ngun d liu Khinghincu,tacthsdngccdliutnhngnguncsn, ccngbhocchacngb,haycthtmnhithutthpdliu mi. Dliu t ngunc sn,thng quatng hp, x l, gild liuth cp. D liu thu thp trc tip t cc i tng nghin cu gi l d liu s cp. CHIU CAO TRUNG BNH CA MN HC NGUYN L THNG K SINH VIN N TI H HOA SENGVHD: L TH THIN HNG Trang 5 a.Ngun d liu th cp kh a dng, c th l: -Cc bo co ni b c quan, doanh nghip: cc s liu bo co v tnh hnh sn xut, tiu th, ti chnh, -Cc s liu ca C quan Thng k nh nc, C quan Chnhph:dns,viclm,mcsngdnc,ti nguyn, -Bo, tp ch, mng internet, b.Ngun d liu s cp D liu s cp c thu thp thng qua cc cuc iu tra kho st. Cn c vo tnh lin tc hay khng lin tc ca vic ghi chp d liu, ngi ta chia ra thnh iu tra thng xuyn hay khng thng xuyn. -iu tra thng xuyn l tin hnh thu thp, ghi chp sliuvhintngnghincumtcchch thng, theo st qu trnh bin ng ca hin tng. -iutrakhngthngxuynltinhngthuthp, ghichochkhicncnhucucnnghincuhin tng. d liu iu tra khng thng xuyn phn nh trngthicahintngtimtthngimnht nh. Cn c vo phm vi kho st, ngita li chia ra thnh iu tra ton b v khng ton b. -iutratonbltinhnhthuthp,ghichpd liu trn tt c cc n v ca tng th. -iu tra khng ton b l ch tin hnh thu thp trn mtsnvcchnrattnthangnghin cu. 3.c phng php thu thp d liu s cp a.Thu thp trc tip CHIU CAO TRUNG BNH CA MN HC NGUYN L THNG K SINH VIN N TI H HOA SENGVHD: L TH THIN HNG Trang 6 -Quan st -Phng vn trc tip b.Thu thp gin tip -Phng vn bng in thoi -Phng php gi th uim,nhcimcaccphngphpthuthpthngtintrnyc th tm tt trong bng sau: ng 1: Phng php thu thp thng tinTnh cht Phng php gi th Phng vn qua Tel Phng vn trc tip Linh hotKmTtTt Khi lng thng tiny Hn chy Tc thu thp thng tin ChmNhanhNhanh T l cu hi c tr li ThpCaoCao Chi phTit kimTn kmTn km 4.c k thut chn mu Mcchcavicchnmulmbochomucchnthtsphn nh trung thc, i in cho ton b tng th. C hai nhm k thut chn mu l ly mu xc sut (ly mu ngu nhin) v phi xc sut (ly mu khng ngu nhin). Phng php ly mu xc sut bao gm cc phng php chn mu ngunhin ngin,chnmuhthng,chnmuphntng,chn mu c khi hay nhiu giai on.Phngphplymuphixcsutbaogmccphngphply muthuntin,lymunhmc,lymuphnon.Muphixc CHIU CAO TRUNG BNH CA MN HC NGUYN L THNG K SINH VIN N TI H HOA SENGVHD: L TH THIN HNG Trang 7 sut khng i din c cho ton b tng th nhng c chp nhn trong nghin cu khm ph v trong kim nh gi thuyt. II.2. TNH Y D LIU 1.ng tn s Bngtnslmtbngtnghp,trnhbydliubngcchphnchia chngthnhtngnhm(lp)khcnhau.Bngtnsthngbaogmba ct: Ct th nht m t cc biu hin hoc cc gi tr (hay khong gi tr)ca d liu. Ct th hai m t tn s tng ng vi cc biu hin hoc gi tr . Ct th ba l cc tn sut (t l %). a.Cch lp bng tn s cho d liu nh tnh i vi cc d liu nh tnh nh gii tnh, nhnh hc,, ta s lp bng tn s gm cc thng tin sau y: Ct th nht lit k tt c cc biu hin c th c ca tp d liu. Ct th hai ghi tn s (s ln tng biu hin xut hin trong tp d liu). tng ca ct tn s phi bng s phn t ca tp d liu. Ct th ba ghi tn sut (bng cch ly tn s chia cho s phn t ca tp d liu v nhn vi 100%). Tng ca ct tn sut phi bng 100%. b.Cch lp bng tn s cho d liu nh lng C hai trng hp: d liu c t gi tr v d liu co nhiu gi tr. (1) Trng hp d liu c t gi tr: Bng tn s cng c ba ct tng t trng hp d liu nh tnh, nhng ct th nht ghi cc gi tr (lng, bin) ca d liu. (2) Trng hp d liu c nhiu gi tr: Trc ht ta phn nhm cho cc gi tr ri mi lp bng tn s trn c s d liu phn nhm. Trn thc t, ngi ta thng phn nhm vi khong cch u nhau. CHIU CAO TRUNG BNH CA MN HC NGUYN L THNG K SINH VIN N TI H HOA SENGVHD: L TH THIN HNG Trang 8 Gismudliucnphnt,gitrlnnht,nhnhtcadliuln ltlXmax,Xmin.Giklsnhmcnchiavhlkhongcchgiacc nhm. Khi , ngi ta thng xc nh k v h bi cng thc: 32n k =, kX Xhmin max=Mt s iu kin phi tun th khi phn nhm: Cc nhm khng c trng nhau, mi gi tr ch thuc v mt nhm. Tt c cc nhm phi bo m bao qut ht tt c cc gi tr ca mu s liu. Khng c nhm rng (tc l nhm khng c phn t no). Ch : Trong bng tn s i khi ngi ta cn thm vo ct tn s tch ly (hoctnsuttchly)thhinslnquanst(hoc%slnquanst) cngdnngiihntr6encamtnhmno.Nicchkhc,tns tch ly cho thy c bao nhiu quan st bng hoc nh hn mt v tr no ca bin kho st. (3) Phn nhm m Ngoi cch phn nhm nh trn ta cn c th phn nhm m, trong nhm u tin khng c gii hn di v nhm cui cng khng c gii hn trn, ccnhmcnlickhongcchuhockhngunhau.Mcchca phn nhmml nhm u tin v nhm cui cng cha cc n v c gitrtbinvtrnhviclpqunhiut.khitnhtoniviphn nhm m ngi ta quy c ly khong cch ca nhm m bng khong cch ca nhm gn n nht. c.Cch lp bng tn s kt hp hai tiu thc thng k Bng tn s c th c dng m t hai tiu thc thng k. Ngoi ra bng kt hp ny c th c xoay theo chiu khc, hoc tch ring thng tin v tn s, tn sut thnh hai bng ring bit. 2. th thng k cc loi CHIU CAO TRUNG BNH CA MN HC NGUYN L THNG K SINH VIN N TI H HOA SENGVHD: L TH THIN HNG Trang 9 a. th thng k cho d liu nh lng (1) Biu phn phi tn s Biu phn phi tn s (Histogram) c s dng chuyn ha thng tin tr6en bng tn s thnh hnh nh trc quan. y l mt loi th biudin s phn phi tn s bng cc ct sao cho din tch ca ct t l vi tn s. (2) a gic tn s Phngphpthhaibiudinphnphitnsbngthldnga gictn s. vagicny,tani cctrungimcacnh nhccct trongHistogramlivinhaubngcconthng.munngbiudin khngcvllngtrnkhng,tathmvohaibncaHistogramhai nhm c tn s bng 0. (3) Biu nhnh l Biunhnhv l(cngilbiu thnvl)lmtcngctm lc v trnh by tp d liu, gip ngi xem thy c d liu gc v cch thc phn tn n. trnh by d liu theo phng php nhnh v l, mi tr s c tch thnh hai phn: Phnnhnh:baogmmthaynhiuchsutin.Phnnhnh c t ct u tin theo th t tng dn. S nhnh c chn sao cho n c t nhnh so vi s quan st (s l). Thng thng s nhnh trong khong t 5 n 20 l va. Phnl:gmccchscnli.Lmtnhnhcngspxptheo thttngdn.cngctchiaimtnhnhthnhnhnhtrnv nhnh di khi c qu nhiu l. b. th thng k cho d liu nh tnh (1)Biu dng thanh (thanh ng hay thanh ngang) Trn biu ny, mi thanh i din cho mt phn loi ca bin (tiu thc thng k) m ta quan tm, chiu di ca thanh th hin tn s ca cc quan st thuc v phn loi . Cn chiu rng ca cc thanh bng nhau. CHIU CAO TRUNG BNH CA MN HC NGUYN L THNG K SINH VIN N TI H HOA SENGVHD: L TH THIN HNG Trang 10 KhngnnnhmlngiaHistogramvibiuthanhng.ylhai cng c thng k khc nhau, th hin hai loi d liu nh lng, nh tnh. GiaccthanhcaHistogramkhngckhongcch,cngiaccthanh ca biu dng thanhphic khongcch vmithanh l mtbiu hin ca bin phn loi. (2) Biu hnh trn Thng dng d mt kt cu (%) ca vn ang nghin cu. Trn biu , ton b din tch hnh trn dc chia thnh nhiu mnh nh hnh r qut, din tch mi mnh tng ng vi t l ca pahn6 loi m n i din trong ton th v manh mt mu khc nhau. Th t ca cc phn loi (theo chiu kim ng h) l th t n c sp xp trong bng tng hp. HNGIII.TMTTDLIUNGILNG THNG K M T i vi d liu nh lng, chng ta c th tm tt tt hn khi s lngd liu ln, l dng cc i lng thng k m t. Cc i lng ny c chia thnh hai nhm: nhm cc i lng th hin mc tp trung ca d liu v nhm th hin phn tn ca d liu. nhm th nht ta c trung bnhcng(csdngnhiunht),mt,turngv.nhmthhaitac khongbinthin,lchtuytibnhqun,phngsai,lchchun (c s dng nhiu nht) v h s bin thin. III.1.TNG O LNG KHUYNH HNG TP TRUNG 1.Trung bnh cng (rithmetic mean) Trungbnhcngcxcnhbngcchcngttcccgitrcatng phn t(cc quan st),sau emchiacho tngs phn t(tng s quan st). CHIU CAO TRUNG BNH CA MN HC NGUYN L THNG K SINH VIN N TI H HOA SENGVHD: L TH THIN HNG Trang 11 C hai loi turng bnh cng l trung bnh cng n gin (mean) v trung bnh cng c trong s (weighted mean). a.Trung bnh cng n gin Trung bnh tng th:Gi s tng th c N phn t (quan st), iXl gi tr ca phn t th i. Khi trung bnh cng ca tng th l ==NiiXN11(1) Trung bnh mu Gi s mu c n phn t (hay cn ni c mu l n), khi trung bnh cng ca mu (hay trung bnh mu) l ==niiXnX11 (2) b.Trung bnh cng c trng s y l trng hp c bit ca trung bnh cng n gin khi gi tr iXxut hin nhiuln.Gisgitr iX xuthinfiln,i= 1,2,, k(tanifi l trng s hay tn s ca gi tr iX ). Khi , ===kiikii iff XX11 (3)vin fkii ==1 l s phn t ca mu. Ch:trnghpdliuphnnhmckhongcchthturngbnhmu ctnhgnngbicngthc ===kiikii iff xX11vi 2min maxi iiX Xx+= ltrs gia ca cc nhm i (min max,i iX Xl gii hn trn, gii hn di ca nhm i) v fi l tn s ca nhm i c.c im ca trung bnh cng Trungbnhcngthngrtnhycmvicctbin(gitrqu ln hoc qu nh), gi tr trung bnh s km tiu biu nu trong dy s c cc gi tr t bin. CHIU CAO TRUNG BNH CA MN HC NGUYN L THNG K SINH VIN N TI H HOA SENGVHD: L TH THIN HNG Trang 12 Trung bnhcng cs dng sosnhgiahau haynhiu tng th. Tnglchgiaccgitr iX vigitrtrungbnhX bng0, ngha l == niiX X10 ) (2.Mt (Mode)a)Khi nimMt l gi tr xut hin nhiu nht trong mt dy s, k hiu l Mo. b)ch xc nh mt (1) Trng hp d liu khng phn nhm: Mt l gi tr c tn s ln nht. (2) Trnghp dliuphnnhm c khongcch unhau:Trcht cn xc nh nhm cha mt l nhm c tn s ln nht. Tr s ca mt c xc nh gn ng bi cng thc: ) ( ) (.1 11min 00 0 0 00 00 0+ + + =M M M MM MM Mf f f ff fh X M(5) Trong min0MXl gii hn di ca nhm cha 0M ; 0Mh l khong cch ca nhm cha 0M ; 10 Mfl tn s ca nhm ng trc nhm cha 0M ;0Mf l tn s ca nhm cha 0M ; 10+ Mfl tn s ca nhm ng sau nhm cha 0M . (3) Trnghpdliuphnnhmckhongcchkhngu:Mtvn ctnhtheocngthc(5)nhngvicxcnhnhmcmtkhng cn c vo tn s m cn c vo mt phn phi. (Mt phn phi = Tn s: khong cch nhm). c)c im ca mt -Mt l c trng o lng khuynh hng tp trung khngb nh hng bi cc gi tr t bin. -Mt c th xc nh cho d liu s dng cc thang o khc nh thang o nh danh, thang o th bc. CHIU CAO TRUNG BNH CA MN HC NGUYN L THNG K SINH VIN N TI H HOA SENGVHD: L TH THIN HNG Trang 13 -Khcvitrungbnhcngvtrungv,mttpsliucthkhngxc nh c mt v khng c gi tr no xut hin nhiu nht. Ngc li, c mt s trng hp c nhiu mt. 3.Trung v (Median) Trong mt tp d liu c sp xp theo th t tng dn th trung v, k hiu Me , l gi tr ng gia ca tp d liu. Ni cch khc, trung v chia dy s lm hai phn, mi phn c s n v tng th bng nhau. a)ch xc nh trung v: (1) Xc nh trung v cho d liu khng phn nhm -Trnghpsphntcamunlsl: eM = 21 + nX (trungvlgitr ng gia, tc l v tr th 21 + ntrong dy cc gi tr tng dn ca mu s liu). -Trng hp n l s chn: eM= 212 2++n nX X(trung v l trung bnh cng ca hai gi tr ng gia trong dy s trn). (2) Xc nh trung v cho d liu phn nhm c khong cch Vi d liu phn nhm, trung v c xc nh mt cch xp x qua cc bc sau: Bc 1: Tnh tn s tch ly. Bc 2: Xc nh nhm cha trung v l nhm c tn s tch ly bng (hoc va ln hn) 21 + n Bc 3: p dng cng thc eM = eee eMMM MfSnh X1min2.+(6) CHIU CAO TRUNG BNH CA MN HC NGUYN L THNG K SINH VIN N TI H HOA SENGVHD: L TH THIN HNG Trang 14 trong mineMXl gii hn di ca nhm chaeM ; eMh l khong cch ca nhm chaeM ; 1 eMSl tn s tch ly ca nhm ng trc nhm chaeM ; eMf l tn s ca nhm cha eM . 4.T phn v - thp phn v T phn v, thp phn v l ch tiu o lng phn tn ch khng phi ch tiuolngkhuynhhngtpturng.Tuynhin,vcchtnhcachng tng t cch tnh trung v, hn na phn v th hai ca t phn v chnh l trung v, nn ta kt hp xt t phn v v thp phn v trong mc ny. a.T phn v chia dy s lng bin thnh bn phn, mi phn c s n v bng nhau. Cch xc nh t phn v nh sau: (1) ividliu khng phnnhm:dyslngbinc ba tphn v l: Q1 : t phn v th nht l lng bin ng v tr th 41 + n Q2 : t phn v th hai chnh l s trung v, ng v tr 214) 1 ( 2 +=+ n n Q3 : t phn v th ba l lng bin ng v tr th 4) 1 ( 3 + n Nu n+1 khng chia ht cho 4 th t phn v c xc nh bng cch thm vo. Chng hn, vi n = 12 (n v) , ta c 41341=+ n , 4394) 1 ( 3=+ n. Do , t phnvthnhtbnglngbinvtrthbacngvi 41gitrchnh lchgialngbinvtrthbavtht.Cntphnvthbabng lng bin v tr th chn cng vi 43 gi tr chnh lch gia lng bin v tr th chn v th mi. (2) i vi d liu phn nhm c khong cch: 111 11min 14.QQQ QfSnh X Q+ =; 333 31min 343.QQQ QfSnh X Q+ =(7) CHIU CAO TRUNG BNH CA MN HC NGUYN L THNG K SINH VIN N TI H HOA SENGVHD: L TH THIN HNG Trang 15 Trong miniQX lgiihndicanhmcha iQ ; iQh lkhongcchca nhm cha iQ ; 1 iQS l tn s tch ly ca nhm ng trc nh cha iQ ; iQfl tn s ca nhm cha iQ . b.Thpphnvchiadyslngbinthnhmiphn, mi phn c s n v bng nhau. Cch tnh thp phn v tng t cch tnh t phn v. ta c cng thc sau y: 111 11min 110DDD DfSnh X D+ =; 222 21min 210DDD DfSnh X D+ =; T phn v, thp phn v c s dng trong thc t khi ngi ta mun bit mc t cao nht ca hay 1/10 s n v xp t thp ln, hoc mc dt thp nht ca hay 1/10 s n v tin tin xp t trn xung. III.2. TNG O LNG PHN TN Strungbnh,sturngvvmtmichchotabitcgitrtrung tm,mc i din ca hin tng m cha phn nh y cctnh cht c th ca dy s lng bin. Do vy, ngoi cc c trng o lng khuynh hng tp trung, ta cn nh gi phn tn ( bin thin) ca d liu. 1.Khongbinthin(ange)khiuR,lchnhlchgiagi tr ln nht v gi tr nh nht ca dy lng binmin maxX X R =(1) Khong bin thin cng nh th tng th cng ng u, s turng bnh cng c tnh i din cao v ngc li. Nhc imca khongbin thinlch ph thuc vo gitrln nht v gi tr nh nht ca dy lng bin. 2.trigia(Interquartilerange)khiu QR ,lchnhlch gia t phn v th ba v t phn v th nht 1 3Q Q RQ =(2) tri gia th hin phn tn ca 50% d liu gia ca dy s. CHIU CAO TRUNG BNH CA MN HC NGUYN L THNG K SINH VIN N TI H HOA SENGVHD: L TH THIN HNG Trang 16 3.lchtuytitrungbnh(Meanabsolutedeviation)k hiud , l s trung bnh cng ca cc lch tuyt i gia cc lng bin v s trung bnh cng ca cc lng bin . Ta c cng thc: = =niiX xnd11 hoc ikiif X xnd= =11 trong ==kiif n1 lch tuyt i trung bnh cng nh, tng th cng ng u, tnh cht i dincastrungbnhcngcao.lchtuytitrungbnhcuim hn khong bin thin v n xt n tt c cc lng bin trong dy s. 4.Phng sai (Variance) l s trung bnh cng ca bnh phng cc lch gia cc lng bin v s trung bnh cng ca cc lng bin . Cch xc nh phng sai Phng sai tnh t tng th chung: = = = =kikii i i if XNf XN1 12 2 2 21) (1 otrong ifl tn s ca gi tr iXv ==kiif N1l s phn t ca tng th. Phng saimu: ikiif X xnS= =12 2) (1trong if l tn s cagitr ixv ==kiif n1lsphntcamu.Phngsaimucnctnhbi cng thc: = =kii iX f xnS12 2 2) (1. Phngsaimuhiuchnh: 2 21SnnS= (phngsaimuhiuchnh c s dng nhiu torng thng k suy din nh c lng, kim nh). 5.lchtiuchun(tandarddeviation)lcnbchaica phng sai. Cng thc tnh: 2o o = ngha lch chun: lch tiu chun th hin lch trung bnh ca tt c cc lng bin so vi gi tr trung bnh. c trng ny dc s dng CHIU CAO TRUNG BNH CA MN HC NGUYN L THNG K SINH VIN N TI H HOA SENGVHD: L TH THIN HNG Trang 17 so snh ph6an tn ca hai hay nhiu tng th, trong trng hp n v tnhgingnhauhocgitrtrungbnhbngnhau.Ngoiralchtiu chun cn cho bit s phn phi ca cc lng bin trong mt tng th, th hin trn hai quy tc sau y a.Quy tc Tchebychev: bt k mt tng th no vi trung bnh lv lchtiuchunlo uctnht)11 ( 1002m %gitrrivokhong o m , vi m >1. b.Quy tc thc nghim: ngi ta nhn thy rng nu d liu c phn phi i xng (hnh chung cn i) th c mt quy tc thc nghim nh sau: Khong 68% gi tr ri vo khongo so vi trung bnh. Khong 95% gi tr ri vo khongo 2 so vi trung bnh. Khong 99.7% gi tr ri vo khongo 3 so vi trung bnh. Lu : i vi nhng tp d liu m phn phi khng phi l hnh chung cnithkhngnnsdngquytcthcnghimmnndngquytc Tchebychev. 6.H s bin thin (oefficient of Variation) Ta bit, lch tiu chun o lng s bin thin ca tp d liu. khi hai tp d liu c cng gi tr trung bnh th tp d liu no c lch chun ln hn s bin thin nhiu hn. Tuy nhin, nu hai tp d liu c gi t turng bnh khc nhau th s khng th kt lu c iu ny bng cch so snh hai lch tiu chun. lc h s bin thin c s dng o lng mc bin ng tng i ca nhng tp d liu c gi tr trung bnh khc nhau. Cng thc tnh h s bin thin cho tp d liu tng th:% 100 .o= CVCng thc tnh h s bin thin cho tp d liu mu:% 100 .XSCV =Khih s binthin cahaitpdliucsosnhvinhua,hs bin thin ca tp no ln hn th tp bin ng nhiu hn. CHIU CAO TRUNG BNH CA MN HC NGUYN L THNG K SINH VIN N TI H HOA SENGVHD: L TH THIN HNG Trang 18 7.hun ha d liu Khilmvicvidliuslng,ikhitacnbinichngthnhd liu mt thang o chun. (Chng hn ta mun so snh cc i tng c obngccphngphpvnvokhcnhau).Viclmnygil chun ha d liu. Gi tr d liu chun ha cho bit mt gi tr quan st trong tp d liu gc s sai lch khi turng bnh ca n gp my ln lch tiu chun. iu ny th hin thng qua cng thc sau y: ng thc tnh gi tr chun haz cho d liu tng th: o =xz , trong xl gi tr d liu gc;l gi tr trung bnh ca tng th;ol lch tiu chun ca tng th; z l im s chun ha cho bitxcch xa trung bnh mt khong bng my ln lch tiu chun. ng thc tnh gi tr chun ha z cho d liu mu: SX xz= , trong xlgitir5dliugc;X lgitrtrungbnhcamu;Sllchtiu chuncamu;zlimschunhachobitx chxatrungbnhmt khong bng my ln lch tiu chun. mt gi tr z gn n 0 c ngha l quan st v tr rt gn trung bnh. Mt gi tr z = -1 c ngha l quan st v tr lch mt lch tiu chun so vi trung bnh v pha tri; gi tr z = 1 c ngha l quan st v tr lch mt lch tiu chun so vi turng bnh v pha phi. III.3.KHOTHNHDNGPHNPHITPD LIU m t d liu, bn cnh cc c trng o lng khuynh hng tp trung v o lng phn tn th hnh dng phn phi ca dy s cng l mt c trng cn xem xt. C th s dng hai phng php sau y xem xt hnh dng phn phi ca dy s. 1.Phng php so snh s turng bnh v trung v Ta c ba dng phn phi sau y: CHIU CAO TRUNG BNH CA MN HC NGUYN L THNG K SINH VIN N TI H HOA SENGVHD: L TH THIN HNG Trang 19 a.Phn phi i xng: khi= Me (hocX = Me). b.Phn phi lch phi: khi> Me (hocX > Me). c.Phn phi lch tri: khi< Me (hocX < Me). 2.Phng php tnh h s lch Pearson a.H s lch xc nh cho mu: SM XSek) ( 3 =trong kS l h s lch, S l lehc65 tiu chun,Xl s trung bnh, Me l s trung v). H s lch Pearson c gi tr torng khong t -3 n 3: H s lch c gi tr gn -3: phn phi ca dy s lch tri. H s lch c gi tr gn 3: phn phi ca dy s lch phi. H s lch gn bng 0: phn phi ca dy s i xng. b.H s lch xc nh cho tng th: o ) ( 3ekMS= , trong ol lch tiu chun ca tng th,l s turng bnh ca tng th. 2.i tng, phm vi nghin cu v phng php nghin cu 2.1.i tng nghin cu SinhvinttccckhoathuctrngihcHoaSen TPHCM. 2.2.Phm vi nghin cu tikhostticccscaTrngiHcHoaSen TPHCM. Sinhvincckhoaticccscatrngcphngvn trc tip (qua bng cu hi). tisdngphngphpchnmungunhinvikch thcmu94,trongtngthsinhvintrngihcHoa Sen. NghincuvchiucaotrungbnhcasinhvinntiH HoaSen vchdnglimtsvn linquanmtthit vi n. CHIU CAO TRUNG BNH CA MN HC NGUYN L THNG K SINH VIN N TI H HOA SENGVHD: L TH THIN HNG Trang 20 2.3.Phng php nghin cu c s dng 2.3.1. Phng php nghin cu nh tnh a.Qu trnh thu thp thng tin Thng tin s cp: c thu thp trn c s mu ngu nhin c chn t 6 c s ca trng i hc Hoa Sen- tp HCM. Chn khong 94 sinh vin hc ti cc c s ca trng. Thng tin c thu thp thng qua quan st v phng vn trc tip bng bng hi. Thng tin th cp: c su tm trn Internet.b.Phng php chn mu Phi xc sut, chn mu ngu nhin vi hnh thc iu tra bng cu hi. c.Qui m mu +Khung chn mu: Tt c sinh vin I HC HOA SEN - TP.HCM+Kch thc mu : 94 sinh vin ngu nhin. p dng cng thc : n =

n : Kch thc mu : Phng sai : tin cy e : Khong dao ng 2.3.2.Phng php nghin cu nh lng a.Thang o Ttcccthangocckhinimnghincutrongmhnhul thang o a bin. Thang o chiu cao trung bnh l mt bin ph thuc bao gm cc thnh phn:hotngththao,dinhdng,genditruyn,tnhtrnggicng.... Thang o mc gen di truyn c o bng 3 bin c lp cp n ni dung : cao, khng cao, khng bit. Thang o cc yu t nh hng n chiu CHIU CAO TRUNG BNH CA MN HC NGUYN L THNG K SINH VIN N TI H HOA SENGVHD: L TH THIN HNG Trang 21 caotp trungchyuvocc bincnidungcp n :hot ngth dc th thao, dinh dng, tnh trng gic ng. Thang o nhng yu t nh hng n chiu cao tp trung ch yu vo s tc ng ca cc yu t vo chiu cao ca sinh vin. Thng qua , chng ta bit c nhng yu t no l quan trng nht nhm c bin php ci thin v khc phc. b.Qui m mu L do ti i su nghin cu chiu cao trung bnh ca sinh vin n ti H Hoa Sen nhm lm r thm cc bn sinh vin v ang c nhng hot ng th dc th thao, ch n ung hp l cha. Vvy,munchnquymmu,xcnhckchthcmucho hp l, nhm nh gi ton din trn vn v mt cch tht chnh xc, l mt vn ht sc kh khn v nan gii. Bi l do n gin v thc t l nu ta chnquymmuqulntastnrtnhiuthigianvchiph.Vd chngtakhngththmdhtkincattcsinhvintrngihc HoaSenTP.HCMtngsdngthvintitrng.iunyskhin chng ta s tn nhiu thi gian, nu ta tin hnh iu tra lm r.Ngclinutachnquymmuqunhthscuimltit kim c nhiu chi ph v thi gian song bn cnh u im ny chn quy mmuqunhtnhidinthpkhngtngquthachomng, nhng thng tin chng ta thu thp iu tra c s khng c tnh chnh xc cao. Nghincunysdngphngphpphngvntrctipbngbng cu hi chi tit vi sinh vinca trng i hc Hoa Sen TP. HCM. Mu chn theo phng php phn tng v khng theo t l vi kch thc mu n = 94. Phng php chn mu nh lng: chn mu theo phng php mu ngu nhin, n gin v phng php phng vn trc tip. CHIU CAO TRUNG BNH CA MN HC NGUYN L THNG K SINH VIN N TI H HOA SENGVHD: L TH THIN HNG Trang 22 3.u hi nghin cu Chiu cao trung bnh ca sinh vin n ti H Hoa Sen l bao nhiu? Nhng yu t tc ng v bin php khc phc? 4.Gi thuyt nghin cu SinhvinntiihcHoaSencchiucaochacaov cha c ch n ung v sinh hot hp l CHIU CAO TRUNG BNH CA MN HC NGUYN L THNG K SINH VIN N TI H HOA SENGVHD: L TH THIN HNG Trang 23 B. NI DUNG a.Biton1:Phntchdliuchiucaotrungbnhca sinh vin n ti H Hoa Sen Theo s liu thu thp, ta c:Kch thc mu: n = 94 S nhm cn chia: k =

5,73 6 Khong cch mi nhm: h =

3,83 4 Ta chia thnh cc nhm sau v lp bng cc gi tr i din, tn s, tn s tch ly: n v tnh: cm ng 2: ng d liu thu thp Chiu caoGi tr i dinTn sTn s tch ly 149-1531511313 153-1571553245 157-1611593075 161-165163984 165-169167892 169-173171294 Biu thanh ng CHIU CAO TRUNG BNH CA MN HC NGUYN L THNG K SINH VIN N TI H HOA SENGVHD: L TH THIN HNG Trang 24 Hnh 1: iu thanh ng th hin chiu cao ca sinh vin n i hc Hoa Sen Tnh gi tr trung bnh, mt v trung v: 96 , 110010 5 , 4 12 5 , 3 22 5 , 2 26 5 , 1 30 5 , 011= + + + + = ===kiikii iff XX (cm) Tnhmt:tanhnthy,mtnhmthhainnpdngcngthc

Tnh trung v:Xc nh nhm cha trung v: :

Ta c tn s tch ly ca nhm th ba l 75( l tn s nh nht > 47,5) Me =

= 157+4.

13 32 30 9 8 2 05101520253035149-153 153-157 157-161 161-165 165-169 169-173Tan so Chieu cao Bieu do the hien chieu cao cua sinh vien nuDai Hoc Hoa SenTn s CHIU CAO TRUNG BNH CA MN HC NGUYN L THNG K SINH VIN N TI H HOA SENGVHD: L TH THIN HNG Trang 25 Tnh t phn v: T phn v th 1 tnh nh sau: Ta c:25 , 2541 10041=+=+ nvy t phn v th nht nm trong nhm 1. 833 , 03004100. 1 04.111 11min 1~+ =+ =QQQ QfSnh X QT phn v th ba tnh nh sau: Ta c:75 , 5 . 741 100. 341. 3 =+=+ n vy t phn v th ba nm trong nhm 3. 86 , 222564100 . 3. 1 243.333 31min 3~+ =+ =QQQ QfSnh X QKhong bin thin: R = X max X min = 172-149 = 23 tri gia:027 , 2 833 , 0 86 , 21 3= = = Q Q RQ lch tuyt i trung bnh:

Ta c: =

| | | | | ||| | |||H s bin thin: CV=

M

= 23,36

CV =

CHIU CAO TRUNG BNH CA MN HC NGUYN L THNG K SINH VIN N TI H HOA SENGVHD: L TH THIN HNG Trang 26 b.Bi ton 2: c lng chiu cao trung bnh ca sinh vin n trng i hc Hoa Sen: Gi (cm) l chiu cao trung bnh ca sinh vin n trng i hc Hoa Sen. Theo kt qu thu thp c, ta c: n = 94; 1 =>

S = Ta c: (

)

Tra bng hm s Laplace, ta c:

Sai s:

=

hay, chiu cao trung bnh ca sinh vin n trng i hc Hoa Sen l t 156,56cm n 159,14cm. c.Bi ton 3: Kim nh Nhmaragi thuytrng chiucao trung bnhca sinhvin ntiH HoaSenl160cm.Hinnay,nhmthchinkhostnhmkimtragi thuyt trn vi 94 sinh vin thy rng chiu cao trung bnh ca sinh vin n ti H Hoa Sen l 157,85 (cm) lch mu hiu chnh l 4,83. Hy kt lun v gi thuyt ca nhm vi mc ngha 5%. Gii:Gi H l t l sinh vin n cao trn 160cm Da vo bng thng k s liu thu thp c, ta c: CHIU CAO TRUNG BNH CA MN HC NGUYN L THNG K SINH VIN N TI H HOA SENGVHD: L TH THIN HNG Trang 27 n=94;

; 1- (

)

(tra bng hm s Laplace)

H =

Vy, t l sinh vin n cao trn 160cm l t 12% n 28% 2.Mtsyuttcngnchiucaocasinhvinnihc Hoa SenThngquavickhost,nhmthymtthctrngrtngccbn sinh vin n Hoa Sen c chiu cao thp so vi trung bnh ca x hi hin nay c n 47,9% s bn c kho st cho bit rng h c chiu cao t 149 cm n 157cm . Mt s nh chim 10,6% cho bit h cao t 165 cm n 173 cm v 41,5 % cn li l i tng c chiu cao t 157cm n 165 cm .Cu hi t ra l ti sao phn ln cc bn sinh vin vn cha ci thin c chiu cao ca mnh ? S tht ny cmu thunvi s pht trin ca x hi hinnaychiucaocangintrngthnhVitnamtrungbnhl 158cm.Nhng yu t no tc ng n chiu cao ca sinh vin n l g ? CHIU CAO TRUNG BNH CA MN HC NGUYN L THNG K SINH VIN N TI H HOA SENGVHD: L TH THIN HNG Trang 28 Hnh 2: iu th hin gi bt u ng ca sinh vin n i hc Hoa Sen - Da vo s liu thu thp c d nhn thy rng sinh vin bt u ng t 11hn12hchim43%.Tuynhin,imnglulccbnnthc khuya trn 12h chim mt con s kh ln 36%. V con s bt u ng t 10h n 11h ch chim 19% v cc bn ng ng gi ch chimmts rt nh 2%. Qua cho thy gi gic sinh hot, ngh ngi ca cc bn n sinh vin Hoa sen khng ph hp, cc bn khng c ch ng hp l bo v sc khe sau nhng gi hc v lm vic - Mt khc, thng qua cuc kho st, nhm cng thy rng kh ng cc bn n khng c ch n ung hp l c n 73,4% bn xem nh vic n ung ng gi, ccbn thng n khi i hoc dng cc ba n n gin khng cht dinh dng thay th.- Ngoi ra, vic tp th dc rt xa l vi cc bn, c n 30,8 % cc bn n khngtpthdcvc57,5%ccbnthamgiatpthdcthnhthong vocuitunhocccbuihcthdccatrngvchcmtsnh 11,7 % sinh vin n c tp th dc thng xuyn. Qua kho st ta d nhn thy sinh vin n khng quan tm n vic tp th dc nhiu v th m vic tng chiu cao ca cc bn cng b hn ch rt nhiu. - Gen di truyn2% 19% 43% 36% Bieu do the hien gio bat dau ngu cua sinh vien nu dai Hoc Hoa Sent 9h -10h t 10h -11h t 11h - 12h trn 12h CHIU CAO TRUNG BNH CA MN HC NGUYN L THNG K SINH VIN N TI H HOA SENGVHD: L TH THIN HNG Trang 29 Hnh 3: iu th hin gen di truyn chiu cao ca sinh vin n i hc Hoa Sen C th thy rng, gen di truyn ca cc gia nh c chiu cao ch chim 28% trong khi khng c chim ti47% vmt phn do ch b hoc m cao nnkhngxcnhcchim25%.Tchothygenditruynchim mtvaitrkhquantrngtrongvicphttrinchiucaocathhsau, nhng a s cc gia nh Vit Nam c gen di truyn chiu cao ch chim mt con s tng i thp. y cng l yu t rt quan trng nh hng n chiu cao ca cc bn sinh vin n i hc Hoa Sen. Tm li, qua kho st cho thy c rt nhiu yu t nh hng v nhn thy c l do ti sao cc bn sinh vin n i hc Hoa Sen vn cha pht huycchiucaocamnh.Thnhtldogianhkhngcgendi truyn chiu cao . Mt khc, cc bn vn cha quan tm tch cc n vic tp th dc v c ch n ung, ngh ngi hp l Vy lm sao c th pht trin chiu cao ? 3.Mtsgiiphpnhmphttrinchiucaocasinhvinn Hoa Sen-Tp luyn th dc, th thao hp l mi ngy s gip tun hon mu lu thong tt hn trao i cht tng cng hormon tng trng Growith Hormon 28% 47% 25% Bieu do the hien gen di truyen chieu caocua sinh vien nu Hoa SenC khng Khng bit CHIU CAO TRUNG BNH CA MN HC NGUYN L THNG K SINH VIN N TI H HOA SENGVHD: L TH THIN HNG Trang 30 tit ra nhiu hn. T , khin chocc bp c tun hon, dy chng, xng khp u c kch thch lm cho ton b c th v chiu cao pht trin. - m bo gic ng ngon. Ng ngon ng su gip c th tit hormon tng trng, tng hp th canxi, kch thch xng di ra v pht trin th cht ton din. S gi nh ty theo la tui.Nhn chung, chng ta nn cn ng khong 8h mi ngy. Chng ta nn chnch ng rng ri, sch s, vi mt khng gian yn tnh. - Chm sc y t : cn phi tim chng y , gi v sinh than th, v sinh an ton thc phm s gip t b nhim khun, ng c , nh s to iu kin cho pht trin chiu cao. - Mt khc, nn c ch n ung hp l m bo ba ba mi ngy v b sung u cht dinh dng. Ngoi ra, chng ta c th s dng them cc loi sa h tr tng chiu cao. CHIU CAO TRUNG BNH CA MN HC NGUYN L THNG K SINH VIN N TI H HOA SENGVHD: L TH THIN HNG Trang 31 C. KT LUNChiu cao ca cc bn sinh vin n i hc Hoa Sen vn cn thp so vi mc trung bnh ca x hi hin nay v vy cc bn nn quan tm nhiu hn na n cc vn v sc khe v chiu cao. iu ng quan tm nht ylccbnnntchcctpthdcvnungnghngiy. CHIU CAO TRUNG BNH CA MN HC NGUYN L THNG K SINH VIN N TI H HOA SENGVHD: L TH THIN HNG Trang b TI LIU THAM KHO cng mn hc Nguyn L Thng K -i hc Hoa Sen S tay sinh vin Hoa Sen Website: www.hoasen.edu.vn http://thuvien.hoasen.edu.vn/default.aspx CHIU CAO TRUNG BNH CA MN HC NGUYN L THNG K SINH VIN N TI H HOA SENGVHD: L TH THIN HNG Trang c PH LC NG KHO T Cho cc bn chng ti n t lp mn Nguyn l thng k. Chng ti ang lm bi kho st v " Chiu cao ca sinh vin n trng i hc oa en". t mong s hp tc ca cc bn chng ti c th hon thnh tt1. Bn cao bao nhiu :.. 2. Bn sinh nm my: 3. Bn c tp th dc thng xuyn khng :a. rt thng xuynb. thnh thongc. khng c 4. Bn c ung sa tng chiu cao khng :a. Cb. Khngc. thnh thong 5. Bn bt u ng khi no : a. t 9h -10hb. t 10h -11h c. t 11h - 12hd. trn 12h 6.Bn c ch n hp l khng : a. CB. Khng 7. Gia nh bn c gen cao khng :a. cb. khngc. khng bitCm n cc bn b thi gian gip chng ti ! TNG I H HOA SEN KHOA KINH T THNG MI CHIU CAO TRUNG BNH CA MN HC NGUYN L THNG K SINH VIN N TI H HOA SENGVHD: L TH THIN HNG Trang d