Thống kê và ứng dụng trong bưu chính, viễn thông

Thong ke hoc chfnh la khoa hoc nghien ci'di he thong cac phuong plidp thu thap, xilr ly va phan ticli cac con so m at I item g cua nhung hien tuong so Ion de tim liieu ban chat va tinh

GS.TS.NGLTT BUI XUAN PHONG

UYEN

l i e u

I r N H A X U A T B A N B U U D I E N

THONG KE V A UI\IG DUNGTRONG BUU CHlNH, VIEN THONG

GS.TS.NGUT BUI XU AN PHONG

THONG KE V A UNG DUNG

T R O N G B U U C H i N H , V I E H T H O N G

N H A X U A T B A N BlTU D I E N

H a Noi, th an g 9 - 2005

Ma so: KK 06 HM 05

L O l NHA X U A T B A N

Thong ke, dac biet la thong ke urng dung la mot mon hoc khong the thicu trong chirong trlnh dao tao nganh Kinh te va Quan tri kinh doanh Buu chfnh, Vien thong Thong ke la hoat dong quan trong, la cong cu khong the thieu trong quan tri doanh nghiep va trong quan ly kinh te

Voi muc dfch cung cap cho ban doc mot phuong phap tong hop, phan tfch so lieu mot cach khoa hoc va hieu qua cao phuc

vu cho nhihig doanh nghiep hoat dong san xuat kinh doanh trong linh vuc Buu chfnh, Vi6n thong; Nha xuat ban Biru dien xuat ban

do GS.TS NGUT Bui Xuan Phong - Pho Truong khoa Quan tri Kinh doanh Hoc vien Cong nghe Buu chfnh V iin thong bien soan Noi dung cuon sach gom 07 chuong de cap nhung kien thuc rat thiet thirc v& thong ke va nhung ung dung trong Buu chfnh, Vi£n thong nhu: Khai niem ve thong ke; Phuong phap trlnh bay so lieu thong ke; Dieu tra so lieu chon m^u; Tuong quan va hoi quy; Chi so trong thong ke

Cuon sach la tu lieu tham khao can thiet cho cac lanh dao, cac can bo hoach dinh chfnh sach, can bo quan ly cua cac co quan, don vi thuoc Bo Buu chfnh, Vi£n thong, T6ng Cong ty Buu chfnh Vi£n thong Viet Nam, cac So Buu chfnh Vien thong, dac biet la cac doanh nghiep kinh doanh dich vu Buu chfnh, Vi6n

thong va Cong nghe thong tin; dong thoi cuon sach la tai lieu tham khao hCru fch doi voi cac giao \ icn suih vien Hoc vien Cong nghe Biru chfnh Vien thong, cac co so dao tao chuyen nganh Biru dien va ban doc quan tain den van de nav.

Cac y kien gop y cua quy \ i ban doc, xin giii ve dia chi:

N ha xu a t ban Biru d ien, 18 Nguyen Du Ha Noi: Dien thoai:

04 9430202; Fax: 04 9431285.

Tran trong cam on./

Ha N oi tlidng 9 nam 2005

NHA XUAT BAN BUU DIEN

Chiwng 1

1.1 TH O NG KE HO C LA GI?

Thuat ngu thong ke co hai nghla:

- Theo nglua thit nhat, thong ke la cac con so diroc ghi chep

de phan anh cac hien tuong tir nhien, ky thuat, kinh te va xa hoi Ch&ng han san luong dich vu, doanh thu kinh doanh buu chfnh viln thong (BCVT)

- Theo nglua th u h ai, thong ke diroc hieu la he thong cac

phuong phap ghi chep, thu thap va phan tfch cac con so \ i nhung hien tuong tir nhien, ky thuat, kinh te va xa hoi de tlm hieu ban chat va tim quy luat von co cua nhung hien tuong ay Chang han nhu lam the nao de co duoc cac con so ve lao dong cua mot doanh nghiep BCVT d mot thoi diem nao do va nghien cuu sau vao co cau lua tuoi, gioi tfnh, trinh do, nghe nghiep tir do ma co cach danh gia dung dan ve thuc trang lao dong, giup cho viec su dung co hieu qua lao dong, dong thoi co chfnh sach dao tao, tuyen dung lao dong nh^m hoan thanh nhiem vu chfnh tri cua doanh nghiep

Thong ke hoc chfnh la khoa hoc nghien ci'di he thong cac

phuong plidp thu thap, xilr ly va phan ticli cac con so (m at I item g) cua nhung hien tuong so Ion de tim liieu ban chat va tinh quy luat von co cua chung (mat chat) trong nhung dieu kien, dia diem va thoi gian cu the.

8 Tliong ke va ifng dung trong Buu chinh Vien tliong

Hien tugng bao gio cung co hai mat chat va luong khong tach rdi nhau Chat cua hien tuong giup ta phan biet hien tuong nay voi hien tuong khac, dong thoi boc lo nhung khfa canh sau kin cua hien tuong Nhung chat khong t6n tai doc lap ma duoc bieu hien qua luong, voi nhung cach xir ly mat lucmg do mot cach khoa hoc So dT can phai sir ly mat luong mdi tim hieu duoc mat chat la vl mat chat cua hien tuong thuong bi che khuat ducri cac tac dong ngSu nhien Phai thong qua tong hop mat lumig cua so Ion don vj cau thanh hien tuong, tac dong cua cac yeu to ngSu nhien moi duoc bii tru va triet tieu Hon nua, cung con phai su dung cac phuong phap phan tfch so lieu thfch hop, ban chat cua hien tuong moi dan dan boc lo qua tfnh quy luat thong ke V6 thuc chat, tfnh quy luat thong ke la su bieu hien ve luong cua cac quy luat phat sinh, phat trien cua hien tuong Tinh quy luat nay khong co tfnh chat chung chung ma rat cu the theo cac di6u kien, dia die’m va thoi gian cu the Do chfnh la dac trung cua thong ke hoc, lam cho no khac voi toan hoc

Tfnh quy luat thong ke co y nghla rat quan trong doi hoat dong kinh doanh, trong do co hoat dong kinh doanh BCVT, vi no cho biet moi lien he giua cac hien tuong, xu the phat trien cua hien tuong cung nhu cac dao dong chu ky cua hien tuong do, quy luat phan phoi cua cac t6ng the chua dung hien tuong dang nghien cun

1.2 TONG THE THONG KE VA fX)N VI TONG THE THONG KEThong ke nghien cuu mat luong cua hien tuong kinh te xa hoi so Ion phai xac dinh pham vi hien tuong duoc nghien cuu cu the’ De chi doi tuong nghien cuu cu the, ngudi ta dung khai mem

Chuong 1: M ot so khai niem ve thong ke 9

tong the Tong the' thong ke la hien tuong kinh te xa hoi so Ion, gom nhung don vi (hoac phan tu, hien tuong) ca biet can duoc quan sat, phan tfch mat luong cua chung de tim hieu ban chat va tfnh quy luat von co cua chung (mat chat) trong nhung dieu kien, dia diem va thoi gian cu the C hing han toan bo can bo, cong nhan vien cua mot buu cuc vao mot thoi gian nao do la mot t6ng the Cac buu cuc thuoc mang buu chinh vao mot thoi gian xac dinh cung la mot tong the

Co truong hop cac don vi cau thanh tong the, co the thay duoc bang true quan Tdng the bao gom cac don vi nhu vay duoc goi la tong the boc lo nhu cac tong the neu tren Tong the cac don

vi cau thanh no, khong the nhan biet duoc bang true quan la t6ng the tiem an nhu tdng the nhung can bo cong nhan vien ua chuong nghe thuat san khau, tong the nhung nguoi me tin di doan, tdng the nhung nguoi trung thanh voi To quoc

Cac don vi t6ng the co the giong nhau tren mot so dac diem, cac dac diem con lai khac nhau Do do, tuy theo muc dfch nghien cuu ma phan biet tdng the’ dong chat hay khong dong chat T6ng the dong chat bao gom cac don vi giong nhau ve mot so dac diem chu yeu co lien quan toi muc dfch nghien cuu, t6ng the kliong dong chat bao gom cac don vi khac nhau v6 cac dac diem, cac loai hinh

T6ng the bao gom tat ca cac don vi thuoc pham vi nghien cuu tdng the chung, chi bao gom mot bo phan don vi trong do la tdng the bo phan

Xac dinh t6ng th6 de dap ung muc dfch nghien cuu thong ke phai tren co so phan tfch ly luan kinh te, chfnh tri hoac xa hoi

10 Thong ke va ring dung trong Biru chinh Vien tliong

djnh nghla ro tong the Dinh nghla t6ng the khong nhurng phai gidi han v& thuc the (t6ng the la gi) ma con phai gidi han v6 thoi gian va khong gian (t6ng the t6n tai vao thoi gian nao, 6 dau) Xac dinh tong the chfnh xac khong dt! dang vi co nhung hien tuong co the tuong tu v6 hinh thuc, nhung lai khac han v6 noi dung Chfnh vi vay phai phan tfch ly luan de: thay ro noi dung cua hien tuong Xac dinh t6ng the thong ke khong chfnh xac se lang phi sue nguoi va tien cua trong nghien cuu, khong du co so de hieu dung ban chat cu the cua hien tuong

Djnh nghla t6ng the lam ro dac trung co ban chung cua hien tucmg kinh te xa hoi, so Ion phu hop voi muc dfch nghien cuu Thong qua viec phan tfch ly luan va thuc te phai lam ro t6ng the g6m nhung hien tuong (phan tir) ca biet nao Hien tucmg ca biet nay la don vi tong the Tat ca cac don vi tong the chi giong nhau tren mot so mat, con cac mat khac khong giong nhau Cho nen trong thuc te phai neu ro rang nhung hien tUOTig ca biet nao duoc ke’ la don vi t6ng the Trong nhung trudng hop kho khan cho viec gidi han, nguoi ta phai lap mot danh muc cac don vi hoac trong giai thfch can xac dinh ro pham vi nao cua cac don vi thuoc t6ng the.Don vi tdng the’ bao gio cung co don vi tfnh toan phu hop Xac dinh don vi tdng th6 la viec cu the hoa tong the’ D on vi t6ng the’ la xuat phat diem ciia qua trinh nghien cuu thong ke vi no co mat luong ma ta can nghien cuu, cho nen xac dinh don vi t6ng the cung quan trong nhu xac dinh tdng the

1.3 TIEU TH l/C THONG KE

Nghien cuu thong ke phai dua vao cac dac diSm cua don \ ’i tong the Don vi t6ng the co nhieu dac diem, tuy theo m uc dfch

Clufang / : M ot so klidi niem ve thong ke 11

nghien cuu, mot so deic diem cua don vi tong the duoc chon ra de nghien cuu Cac dac diem nay duoc goi la car tieu tlii'(c. Vi du m6i can bo cong nhan vien cua buu cuc co cac tieu thuc: ten, tuoi, gidi tmh, trinh do van hoa, nghe nghiep, noi d M6i buu cuc trong tong the co tieu thuc: ten buu cuc, dia chi, so luong can

bo cong nhan vien

Don vi tdng the duoc lam ro dac trung cua no qua cac tieu thuc: thuc the, thoi gian va khong gian

1.3.1 Tieu thurc thirc the

Tieu thuc thuc the neu len ban chat cua don vi tdng the va no bien doi trong ban chat nay Cac tieu thuc: gidi tfnh, tuoi, trinh do van hoa, nghe nghiep, so' luong can bo cong nhan vien chuc la cac tieu thurc thuc the Theo noi dung cua no, tieu thuc thuc the gom hai loai: thuoc tfnh va so luong

Tieu thuc thuoc tfnh khong co bieu hien true tiep la cac con

so, nhu tieu thuc gidi tfnh, trinh do van hoa, nghe nghiep Tieu thuc thuoc tfnh co bieu hien true tiep va gian tiep, nhu gidi tfnh

co bieu hien true tiep la nam va nu Tieu thuc ddi song vat chat co bieu hien gian tiep la luong tieu dung luong thuc, thuc ph&m theo dau ngudi, dien tfch nha d theo dau nguoi Cac bieu hien gian tiep cua tieu thuc thuoc tfnh con duoc goi la cac chi bao thong ke.Tieu thirc thuoc tfnh khong co bieu hien true tiep la con so, nen con duoc goi la tieu thuc phi luong hoa

Tieu thuc so luong co bieu hien true tiep la con so (goi la luong bien) No la ket qua cua qua trlnh quan sat (can do, dong deni) nhu tudi ddi, tuoi ngh6, so luong dien thoai, so buu cuc

12 Thong ke va ifng dung trong Bifu chinh \ ten tliong

Tieu thuc so luong con goi la tieu thuc luong hoa vi no co bieu hien true tiep la con so

Tieu thuc thuc the khi chi co hai bieu hien khong trung nhau

tren mot don vi tong the duoc goi la tieu thuc tliay p h ie n , nhu

gioi tfnh (nam va nu), chat luong san pham dich vu (tot va xau) Tieu thuc thuc the co ba loai bieu hien tro len co the tro thanh

tieu thuc thay phien Vf du nhu so luong can bo cong nhan vien

cua buu cuc neu tren co nhieu bieu hien nhung rut gon thanh hai bieu hien, hoac cac bieu hien cua tieu thuc trinh do van hoa co the rut gon thanh hai bieu hien: chua tot nghiep ph6 thong trung hoc va tot nghiep ph6 thong trung hoc tro len Nhung trudng hop nay duoc tien hanh khi nguoi ta chi quan tarn den mot bieu hien nao do xuat hien hay khong xuat hien tren don vj t6ng the

Tieu thuc thuc the co phu hop nhieu hay ft voi viec dap ung muc dfch nghien cuu la tuy thuoc vao viec chon nhung tieu thuc nao cho nghien cuu

1.3.2 Tieu thuc thoi gian

Tieu thuc thoi gian neu hien tuong kinh te xa hoi theo su xuat hien cua no vao thoi gian nao Nhung bieu hien cua tieu thuc thoi gian la phut, gio, ngay, thang, nam Thoi han co gia tri cua cac chi dan \6 doi tuong nghien cuu va nhung don vi t6ng the, v6

su phan phoi chung trong mot thoi gian cung nhu ve su thay doi

tu thoi ky nay toi thoi ky khac duoc khang dinh qua tieu thuc thoi gian Vf du tong so m ay dien thoai co den ngay 31/12/2001 la 4.301.120, trong do 70.01% may co dinh; 29,99% may di dong

Clufcrng 1: M ot so kliai niem ve tliong ke 13

1.3.3 Tieu thurc khong gian

Tieu thurc khong gian neu pham vi lanh tho bao triim cua doi tuong nghien cuu va su xuat hien theo dia diem cua cac don vi t6ng the Nhung bieu hien cua no duoc chi ra nho su phan dinh vd mat quan ly hanh chinh hoac theo dieu kien tu nhien, phan vung kinh te Nghien cuu thong ke theo tieu thuc khong gian co y nghla quan trong truoc het la gan voi tieu thuc thuc the de quan sat sir phan phoi ve mat lanh tho cua cac don vi tong the

Cac tieu thuc nay gop phan vao viec khang dinh don vi tong the cung nhu tong the vi chung neu ro cac mat va tfnh chat nhat dinh cua don vi tong the cung nhir cua tong the; nho do co the phan biet don vi nay vdri don vi khac cung nhu tong the nay voi t6ng the kia

1.4 CHI TIEU THONG KE

Nghien cuu thong ke khong chi phan anh luong va chat cua hien tuong kinh te xa hoi ca biet ma con phan anh mat luong va chat cua hien tuong kinh te xa hoi so Ion trong di6u kien thoi gian

va dia diem cu the’ Tfnh chat cua cac hien tuong ca biet duoc khai quat hoa trong chi tieu thong ke Do do chi tieu thong ke chi

ra nhung moi quan he can thiet, cai chung cua tat ca cac don vi hoac cua nhom don vi Ngoai ra chi tieu thong ke con phan anh cac moi quan he ton tai khach quan, nhung cung khong tu boc lo

ra de hi£u true tiep la moi quan he Phai dieu tra mat luong cua don vi ca biet va tu do phat hien y nghla theo so luong cua moi quan he bang chi tieu thong ke Cac moi quan he nay se duoc nghien cuu trong cac phuong phap thuoc cac chuong sau

14 Thong ke va tfng dung trong Bifu chinh \ ien tliong

Chi tieu thong ke co hai mat: kliai niem va con so Khai niem cua chi tieu thong ke bao gom dinh nghla va gidi han ve thuc the, thdi gian va khong gian cua hien tuong kinh te xa hoi Mat nay chi ro noi dung cua chi tieu thong ke Con so cua chi tieu thong

ke la tri so duoc phat hien vdi don vi tinh toan phu hop va no neu len muc do cua chi tieu thong ke Vi du doanh thu phat sinh nam

2001 la 18.617,15 ty dong ; trong do doanh thu phat sinh 2001 la mat kliai niem cua chi tieu, 18.617,15 ty ddng la mat con so cua chi tieu

Theo noi dung, chi tieu thong ke bieu hien quy mo, co cau,

su phat trien va moi quan he cua hien tuong so' ldn trong difiu kien thdi gian va dia diem cu the

Can cu vao noi dung co the chia cac chi tieu thong ke thanh hai loai: khoi luong va chat luong Chi tieu thong ke khoi luong bieu hien quy mo cua tdng the nhu so can bo cong nhan vien, so may dien thoai, khoi luong san pham dich vu Chi tieu thong ke chat luong bieu hien trinh do pho bien, mo'i quan he cua tdng the cung nhu gia thanh san pham dich vu Viec phan loai nay nham dap ung yeu cau cua mot so phuong phap phan tfch thong ke

1.5 CAC LOAI THANG DO

Theo tinh chat cua viec do ludng, ngudi ta thudng co 04 loai thang do:

- Thang do dinh danh (hay la dat ten) la danh so cac bieu hien cung loai cua mot tieu thirc Nhu gidi tinh bieu hien “ nam ” duoc danh so 1 va “ nu” danh so 2 Giua cac con so d day khong

co quan he hon, kem cho nen cac phep tinh vdi chung d£u vo nghla Loai thang do nay dung de: dem tan so cua bi£u hien tieu thuc

C huang I : M ot so kliai niem ve tliong ke 15

- Thang do th u bac cung la thang do dinh danh, nhirng giua cac bieu hien tieu thuc co quan lie thu bac, lion kem Su clienh lech giua cac bieu hien khong nhat thiet phai bang nhau, nhu Huan chuang co ba hang: Nhat, Nhi va Ba Hang Nhat han hang Nhi, hang Nhi han hang Ba Trinh do van hoa pho thong co ba cap: Tieu hoc, Trung hoc c a s a va Trung hoc pho thong Trung hoc pho thong lion Trung hoc c a sa, Trung hoc c a sd han Tieu hoc Con so co tri so lan han khong co nghla a bac cao lion va ngugc lai, ma do su quy dinh Thang do loai nay duoc sir dung de tfnh toan dac trung chung cua tong the mot cach tuong doi, trong mot so trudng hap nhu tfnh cap bac binh quan cua mot doanh nghiep, mot dan vi, bo phan

- Thang do khoang la thang do thu bac co cac khoang cach deu nhau va co the danh gia sir khac biet giua cac bieu hien bang thang do loai nay Viec cong tru cac con so co y nghla, co the tfnh cac dac trung chung nhu so binh quan, phuong sai Yeu cau

co khoang cach deu la dat ra doi voi thang do, con doi voi bieu hien cua tieu thuc duoc do khong nhat thiet phai bang nhau

- Thang do ty le la thang do khoang vdi mot diem khong (0) tuyet ddi (diem goc) de co the so sanh duoc ty le giua cac tri so

do Vdi thang do loai nay, co the do ludng cac bieu hien cua tieu thuc nhu cac dan vi do ludng vat ly thong thudng (kg, m, ) va thuc hien duoc tat ca cac pliep tfnh vdi tri so do

Chuang 2

CAC PHUONG PHAP TRINH BAY

SO LIEU TH O N G KE

2.1 TRINH BAY SO LIEU BANG BANG THONG KE

2.1.1 Doi voi tieu thurc thuoc tinh

Khi trinh bay so lieu bang bang thong ke doi vdi tieu thuc thuoc tfnh, co the gap nhung trudng hop sau:

Trudng hap 1: Chi xet nhung bieu hien cua m ot tieu thuc

Trong trudng hop nay bang thong ke co nhung dang sau:

C huang 2: Cac phuang phap trinh bay so lieu thong ke 17

Cot "Tan suat dj" ghi tan suat tuong ung la tan so tinh bang

so tuong doi, duoc xac dinh theo cong thuc:

Vf du: Doanh thu cua mot so Buu dien tinh nhu sau: Buu dien tinh A la 4.000 trieu dong; Buu dien tinh B: 2.400; Buu dien tinh C: 11.000 va Buu dien tinh D: 2.600 Yeu cau ghi vao bang thong ke so' lieu tren

d day d6 dang thay tieu thurc A la Buu dien tinh No co 04 bieu hien do la Buu dien tinh A (A,), Buu dien tinh B (A2), Buu dien tinh C (A^) va Buu dien tinh D (A4) Tan so tuong ung o day chfnh la doanh thu cua m6i Buu dien tinh

18 Thong Ice va Ung dung trong Bun chinh I ien thong

Being 2.3

Trong bang thong ke nay m6i f(J la so lan quan sat (tan so), ket qua cua su ton tai dong thoi 02 bieu hien A, va B, Cot cuoi cung ( fjA) va hang cuoi cung ( ) la tdng rieng cac tan sd ung vdi tung bidu hien cua m6i tieu thuc A va B

Nhu vay, bang thong ke sd lieu cua 02 tieu thuc chinh la bieu hien su ket hop 02 bang thong ke (loai mot tieu thuc) trong do co

su b6 sung cac tan sd ket hop (f,j)

Vi du: Them sd lieu d trudng hop 1 vdi cac di6u kien doanh thu theo loai dich vu:

- Doanh thu dich vu buu pham thudng la: 3.500 trieu dong cua Buu dien tinh A

- Doanh thu dich vu buu ph^m ghi sd la:

500 trieu dong cua Buu dien tinh A1.500 trieu d6ng cua Buu dien tinh B

500 trieu dong cua Buu dien tinh C

Chuong 2: Cac phuong phap trinh hay sd lieu thong ke 19

- Doanh thu dich vu EMS la:

500 trieu dong cua Buu dien tinh B1.000 trieu dong cua Buu dien tinh C

- Doanh thu dien thoai dudng dai la:

400 trieu dong cua Buu dien tinh B1.500 trieu dong cua Buu dien tinh C

- Doanh thu dien thoai noi hat la:

8.000 trieu dong cua Buu dien tinh C

- Doanh thu dien thoai quoc te la:

2.600 trieu dong cua Buu dien tinh DNeu chi quan tam den tong so' doanh thu timg dich vu thi tieu thuc la dich vu vdi 06 bieu hien

Bang 2.4

Loai dich vu Doanh thu f> (Trieu dong) Tan suat d,

Trudng hop xet bieu hien ca 02 tieu thuc Buu dien tinh va loai dich vu, ta co bang thong ke nhu sau:

20 Thong ke va ung dung trong Bun chinh \ ien tliong

Bang 2.5

Don vi Trieu dong

^ ^ \ L o a i djch vu Biru pham Dien thoai Cong

th e o bi/u dien tinh

2.1.2 Ddi voi tieu thurc so luong

Trudng hop I : Tieu thuc so luong voi cac luong bien rdi rac

Gia tri cua cac luong bien nay thudng la nhirng so nguyen nhu so may moc, so cong nhan Trinh bay so lieu bang bang thong ke doi voi tieu thuc so luong co cac luong bien roi rac tuong doi don gian Voi tap hop so lieu da co, chi viec dem xem m6i gia tri luong bien xuat hien bao nhieu lan, r6i ghi ket qua do vao bang thong ke

Chuang 2: Cac phuong phap trinh hay so lieu thong ke 21

Trong bang x( (i = 1 , 2 k) - Gia tri cac lugng bien thuoc tieu thuc x

f, (i = 1,2 k) - T^n so tuong ung vdi m6i x,

Can phan biet luong so lieu tuc la t6ng so lan quan sat (n) voi luong cac gia tri (k)

Vi du: Khao sat 50 buu cuc cho thay doanh thu hang thang tfnh bang trieu dong nhu sau:

22 Thong ke va ifng Jung trong Bifu chinh \ ien tliong

Trudng hop 2: Tieu thuc so luong vdi cac luong hien lien tac

Voi loai tieu thuc nay, trong mot khoang nao do cac luong bien co the lay nhung gia tri bat ky Trong thuc te quan sat chi thu nhan duoc cac gia tri tach biet tuc la cac luong bien lien tuc

da bi rdi rac hoa Dieu nay khong co nghla la viec trinh bay so lieu voi cac luong bien lien tuc hoan toan giong nhu cac luong bien rdi rac (trir trudng hop sd luong cac gia tri tuong ddi ft) Thong thudng hay gap nhung trudng hcrp sd lieu quan sat cung nhu luong cac gia tri rat ldn De cho gon, phai he thong hoa lai thanh bang phan phoi gh ep 'to , tuc la cac gia tri se duoc ghep thanh tung to Can cu vao gidi han cua cac to, xac dinh tan sd (tan suat) tuong ung va ghi vao bang phan phoi ghep td

Khi tien hanh phan to, neu sd td qua nhieu se bi xe le va sd don vi cua tdng the bi phan tan vao nhi6u td co tfnh chat giong nhau Nguoc lai neu sd td qua ft thl nhieu don vi co tfnh chat khac nhau se bi phan vao cung mot to lam cho moi ket luan rut ra sau nay kem chfnh xac Neu goi K la sd td can thiet thi co the xac dinh bang cong thuc xap xi sau:

K = 3,322 Ign + 1Trong do: Ign - Lo-ga-rit co sd 10 cua n

n - Tdng sd lan quan sat

Sau khi xac dinh sd to can thiet, tfnh do ldn cua moi td:

h — m a x m i n

KTrong do: h - Do ldn moi td

Chuang 2: Cac phitcrng phap trinh hay so lieu tliong ke 23

xnlax, xmln - Gia tri lan nhat va nho nhat trong so tat ca cac gia tri cac luong bien x, ma ta quan sat duoc

Viec xac dinh tan so cua m6i t6 duoc tien hanh tuong tu nhu trong trudng hop doi vdi luong bien rdi rac tuc la lan luot dein cac gia tri luong bien thuoc tung to Nhung gia tri nam vao ranh gidi cua hai to li6n nhau tuy theo quy udc ma gia tri do xep vao to trudc hay to sau

2.1.3 Nhung yeu cau ddi vdi viec xay dung bang thong ke

- Quy mo bang thong ke khong nen qua ldn (qua nhieu to hoac qua nhieu chi tieu giai thfch) Khi co nhifiu tieu thuc can phan to co nhiSu chi tieu giai thfch thi nen tach ra xay dung mot

sd bang thong ke

- Cac tieu de, tieu muc trong bang thong ke phai duoc ghi chfnh xac, day du, ng&n gon va dd hieu

- Cac chi tieu giai thfch trong bang thong ke can duoc s^p xep theo thu tu hop ly, phu hop vdi muc dfch nghien cuu Cac chi tieu co lien he vdi nhau nen s£p xep gan nhau

- Cac o trong bang thong ke dung de ghi cac con sd thong ke Neu khong co sd lieu de ghi vao mot hoac mot sd o nao do thi dung cac ky hieu theo quy udc

Trong bang thong ke phai dung don vi tfnh cu the cho tung chi tieu Neu tat ca cac sd trong bang co cung don vi thi don vi tfnh ghi d dau bang Neu cac chi tieu co don vi tfnh khac nhau thi don vi tfnh ghi ngay dudi tieu muc

Dudi bang thong ke can ghi ro nguon tai lieu su dung va cac chi tiet can thiet ma khong the hien duoc trong bang thong ke

24 Thong ke va Ung dung trong Bi(u chinh \ ien tliong

2.2 TRINH BAY SO LIEU BANG DO THI

2.2.1 Y nghla va tac dung cua do thi

Do thi thong ke la cac hinh ve hoac dudng net hinh hoc dung

de mieu ta co tfnh chat quy uoc cac tai lieu thong ke Vi du co tai lieu x i toe do phat trien doanh thu kinh doanh BCVT cua mdt doanh nghiep nhir sau:

Nam 2002 dat 13.177,80 ty dong = 100%

Nam 2003 dat 15.294,04 ty dong = 116,59%

Nam 2004 dat 18.617,15 ty dong = 121,73%

Voi tai lieu tren, de’ dd thay, dd hieu sir phat trifen doanh thu phat sinh, ngirdi ta co the dung hinh ve sau:

Toe do phat trien (%)

Chuang 2: Cac phuang phap trinh hay so tieu tliong ke 25

Do thi thong ke co may dac diem sau:

- Do thi thong ke sir dung con so ket hop vdi hinh ve, dudng net va mau sac de trinh bay va phan tfch cac dac trung sd luong cua hien tuong Vi vay ngudi xem khong mat nhi£u thdi gian doc con sd ma van nhan thuc duoc van d6 chu yeu mot cach d ! dang, nhanh chong

- Do thi thong ke chi trinh bay mot cach khai quat cac dac diem chu yeu ve ban chat va xu hudng phat trie’n cua cac hien tuong

Do cac dac diem neu tren, do thi thong ke co tfnh ph6 cap,

co sire hap dan va sinh dong, lam cho ngudi hieu biet ft ve thong

ke vSn llnh hoi duoc van de chu yeu mot cach de dang

Phuong phap do thi thong ke duoc ung dung rong rai trong nghien cuu, nham muc dfch hinh tuong hoa:

- Sir phat trign cua hien tuong qua thdi gian;

- Ket cau va bien dong cua ket cau qua hien tuong;

- Trinh do pho bien cua hien tuong;

- Sir so sanh giua cac muc do cua hien tuong;

- Moi lien he giua cac hien tuong ;

- Tinh hinh thuc hien ke hoach

Ngoai ra, do thi thong ke con duoc coi la mot phuong tien tuyen truyen, mot cong cu dung de bieu thi cac ket qua san xuat

2.2.2 Cac loai do thi thong ke

Can cu theo noi dung phan anh, ngudi ta co the phan chia do thi thong ke thanh cac loai sau:

- D6 thi so sanh;

26 Thong Ice va tfng clung trong Bifu chinh \ ien thong

- Do thi phat trien;

- D6 thi ket cau;

- Do thi hoan thanh ke hoach;

- Do thi lien he;

- Do thi phan phoi

Can cur vao hinh thuc bieu hien, nguoi ta co the phan chia thanh:

- Bieu do hinh cot;

- Bieu do tuong hinh;

- Bieu do dien tfch;

- Do thi dudng gap khuc

Tiiy theo noi dung can phan anh va trudng hop cu the de’ lira chon cac hinh thuc bieu hien phu hop

2.2.3 Yeu cau ddi vdi viec xay dung do thi thong ke

Mot do thi thong ke phai dam bao cac yeu c^u la chinh xac, d<! xem, d l hieu; ngoai ra con phai the hien tfnh tham my cua d6 thi, cho nen khi xay dung do thi thong ke can thuc hien cac yeucau sau:

- Lira chon loai do thi cho phu hop vdi noi dung, tfnh chat cac sd lieu can di£n dat De dam bao nhung yeu cau tren, can chu

y den cac yeu td cua do thi, quy mo, cac ky hieu hinh hoc hoac cac hinh ve, he toa do, thang va ty le xfch, phan giai thfch

- Xac dinh quy mo do thi cho thfch hop Quy m o cua do thi duoc quyet dinh bdi chieu dai, chi£u cao va quan he ty le giura

02 chieu do Quy mo cua do thi ldn hay nho con phai can cu vao muc dfch su dung Quan he ty le giua chieu cao va chieu dai cua

do thi tliong thudng duoc dung tir 1 : 1,33 den 1 : 1,50

Clitorng 2: Cue plufc/ng phap trinh bay s d licit tliong ke 27

- Cac ky hieu hinh hoc hoac hinh ve quyet dinh dang cua do thi Cac ky hieu hinh hoc co nhieu loai nhu: cac chain, cac dudng thang hoac cong, cac hinh cot, hinh vuong, hinh chu nhat, hinh tron v.v Cac hinh ve khac tren do thi cung co the thay doi nhieu loai tuy theo tinh chat cua hien tuong nghien cuu Viec lira chon cac ky hieu hinh hoc hoac hinh ve cua do thi la van de quan trong, vi mdi hinh co kha nang difin ta rieng, nhu khi can bieu hien ket cau thanh phan thdi gian quay vong toa xe co the ve cac hinh cot hoac cac hinh tron (co chia thanh cac hinh quat)

- He toa do giup cho viec xac dinh chinh xac vi tri cac ky hieu hinh hoc tren d6 thi Cac do thi thong ke thudng dung he toa

do vuong goc Tren he toa do vuong goc, true hoanh thudng duoc dung de bidu thi thdi gian, true tung bieu thi tri sd cua chi tieu Trong trudng hop phan tfch moi lien he giua hai tieu thuc, thi tieu thirc nguyen nhan duoc ghi tren true hoanh, tieu thuc ket qua duoc ghi tren true tung

- Thang va ty le xfch giup cho viec tfnh chuyen cac dai luong len do thi theo cac khoang cach thfch hop Ngudi ta thudng dung cac thang dudng thang, duoc phan theo cac true toa do, cung co khi dung thang dudng cong nhu thang tron (d do thi hinh tron) duoc chia thanh 360" Cac thang ty le co the’ co khoang cach bang nhau hoac khong bang nhau Cac thang ty le co cac khoang cach khong bang nhau chi dung de bieu hien cac toe do khi khoang bien thien cua cac muc do qua ldn ma ngudi ta chi chu y den bien dong tuong doi ciia chung

- Phai giai thfch ten do thi, cac con sd va ghi chu doc theo thang ty le, cac con sd ben canh tirng bo phan ciia dd thi giai thfch cac ky hieu quy udc can duoc ghi ro, ngan gon, d£ hieu

Chuang 3

3.1 SO TUYET DOI

3.1.1 Khai niem va y nghla cua so tuyet doi

Trong thong ke, so tuyet doi bieu hien quy mo, khoi luong hien tuong trong dieu kien thoi gian va khong gian cu the’

So tuyet doi trong thong ke co the bieu hien so dan vi cua tong the’ hay bo phan (So doanh nghiep, so cong nhan) hoac cac tri so cua mot tieu thuc hay chi tieu thong ke nao do (khoi luong san pham dich vu, tdng chi phi san xuat BCVT)

So tuyet ddi co y nghla quan trong doi vdi cong tac quan ly kinh te nhu sau:

- Thong qua sd tuyet ddi co the nhan thuc duoc cu the ve quy

mo, khoi luong cua hien tuong nghien curu, kha nang tiem tang va ket qua dat duoc ve su phat trien kinh te xa hoi

- Sd tuyet ddi la c a sd dau tien de phan tich thong ke va la ca

sd d6 tinh cac loai chi tieu thong ke khac nhu sd tuong doi, sd binh quan

- La can cur de xay dung ke hoach va chi dao thuc hien ke hoach

3.1.2 Dac diem cua sd tuyet doi

Sd tuyet ddi trong thong ke bao gid cung phai mang mot noi dung kinh te nao do trong thdi gian va khong gian cu the co

Cliifang 3: Cac muc do cua hien tuong thong ke 29

nghla la so tuyet doi trong thong ke phai phan anh diroc noi dung gl? Cua don vi nao? Khi nao?

So tuyet doi trong thong ke phai duoc xac dinh qua di£u tra

va tong hop thong ke, no khong phai la con so lira chon tuy y, no duoc xac dinh thong qua mot hoac mot so phep tfnh toan

3.1.3 Phan loai so tuyet ddi

Tuy theo tfnh chat cua hien tuong nghien curu, ngudi ta co the phan biet hai loai sd tuyet ddi sau:

3.1.3.1 So tuyet doi thdi ky

Sd tuyet ddi thdi ky la sd tuyet ddi phan anh quy mo, khoi luong cua hien tuong trong mot do dai thdi gian nhat dinh No duoc hinh thanh thong qua sir tfch luy v& luong cua hien tuong trong suot thdi gian nghien cuu

Vi du: Doanh thu kinh doanh cac dich vu BCVT nam 2004 la 30.662,77 ty dong; tdng sd may dien thoai tren mang hien co den

31 thang 12 nam 2004 la 9.906.091 may

Cac sd tuyet ddi thdi ky cua cung mot chi tieu co the cong lai vdi nhau de co tri sd cua thdi ky dai han Thdi ky cang dai, tri sd cua chi tieu cang ldn

3.1.3.2 So tuyet ddi thdi diem

Sd tuyet ddi thdi diem la sd tuyet ddi phan anh mat luong cua hien tuong nghien cuu tai mot thdi diem nhat dinh Vdi sd tuyet ddi thdi die’m thi khong the cong lai vdi nhau vl khi cong lai chung khong phan anh duoc noi dung kinh te nao

30 Tliong ke va ung clung trong Bitu cliinli \ ien thong

Vi du: Khong the cong so lao dong hien co tai hai thoi diem

la 01/4/2003 va 01/4/2004

So tuyet doi thoi diem chi phan anh tinh hinh cua hien tuong tai mot thoi diem nao do, trudc va sau thoi diem trang thai cua hien tuong nay co thd khac nhau Muon co so tuyet doi thoi diem chinh xac phai quy dinh thdi diem hop ly va phai td churc dieu tra kip thdi

3.1.4 Don vi tinh sd tuyet ddi

Trong thong ke, cac sd tuyet ddi deu co don vi tinh cu the de’ bieu thi noi dung cua hien tUOTig nghien cuu Tuy theo tinh chat cua hien tuong va muc dich nghien cuu, ngudi ta co the’ sir dung cac don vi tinh khac nhau nhu sau:

Don vi tit nliien: La don vj tinh phu hop vdi dac diem vat ly cua hien tuong nhu cai, con, chiec hoac thdi gian (phut, gid, ngay ) Trong nhidu trudng hop phai dung don vi kep nhu mat

do dien thoai (may/100 dan)

Don vi thdi gian: Thudng dung de tinh luong lao dong hao phi san xuat ra nhung san pham dich vu khong the’ tdng hop hoac

so sanh vdi nhau bang don vi tinh toan khac, hoac nhung san pham dich vu phuc tap do nhieu ngudi thuc hien qua nhi£u giai doan khac nhau

Don vi tien te (\'ND, USD, EURO, ): duoc sir dung rong rai nhat de bieu thi gia tri ciia san pham dich vu No giup cho viec tdng hop va so sanh nhi£u loai san pham co gia tri sir dung va do ludng khac nhau Tuy nhien do gia ca luon thay ddi nen don vi tien te khong co tinh chat so sanh duoc qua thdi gian De: khac

CliUf/ng 3: Cac mite do cua hien tuong thong ke 31

phuc nhirgc diem nay, nguoi ta phai dung “gia co dinh” 6 thdi gian nao do

Vi du: Doanh thu khoi hach toan phu thuoc Tong Cong ty BCVT Viet Nam nam 2004 so vdi nam 2003 bang 122,66% Cung co the so sanh cac muc do khac loai nhung co lien quan vdi nhau nhu mat do dien thoai, sd dan phuc vu cua mot buu cuc

3.2.1.2 Y nghla

Trong thong ke, sd tuong ddi co y nghla quan trong No la mot trong nhung chi tieu phan tich thong ke Neu nhu sd tuyet ddi chi khai quat duoc ve quy mo khoi luong cua hien tuong nghien cuu, thi sd tuong ddi cho phep phan tich dac diem cua hien tuong, nghien curu cac hien tuong trong moi quan he so sanh vdi nhau

Trong thong ke, sd tuong ddi phan anh cac mat sau:

- Sd tuong ddi cho biet ket cau cua hien tuong;

- Bieu hien moi quan he giua hai chi tieu;

32 Thong ke vd ung dung trong Biru chinh Vien thong

- Bieu hien trlnh do phat trien cua hien tuong (so sanh thirc hien giura cac nam);

- Trlnh do ph6 bien cua hien tirong (ban kinh phuc vu, mat

do dien thoai );

- Giup ta kiem tra danh gia tinh hinh thirc hien ke hoach;

- Di sau phan tfch so sanh dac diem cua hien tuong va giu bi mat so tuyet doi

3.2.2 Dac diem cua so tuong ddi

Trong thong ke sd tuong ddi khong phai la con sd true tiep thu duoc qua dieu tra ma la ket qua so sanh giua hai sd tuyet ddi

da co VI vay m6i sd tuong ddi phai co goc de so sanh (goc so sanh goi la chi tieu goc) Tuy theo muc dich nghien cuu ma ngudi

ta chon goc so sanh cho phu hop

Vi du, de bieu hien su phat trien cua hien tucmg theo thdi gian thi goc la muc do ky trudc; de bieu hien ket cau thi goc la muc do t6ng the’, de’ bieu hien muc do hoan thanh ke hoach thi goc la muc do ke hoach

Trong thong ke sd tuong ddi co the bieu thi bang lan hoac phan tram (%), phan nghin (% o ).

3.2.3 Cac loai so tuong ddi

Can cu vao noi dung kinh te ma sd tuong ddi phan anh thi sd tucmg ddi duoc chia lam 06 loai nhu sau: Sd tuong ddi dong thai,

sd tuong ddi hoan thanh ke hoach, sd tuong ddi nhiem vu ke hoach, sd tuong ddi ket cau, sd tuong ddi so sanh, sd tuong ddi cudng do

C huang 3: Cac mifc do cua liien tuong thong ke 33

3.2.3.1 So tuong doi dong thdi (toe do phat trien, chi so phat trien)

So tirong doi dong thai bieu hien sir bien dong \6 muc do cua hien tuong nghien cuu qua thoi gian No duoc xac dinh bQng cach

so sanh hai muc do cua chi tieu cung loai nhung khac nhau \6

thdi gian, duoc bieu hien bang so lan hoac so phan tram

Trong do: y, - Muc do cua hien tuong ky nghien cuu (ky bao cao);

y„ - M fc do cua hien tuong ky goc;

tj, - Sd tuong ddi dong thai

Muon co sd tuong ddi dong thai chinh xac can dam bao tinh chat so sanh duoc giua cac muc do cua ky bao cao va ky goc, tuc

la phai dam bao giong nhau ve noi dung kinh te, v t phuong phap tinh va don vi tinh, ve pham vi va do dai thdi gian ma muc do phan anh

3.2.3.2 So tuong doi ke hoach

Sd tuong ddi ke hoach duoc dung de lap va kiem tra tinh hinh thuc hien ke hoach x t mot chi tieu nao do, co hai loai sd tuong ddi ke hoach:

giua mure do thuc te dat duoc trong ky so vdi muc do ke hoach da d6 ra cua chi tieu kinh te nao do

y kh

34 Thong ke va ung dung trong Bifu chinh \ ien tliong

y, - Mure do thirc te cua ky bao cao;

thlkh - So tuong doi ke hoach

le giua muc do can dat toi cua chi tieu kinh te nao do trong ky ke hoach so vdi muc do thuc te ciia chi tieu do d ky goc Nhu vay sd tuong ddi nhiem vu ke hoach phan anh muc tieu can dat toi ciia don vi

h o s e t „ l h = I “ L x 1 0 0

Trong do: tnvkh - Sd tuong ddi nhiem vu ke hoach;

Giua sd tuong ddi dong thai, sd tuong ddi hoan thanh ke hoach, sd tuong ddi nhiem vu ke hoach ciia cung mot chi tieu, cung mot thdi gian co quan he nhu sau:

*(]! = ^nvkh X ^hikh

Quan he nay duoc van dung de tinh mure do chua biet khi da biet cac muc do kia

3.2.3.3 So tuong doi ket cau

So tuong ddi ket cau phan anh ty trong ciia moi bo phan cau thanh trong mot tong the Qua chi tieu nay co the phan tich duoc dac diem cau thanh ciia hien tuong

So tuong ddi ket cau duoc tinh bang cach so sanh tri sd tuyet ddi ciia chi tieu ciia tung bo phan so vdi tri so tuyet doi cua chi tieu ciia ca tdng the No thudng duoc bieu hien bang lan hoac so phan tram

Chitting 3: Cac mice do cua hien titang thong ke 35

Trong do: ybp - Tri so tuyet doi cua chi tieu cua bo phan;

y „ - Tri so tuyet doi cua chi tieu cua t6ng the;

tkc - So tuong doi ket cau

Muon tinh so tuong doi ket cau chinh xac phai phan biet duoc cac bo phan co tinh chat khac nhau trong tong the nghien cuu, co nghla la phai phan to chinh xac, tuc la phai dua vao phuong phap phan to thong ke

3.2.3.4 So tuong doi so sanh

So tuong doi so sanh bieu hien quan he so sanh giua cac hien tuong cung loai khac nhau v6 khong gian So tuong doi so sanh con bieu hien su so sanh giua cac bo phan trong cung mot t6ng the, khi so sanh nguoi ta lay mot bo phan nao do lam goc roi dem cac bo phan khac so sanh vdi no

3.2.3.5 So tuong ddi cu&ng do

Bieu hien trinh do ph6 bien cua hien tuong nghien cuu trong di^u kien lich sir nhat dinh, no duoc xac dinh bang cach so sanh chi tieu cua hai hien tuong khac nhau nhung co lien quan voi nhau Muc do cua hien tumig ma ta can nghien cuu trinh do ph6 bien duoc dat o tu so, con muc do cua hien tuong co lien quan duoc dat 6 m iu so Hinh thuc bieu hien cua so tuong doi cudng

do la don vi kep do don vi tinh cua tu so va mau so hop thanh

Vi du: Mat do dien thoai tren 100 dan

= So may dien thoai x 100/T6ng dan so (may/100 dan)

36 Thong ke va ung dung trong Biru chinh, Vien thong

3.3 SO BINH QUAN

3.3.1 Khai niem so binh quan

So binh quan trong thong ke la loai chi tieu bieu hien mure do dien hinh theo mot tieu thirc hoac chi tieu thong ke nao do ciia mot tdng the’ bao gom nhieu don vi ciing loai

Mot tong the thong ke thudng bao gom nhieu don vi, cac don

vi nay co ban la giong nhau nhung bieu hien cu the x i mat luong theo cac tieu thuc nao do thudng chenh lech nhau Nhung chenh lech nay do nhieu yeu td, ngoai cac nguyen nhan chung quyet dinh dac diem co ban ciia hien tuong, con co nhung nguyen nhan rieng anh hudng toi timg don vi Khi nghien cuu tdng the’ thong ke khong chi neu cac dac diem rieng biet ciia timg don vi, ma can tim mot chi tieu co kha nang mo ta mot cach khai quat dac diem chung, di^n hinh nhat ciia hien tuong Muc do do chinh la sd binh quan

Vi du khi so sanh thu nhap ciia lao dong trong cac don vi Buu dien khong the lay tien luong ciia bat ky mot nhom cong nhan nao do lam dai dien Bdi vi tien luong ciia cac nhom cong nhan la khac nhau do trinh do, do dieu kien lam viec, sure khoe

Do do co the lay tien luong binh quan ciia tat ca cac cong nhan trong mot don vi de’ so sanh x i muc do thu nhap ciia cac don vi vdi nhau

3.3.2 Y nghla cua sd binh quan

Sd binh quan co tinh tdng hop va khai quat cao chi can mot tri sd la sd binh quan co the neu len muc do chung nhat, phd bie'n nhat ciia tieu thuc nghien cuu No khong ke’ den chenh lech thuc

te giua cac don vi tdng the Sd binh quan khong bieu hien mure do

C huang 3: Cac muc do cua hien tuong tliong ke 37

ca biet ma bieu hien muc do tinh chung nhat cua cac don vi tdng the

Do so binh quan bieu hien dac diem chung cua ca tdng the nghien cuu cho nen nhung net rieng biet co tinh chat ngSu nhien cua tung don vi ca biet bi loai tru, tuc la so binh quan da san bang moi chenh lech giua cac don vi tdng the v& luong bien cua tieu thuc nghien cuu Su san bang nay chi co y nghla ldn khi tinh cho mot sd kha nhiSu don vi

Sd binh quan co vi tri quan trong trong ly luan va trong cong tac thuc te No duoc su dung de:

- Neu len dac diem dien hinh cua hien tuong kinh te xa hoi

sd ldn trong dieu kien thdi gian va dia diem cu the;

- Dung de so sanh cac hien tuong khong cung quy mo (co the so sanh ket qua cua hoat dong san xuat kinh doanh cua 02 don vi A, B, co the’ 02 don vi nay co sd von khac nhau, co sd lao dong khac nhau nhung co the so sanh nang suat lao dong binh quan cua 02 don vi);

- Co the dung de nghien cuu sir bien dong cua hien tuong theo thdi gian, nham thay duoc xu hudng phat trien co ban cua hien tuong sd ldn, nghla la cua dai bo phan cac don vi

- Sd binh quan duoc dung trong cong tac lap ke hoach, phan tich thong ke

3.3.3 Cac loai sd binh quan trong tliong ke

Trong thong ke co rat nhieu loai sd binh quan va khi sir dung loai nao can can cu vao dac diem nguon tai lieu s5n co, muc dich

38 Tliong ke va ung dung trong Biru cliinli Vien thong

nghien curu va y nghia kinh te xa hoi cua s6 binh quan So binh quan duoc phan thanh hai nhom:

- Nhom 1: Cac so binh quan duoc tfnh tir tat ca cac lirong bien bang cach chia deu tdng cac luong bien cho so don vi co luong bien do Nhom nay bao gom sd trung binh cong, trung binh nhan, trung binh didu hoa

- Nhom 2: Sd binh quan chuyen dung de mo ta dac trung phan phoi cac don vi ciia tdng the theo tri sd tieu thurc nghien cuu Nhom nay gom co mot va trung vi

3.3.3.1 So binh quan so hoc (Trung binh cong)

Sd binh quan sd hoc con goi la sd trung binh cong duoc xac dinh bang cach dem chia tdng luong bien ciia tieu thirc cho tdng

sd don vi tdng the

* So trung binh cong gian don

No duoc sir dung trong trudng hop mdi luong bien chi xuat hien mot lan, cong thirc tinh nhu sau:

n

_ _ x , + x 2 + x , + + x n ^ S x>

Trong do: xr Luong bien ciia tieu thirc ciia don vi thu i;

x - Sd trung binh ciia tdng the;

Chitong 3: Cac m uc do cua hien tuong tliong ke 39

luong bien x, vdi tan so fj tuong ting, sau do cong lai va dem chia cho so don vi tong the:

x,fj - Goi la gia quyfin

* Cac dang dac biet cua so trung binh cong gia quyen

khoang cach to

Trong trudng hop m6i td co mot pham vi luong bien, can co luong bien dai dien de lam can cur tinh toan va luong bien dai dien la cac trj sd giua:

x la tri sd giua cua to thur i

xiniin, ximax la gidi han dudi, gidi han tren cua td i

m

X*'fi

x = ^ -m

If,

40 Thong ke va ring dung trong Bifu chinh, Vien tliong

Trong trudng hop nay, so trung binh cong chung se la so trung binh cong gia quyen cua cac so trung binh cong to, trong

do quyen so la sd don vi cua moi td:

XV,

X = 1 = 1

I f ,i=lTrong do: X; - La sd trung binh cong cua tieu thurc cua td thu i;

f, - La tan sd cua td thur i;

m - La sd td

don vi tdng the’ cua mdi td:

De tmh sd binh quan cong nhanh chong can biet cac tfnh chat cua chung

Tinh chat 1: Neu dem tat ca cac luong bien x, cong them (hoac tru di) mot sd a bat ky thi sd binh quan tfnh duoc cung se tang them (hoac giam di) mot tri sd bang a

S ( x , ± a ) x f , = _ ± a

I f ,