Thống kê và ứng dụng trong bưu chính, viễn thông

GS.TS.NGLTT BUI XUAN PHONG
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UYEN
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I r N H A X UA T B AN BU U D IE N
THONG KE VA UI\IG DUNG
TRONG BUU CHlNH, VIEN THONG
GS.TS.NGUT BUI XUAN PHONG
THONG KE V A UNG DUNG
TRONG BUU CHiNH, VIEH THONG
NHA X U A T BAN BlTU DIEN
Ha Noi, thang 9 - 2005
Ma so: KK 06 HM 05
LOl NHA XUAT BAN
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
cuon sach “Thong ke va img dung trong Bitn chinh, Vien thong"
do GS.TS. NGUT Bui Xuan Phong - Pho Truong khoa Quan tri
Kinh doanh. Hoc vien Cong nghe Buu chfnh Viin 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 xuat ban Biru d ien, 18 Nguyen Du. Ha Noi: Dien thoai:
04. 9430202; Fax: 04. 9431285.
Tran trong cam on./.
Ha Noi. tlidng 9 nam 2005
NHA XUAT BAN BUU DIEN
Chiwng 1
M 0 T SO KHAI NIEM VE THONG KE
1.1. THONG KE HOC 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 thu hai, 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 (mat 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 KE
Thong 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: Mot 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. Ching 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’. Don 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 THl/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 muc dfch
Clufang / : Mot 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 ien, 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 may 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.
Chuang I : Mot so kliai niem ve tliong ke
15
- Thang do thu 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 ca sa va Trung hoc pho thong. Trung
hoc pho thong lion Trung hoc ca sa, Trung hoc ca 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 THONG 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 mot tieu thuc.
Trong trudng hop nay bang thong ke co nhung dang sau:
Bang 2.1
Tieu thurc A,
Tan so fi
Tan su a t d,
A,
f.
d,
a 2
^2
d,
\
d.
Cong
I f i
I d , = 1
Cot "Tieu thuc A," ung vdi m6i dong ta ghi cac bi£u hien cua
tieu thuc A (i = 1,2, k).
Cot "Tan sd f," ghi sd lan quan sat duoc ung vdi timg bieu
hien A,.
Chuang 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.
Bang 2.2
Biru dien
Doanh thu f> (Trieu dong) Tan suat d^
Tinh A
4.000 0,20
Tinh B
2.400
0,12
Tinh C
11.000
0,55
Tinh D 2.600
0,13
Cong
20.000
1
Trudng hap th u hai: Xet dong thdi bieu hien cua 02 tieu tliuc
lien quan.
Gia sir ngoai tieu thuc A, con xet d6ng thoi tieu thuc B voi
nhung bieu hien B, (j = 1, 2, , /). Khi do bang thong ke co
dang sau:
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 A
1.500 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 B
1.000 trieu dong cua Buu dien tinh C
- Doanh thu dien thoai dudng dai la:
400 trieu dong cua Buu dien tinh B
1.500 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 D
Neu 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,
Bull pham thuting
3.500 0,175
Biru pham ghi so
2.500 0,125
Chuyen phat nhanh
1.500
0,075
Dien thoai dirdng dai
1.900
0,095
Dien thoai noi hat
8.000
0,400
Dien thoai quoc te
2.600
0,130
Cong 20.000 1
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
theo bi/u

dien tinh
Biaj
dien tinh
Thudng
Ghi so
EMS
Di/dng
dai
Noi hat
Quoc
te
A
3.500
500
4.000
B
1.500
500
400
2.400
C
500
1.000
1.500
8 000
11.000
D
2 600
2.600
Cong theo loai

dich vu
3.500 2 500 1.500
1.900
8 000
2 600
20.000
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.
Bang 2.6
Cac lirdng bien x{
Tan so f,
Tan suat d,
x,
f,
d,
x2
u
X,
f,
d
Xk
fk d.
Cong
W

ii
c
I d , = 1
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:
30 38
34
25 35 33 27
25 33
30
33 30 35 34 27
25 30 37
28 30
35
28 33
28 30 33 28 27
30
28
33
27 30
35 28 34 30
35 38 34
34

33
34
30 38 33 33
33 34
30
Vdi mau bieu 2.6 ta co the trinh bay sd lieu doanh thu nhu sau:
Bang 2.7
Doanh thu (trieu dong)
x.
So buu cuc
fi
Tan suat
d,
25 3
0,06
27
4
0.08
28
6
0,12
30
11
0,22
33
10
0,20
34
8
0,16

35
5
0,10
38
3
0,06
Cong
50
1
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 ghep'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 + 1

Trong 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:
\ — v
h — max min
K
Trong 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. V i du co tai
lieu xi 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 (%)
150
100
50
2002 2003
2004
Nam
Trong hinh ve tren, cac cot dung noi len sir phat trie’n cua
doanh thu phat sinh cua doanh nghiep qua cac nam 2002. 2003,
2004. Voi cung mot b& rong, cac chieu cao khac nhau cua m6i
hinh cot cho ta mot nhan thuc co so sanh cu the v6 su phat trie’n
cua hien tuong nghien cuu. Cac hinh ve goi la bidu d6 thong ke,
con phuong phap dung cac hinh ve de mieu ta hien tuong qua cac

con so thong ke goi la phuong phap do thi thong ke.
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;