bài giảng thống kê y tế phần 1

C K .0 0 0 0 0 4 5 7 6 2

B

A

UXTNG CAN BO QUAN LY Y TE
BO MON THONG KE - TIN HQC

. I

G

I

A

N

G

A

THONG KE Y TE
(DUNG CHO BAC ST CHUYEN KHOA SAU DAI HQC
CHUY£ n NGANH Y TE CONG C0NG)

NHA XUAT BAN Y HOC
■ _ J

T R l/d N G CAN BO QUAN LY Y TE
Bo m on Thong ke - Tin hpc

Bai giang

THONG KE Y TE
DUNG CHO BAC SY CHUYEN KHOA SAU DAI HOC
CH UYEN NGANH Y T E CONG CONG

NHA XUAT BAN Y HOC
HA NOI - 1997


B a n bien soan:

T hacsl

: NGUYEN D l/C AN

B dcsl

: TRAN THI TUtJNG VY

B dc si

: TRAN THI LlTU

Cit n h a n :

PHAN VU D lfiM HANG

Ldl NOI DAU
Tap bai giang nay dugc bien soan voi muc tieu la trinh bay nhirng van de c a
s a cua Thong ke y te, diroc ung dung trong Nganh. Doi tirgng cua tap bai giang
chu yeu la cac hoc vien chuyen khoa cap mot cua Tnrong Can bo Quan ly Y te.
Nhirng bai giang nay da ft nhidu dugc Bo mon Thong ke dua vao giang day nhi6u
nam cho cac lop bac sy chuyen tu va chuyen khoa cap mot 6 trucmg nay. Vc noi
dung khoa hoc, cac bai giang dugc xem xet. sira chua va b6 sung ciin than; c a c vi
du va bai tap gSn ly luan vo'i thu'c ti6n cua Nganh Y te Viet Nam.
Noi dung cua tap bai giang nay dugc chia thanh ba phan:
• Phfin thir nhat: Thong ke mo ta.
• Phan thu hai: Suy luan thong ke.
• Ph^n thu' ba: Bo chi so thong ke y te co ban va phan loai thong ke
Quoc te benh tat Ian tlur X.
Tap bai giang gio'i thieu voi cac hgc vien cua Truong Can bo Quan ly Y te
co su tham khao cua cac tai lieu:
1. Betty R. Kirkwood. Essentials
Scientific Publications, 19S8

of

Medical

Statistics.

Blackwell

2. Phirong phap nghien cuu khoa hoc y hoc, Hoc vien quan y, Nha xuat ban
quan doi nhan dan, Ha Noi, 1995.

3. Dr. J.F . Osborn. Intensive Course in Medical Statistics. London School
o f Hygiene and Tropical Medicine. Centre for Population Studies,
Department o f Epidemiology and Population Sciences, 1991.
4. Phuong phap nghien cuu y te. To chii'c Y te The gioi, Khu vuc l ay Thai
Binh Duong, Manila, 1992. Vien Vc sinh Dich td hgc. Ha Noi, 1993.
5. PGS, PTS. Pham Huy DCing. Chi so y te cho tuyen co so' xa, phuong.
Khoa hgc y te cong cong Viet Nam, Truong dai hgc Y Ha Noi, 1990.
va mot so tai lieu khac.
Chung toi hy vgng rang voi noi dung nhu tren, tap bai giang nay co the: phu
hop voi cac hgc vien chuyen khoa cap mot, chuyen nghanh y te cong cong cua
Truong C B Q L Y T Ha Noi.
Vi kien thiic va kinh nghiem con han che, chac chdn rang tap bai giang nay
con nhi6u thieu sot. Chung toi rat mong nhan dugc nhung y kien phe binh va dong
gop cua ban trong va ngoai nganh de tap bai giang ngay cang chat lugng hon v6
n6i dung, phong phu hon vt hinh thuc, da dang hon v6 cac loai bai tap .

Xin chan thanh cam on.
Ha Noi, ngay I thdng 7 nam 7 9 9 7

Tran Thi Liru



THONG KE Y TE
MUC
TIEU MON HOC
•
•
♦

Trinh bay dudc cac so lieu nghien ctiu bAng bang thong ke, do thi, bieu do va
cac chi so thong ke thich hdp.

♦ Kiem dinh dtfdc so trung binh, so' titdng doi bang test t , x '

tieu chuan hoa .

♦ Danh gia dudc mol lien he tUdng quan gitia cac hien tadng nghien cCtu .
♦ Trinh bay dudc viec phan loai thong ke quoc te" cac benh tat (sUa doi lan thuf
mUdi) va cac qui tac hu6ng dan ma hoa tu vong .
♦ Phan tich dudc cac so lieu thong ke y te.
♦ Biet xay dung va to chiic cac nghien cCfu thong ke y te

NOIDUNG
Bai 1.
Bai 2.

Do thi, bieu do thong ke y te"

Bai 3.

Phep do vi tri va do bien thien

Cac phan phoi tan so

- Trung binh, trung vi, mode
- Do bien thien, phudng sai, do lech tieu chuan, he so bien thien

Bai 4.

Xac suat, cac luat phan phoi xac suat cua dai ludng ngau nhien
- Bien co* ngau nhien - khai niem xac suat
- Dinh nghla co dien ve xac suat, dinh nghia thong ke ve xac suat
- Phan loai sU kien ngau nhien
- Phan phoi nhi thtic, phan phoi poisson, phan phoi chu^n
- Lien he giuta ba luat phan phoi
- Ung dung va tAm quan trong cua phan phoi chu&n.

Bai 5. Cac phan phoi mau va cac khoang tin cay
Bai
Bai
Bai
Bai

6. Cac phep kiem dinh co y nghia
7. Kiem dinh gia thuyet thong ke
8. Lien he tUdng quan va hoi qui
9. Phudng phap tieu chuftn hoa
- Phudng phap true tiep
- Phudng phap gian tiep

Bai 10. Thong ke tinh hinh mac benh cua nhan dan
Bai 11. Bo chi so' thong ke y te cd ban
Phu luc. Phan loai thong ke quoc te cac benh tat va cac qui t&c hu6ng d^n ma hoa
tii vong.
1


GIClI THIEU
Thong ke y te la mot mon khoa hoc ting dung, ngUdi ta da svt dung cac

phudng phap thong ke y te vao cong tac nghien ctiu y te. No la mot trong nhQng
mon khoa hoc cd sd c&n thiet cho viec dieu tra, danh gia cac van de trong y te : Tit
sinh ly hoc te bao den nghien ciiu stic khoe cong dong...v.v.
Mac du tvf lau sinh hoc da ufng dung cac phudng phap cua khoa hoc thong ke
mot cach rong rai, nhung chi trong mot vai nam gan day, thong ke y te mdi thtfc sU
la van de noi com . Su dung thong ke y te doi hoi phai dudc dao tao kien thtic ca ve
toan hoc va y hoc.
Tuy nhien de hieu va ap dung dudc cac phudng phap thong ke cd ban doi hoi
phai biet mot it toan hoc dang ke . L6p hoc chuyen khoa mot cua TrUdng Can bo
Quan ly Y te khong can biet trudc kien thtic toan hoc hoac thong ke, ma mot it kien
thiic do neu ckn se dudc gi6i thieu trong qua trinh hoc tap.
Cac phudng phap thorig ke cd ban dudc chia thanh hai ph^n chinh : Trong
ph^n thti nhat chung ta co mot tap hdp so' lieu dudc quan sat va can tom tat chung,
xay dilng chung thanh cac bang qua do co the hieu dudc de dang va mo ta dudc
nhflng dac trUng cua chung. Cac phudng phap sik dung cho muc dich nay thUdng
dudc goi la thong ke mo ta.
NgUdc l a i , chung ta co the tong quat hoa cac thong tin tren m lu quan sat. Vi
du: Co the chung ta muon ket luan rang , nhin chung dung thuoc A tot hdn dung
thuoc B cho nhiing benh nhan co chan doan dac biet , vi vay chung ta phai sU dung
cac phep thu co y nghia va cac khoang tin cay. Cac phudng phap sU dung cho muc
dich nay dudc goi la phudng phap suy luan thong ke.
Cac nha nghien cilu sinh y hoc, cac bac sy lam cong tac quan ly y te va y
te cong cong , cac nha chilc trach c&n lam gi ? chdc r&ng ho c4n mot it thdi
gian de hoc nhflng tu tUdng cd ban cua thong ke , muc dich la hieu day du y
2

nghia, cach trinh bay va cac ky hieu thong ke nhu: p, t, X’ , r ... v.v. va cac
th u at ngiJ chuyen mon khac ma ho se tim thay trong cac bao cao cung nhvt
trong cac tap chi chuyen nganh.

2


B a i l . CAC PHAN PHOI TAN SO
MUC TIEU
Hoan thanh bai 1 hoc vien co the:
• Phan loai cac bien dinh tinh , dinh ltfdng, rdi rac, lien tuc
• Chia khoang bien thien cua mot day so' lieu thanh cac khoang cach to, va
chi ro cac gia tri nao nam d khoang cach to nao.
• Cho mot tap hdp lieu ban d&u, xay dung phan phoi t&n so ,t&n suat va tan
suat tich luy
• Ve bieu do phan phoi tin so' co khoang cach to blng nhau va khong bang nhau
• Ve bieu do tin suat tich luy, va xac dinh trung vi
Trong mot cuoc dieu tra thong ke, so' lieu thu th&p thudng chua dudc sap
xep, cho ta mot hinh anh hon don, kho nhin , kho rut ra qui luat cua hien tUdng
nghien ciiu.
De trinh bay cac ket qua nghien ciiu ngUdi ta thudng dung 3 hinh thtfc: bang,
do thi hoac cac tham so' dac trung. De bieu di§n cac so lieu ro hdn c&n s£p xep
chung theo thti tu, thudng tti nho den 16n. Nhu vay ta se thay dudc tinh chat phan
phoi va tinh quy luat cua chung, dong thdi cung biet dudc do bien thien do la hieu
so cua gia tri 16n nhat va gia tri nho nhat cua day.
Neu bang so' lieu chila toan bo day so' se rat kho nhin. Thong thudng ngUdi ta
tap hdp 2 hoac nhieu gia tri quan sat vao mot to.

1. Muc dich va y nghia cua phan to thong ke.
- La can ci'i vao mot hoac mot so' dac tinh de phan chia cac ddn vi cua hien
tUdng nghien ciiu thanh cac to co tinh chat khac nhau.
- La sap xep co he thong cac so lieu ban d&u de thay ro thanh ph&n, cd cau
nhutng net gio'ng nhau, khac nhau cua hien tUdng nghien ciiu.
- Bu6c d&u chuan bi cho tinh toan phan tich sau nay

2. Mot vai y nghia.
- To: La so lifdng cac gia tri quan sat nam trong mot gidi han nhat dinh.
- Gi6i han to: Do tri so' 16n nhat va tri so be nhat cua to tao nen.
- Tri so giuta: So' trung binh cong cua 2 gicfi han to.
3


- Khoang cach to (k) ( con ky hieu la h ,d ......) la tri so cua 2 tri so giCta lien
tiep nhau.

<

.

.

„

r

- To md: La to bao gom cac gia tri nam du6i hoac tren mot gia tri gidi han. Vi
du: Tren 100 tuoi, du<3i 18 tuoi.......

3. Dac tinh phan to ( con goi la dac tinh nghien ciifu).
Moi don vi nghien ciiu co nhving dac diem (dau hieu) noi len mat liidng hay
mat chat cua ddn vi do. Nhiing dac diem lien quan den muc dich nghien ciiu goi la
dac tinh nghien ciiu.
Co 2 loai dac tinh nghien ciiu:
a. Dac tinh dinh tinh:

La nhiing dac tinh nhan thiic bang giac quan. chung dac trifng cho chat
lUdng, co tinh ch a t mieu ta , dien dat bang ldi noi, chut viet (vi du: Gi6i tinh, loai
benh, nghe nghiep.......)

,

b. Dac tinh dinh-luc/ng:

La nhufng dac tinh bieu hien bang nhiing con so' nhu can nang , chieu cao,
huyet ap........ ) la nhiing dfic tfnh co the dem dudc hoac do dudc.

4. So to va khoang cach to.
Tuy tfnh chat cua dac tinh nghien ciiu va muc dich nghien ciiu.
a. Dac tinh dinh tinh:

Neu the hien bang 2 tinh huong (vi du gi6i tinh nam , mi) hai bieu hien doi
lap (dac tinh luan phien) thi chi co hai to.
Neu the hien bang nhieu tinh huong (vi du nhu ket qua dieu tri) thi co nhieu
to. Moi loai hinh la mot to hoac ghep nhieu to nho giong nhau thanh mot to 16n.
Tu: bang so lieu ban dau ta xay diing bang phan

Xi

n,

phoi thuc nghiem hay con goi la bang phan phoi tan so'

Xi

ni

gom 2 cot cd ban:

X,

n2

Xk

nk

Cong

In , = n

- Cot 1: Ghi cac dac tinh nghien ciiu ky hieu la
Xj neu la dac tinh dinh lUdng v6i i= l,2 ,3 ........ ,k
- Cot 2 : Ghi so' lan xuat hien dac tinh nghien ciiu,
con goi la tan so, ky hieu la n, (i= l,2 ,3 ............,k)

4


Tong so cac t in so" quan sat bang tong so ddn vi nghien ciiu (ky hieu la n)
Snj = n
(E : ky hieu cua tong )
b. D ac tinh d in h lUQng:
- Dac tinh dinh lufdng rdi rac : Bieu hien bang so" nguyen ( so" benh nhan, so cd
sd dieu tri....... ). Ta ghi cac gia tri x; theo chieu tang hoac giam din vao bang phan

phoi t in so, roi ghi tan so xuat hien cua moi gia tri x, (tiic la cac tin so n, . Khi sU
bien thien ve mat lildng giuta cac ddn vi it, co vai tri so, thi moi tri so hinh thanh
mot to (so con trong gia dinh)
Khi cac tri so bien thien nhieu, so to se qua nhieu, can phai phan to co
khoang cach to, bao gom mot pham vi cac gia tri : Co gi6i han du6i cua to la tri so"
nho nhat va gidi han tren cua to la tri so' 16n nhat cua to do. Neu mot gia tri rdi vao
gidi han tren va cung la gidi han dudi cua to sau thi quy udc xep vao to sau.
- Dac tinh dinh ltfdng lien tuc : Bieu hien bang so' nguyen, so' thap phan.
Thudng ta phan to co khoang cach to deu ( k = 1, 2, 3, 5, 10, 20......). De tien viec
tinh toan, khoang cach to nen la mot so le, de tri so' giiia la so nguyen.
Co the phan to v6i khoang cach to khong deu tuy muc dich nghien ciiu (vi du :
Bien tuoi trong dieu tra dan so...)
Phan to theo khoang cach to deu thi tri so khoang cach to dudc xac dinh theo
cong thiic :
X m —Xm

xM : Tri so' 16n nhat trong day so lieu.
xm : Tri so' nho nhat trong day so' lieu.
T

: So' to dii dinh chia

Nen chon cach phan to do'i xiing : Tri so' co tan so 16n nha't d g in giuta phan
phoi va khong co to trong (ns = 0 )
Phan nhoi tan so .
Ddn gian la mot bang ghi cac gia tri co the la'y bdi mot bien va ghi tan so ling
vdi moi gia tri da diidc quan sat.

5

B a n g 1: Phan phoi ket qua xet nghiem ddm , bien dinh tinh lay gia tri:
- Soi lam am tinh
- Cay am tinh
- Soi lam am tinh, khong cay
- Soi lam hoac cay dUdng tinh
Streptomycin
T in so
Soi lam am , cay am tinh

T in suat(%)

Khong Streptomycin
T in so T in suat(%)

141

45,0

117

41,8

Soi lam am tinh, khong cay

90

28,8

67

23,9

Soi lam hoac cay dUdng tinh

82

26,2

96

34,3

Tong cong

313

100,0

280

100,0

Cac ket qua khong biet

12

17

325

297

B a n g 2: Phan phoi so tre em nam trong cac gia dinh co 8 con
So' tre nam

6

So gia dinh

T in suat(%)

0

161

0,4

1

1152

3,0

2

3951

10,3

3

7603

19,7

4

10236

26,7

5

8948

22,1

6

4948

12,8

7

1655

4,3

8

264

0,7

38495

100,0


B a n g 3: Phan phoi cac ton thudng gay nen bdi virus d§u mua trong
mang triing
So ton thudng

T in so (so mang)

0_

1

10_

6

20_

14

30_

14

40_

17

50_

8

60_

9

70_

3

80_

6

90_

1

100_

0

110 119

1

Tong cong

80

B an g 4: Phan phoi tin so' co khoang cach tuoi cua 1375 benh nhan nam m ic
ung thu phoi.
T in so

T in suat

25_

17

1,2

1,2

35_

116

8,5

9,7

45_

493

36,3

46,6

55_

545

40,2

86,2

65_74

186

13,7

99,9

Tong cong

1357

99,9

Tuoi

T in suat tich luy

Co vai phudng phap xay dung phan phoi tin so tti so' lieu ban diu :
7


1

CO

4 6 2 2 2

5

1 2 2

CO

B a n g 5: Dem khac ciu trung trong mau d duoi cua cac con chuot
2 4 1 1

1 2 6 7 3 5 5 2 2

5 5 6 2 5

1 3

1 9

1 1 2 2 4 1 1

1 2 2

1 2

1 0 3 3 4 3 1

to

CO

4 4

1 4 6 4 2 5 4 5 4 5 5 6 2

1 0

1 5 5 2 2 6

6 2

CO

4

CO

4 4 4 6

CO

5 3 2 6 4 3 3

7 4 2 6

1 3

1 5 3 3 6 8 2 0

1 0

1 5 2 2 1 9

1 1 1 5 3

1 3 6 2 3 5

Trong vi du nay chung ta se phan thanh 10 16p hoac ( 10 to), cac to danh so tu:
0,1,2 3...9 xem qua so' lieu mot lin ,phan phoi cac quan sat vao cac to va danh dau

0

////

4
7 ^

1
2

iW

-

3

7 ^
tW

7 ^
7 ^

4

tW

//

27

//

27

7 ^

20

/

16

//

17

5

im -

7 ^

6

tW

tW

7

//

2

8

/

1

9

//

2

To ta i

8

Frequency

Tally

Count

//

12

128


B an g 6 : Do day cua da (mm) do d diem giiia cd tam dau cho 121 nam gicii
11.4

15.3

9.1

18.4

10.9

4.7

9.6

20.6

10.4

20.5

22.4

14.3

11.7

11.4

12.7

18.2

15.1

14.6

25.3

11.5

13.2

7.9

12.6

13.9

1.8

11.4

27.3

16.3

13.9

13.2

11.9

20.0

13.2

9.4

18.9

10.7

14.8

17.8

10.8

16.0

15.7

17.7

13.5

11.5

11.1

9.6

15.1

13.6

13.6

8.6

6.9

19.1

18.7

10.1

16.0

20.4

7.9

16.6

18.5

16.2

17.4

18.8

12.6

22.0

9.6

11.1

15.7

23.7

13.3

4.9

8.3

20.1

15.5

23.1

10.2

10.7

15.8

17.6

21.3

16.2

14.9

9.9

9.1

9.9

9.8

8.6

11.8

9.3

14.8

17.3

9.5

13.6

12.4

9.5

14.3

25.7

12.9

22.7

12.1

10.7

16.8

11.3

11.3

11.4

5.9

10.7

14.6

19.8

25.5

7.7

18.4

7.9

7.6

23.3

9.6

8.4

9.0

30.1

10.4

8.1

12.5

B a n g 7: Bang phan phoi do day cua da

Do day cua da
4681012141618202224262830-31,9

Tong cong

Tan so
3
6
19
23
17
14
13
9
6
6
3
1
0
1

Tan suat(%)
2,5
5,0
15,7
19,0
14,0
11,6
10,7
7,4

5,0
5,0
2,5
0,8

T in su it tich luy
2,5
7,5
23,2
42,2
56,2
6,8
78,5
85,9
90,9
95,9
98,4
99,2

0,0
0,8

100,0

121

100,0

99,2

9


B an g 6 : Do day cua da (mm) do 0 diem giiia cd tam dau cho 121 nam gicii
11.4

15.3

9.1

18.4

10.9

4.7

9.6

20.6

10.4

20.5

22.4

14.3

11.7

11.4

12.7

18.2

15.1

14.6

25.3

11.5

13.2

7.9

12.6

13.9

1.8

11.4

27.3

16.3

13.9

13.2

11.9

20.0

13.2

9.4

18.9

10.7

14.8

17.8

10.8

16.0

15.7

17.7

13.5

11.5

11.1

9.6

15.1

13.6

13.6

8.6

6.9

19.1

18.7

10.1

16.0

20.4

7.9

16.6

18.5

16.2

17.4

18.8

12.6

22.0

9.6

11.1

15.7

23.7

13.3

4.9

8.3

20.1

15.5

23.1

10.2

10.7

15.8

17.6

21.3

16.2

14.9

9.9

9.1

9.9

9.8

8.6

11.8

9.3

14.8

17.3

9.5

13.6

12.4

9.5

14.3

25.7

12.9

22.7

12.1

10.7

16.8

11.3

11.3

11.4

5.9

10.7

14.6

19.8

25.5

7.7

18.4

7.9

7.6

23.3

9.6

8.4

9.0

30.1

10.4

8.1

12.5

B an g 7: Bang phan phoi do day cua da
Do day cua da
4681012141618202224262830-31,9

Tong cong

Tan so

Tan suat(%)

T^n suat tich luy

3
6
19
23
17
14
13
9
6
6
3
1

2,5
5,0
15,7
19,0
14,0
11,6
10,7
7,4
5,0
5,0
2,5

0

0,0
0,8

100,0

121

100,0

1

0,8

2,5
7,5

23,2
42,2
56,2
6,8
78,5
85,9
90,9
95,9
98,4
99,2
99,2

9


Bang 7: La bang phan phoi co khoang cach to bang nhau . Day la bien dinh
lUdng lien tuc . Khoang cach 20_ la bao gom cac quan sat tit 20,0 den 21,9 va tri
so' giiia cua khoang cach nay la 20,95. Do thi so' 1 la phan phoi tin suat tich luy. Do
thi so' 2 la mot to chiic do bieu diln cac phan phoi tin so'.
B an g 8: Phan phoi theo nhom tuoi cua nhiing ngtfdi khong co rang (chie'c rang
cuoi cung cua ho da mat)
Tuoi

So ngUdi

Khoang cach to

(n i)

n,

00

k,

11-15

1

5

0,02

16-19

7

4

1,75

20-24

21

5

4,20

25-29

35

5

7,00

30-34

40

5

8,00

35-44

58

10

5,80

45-54

28

10

2,80

55-74

10

10

0,50

Trong trUdng hdp phan to co khoang cach to khong bang nhau ta phai chu y
tinh chieu cao cua kho'i hinh chut nhat khi ve do thi . Chieu cao cua kho'i do thi la
ty so' giiia t&n so' v6i tri so' khoang cach to.

Trung vi 13,0mm

10


18

% tong so
trong m6i
khoang cach

So 2
Do thi tan so cac do day cua da

16
14
12

10

8
6 ..

4 ..
2 ..
0
6

8

10

12

14

16

18

20

22

24

26

28

30

32

Cac do day cua da (mm)

8
7 ..

So trung
binh theo
nSm cua
do tuoi

So 3
Do thi t in so cua do tuoi
mat chiec r&ng cuoi cung

6 ..
5 -4 -3 -2 -1 -0
10

i
15

20

r~
25

30

------ 1 ■
35 40 45

i------ 1— i------ 1------r
50 55 60 65 70

75

Do tuoi mat chiec rang cuoi cung
11


Bai tap
1. Xay dung bang phan phoi tin so theo tuoi cua 16p chuyen khoa mot sau:
Nam sinh

Nam sinh

Nam sinh

Nam sinh

1953

1963

1962

1958

1957

1965

1957

1954

1965

1957

1950

1958

1955

1960

1964

1950

1959

1955

1964

1949

2.
Trong mot cuoc dieu tra 54 phu nii co thai tai benh vien X dudc phong van
tien su ve tuoi va lan de cua ho ket qua du6i day :
S tt

Tuoi

S o la n de

Stt

Tuoi

So' lan de

Stt

Tuoi

S o lan de

1
2

3
4
5
6
7
8
9
10
11
12
13
14
15
16
17

20
30
33
27
35
22
31
25
40
23
32
19
37

19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35

28
38
25
22
21
27
35
21
31
20
18
36

28
30
18
34
17

18

36

19

0
2
1
0
0
2
0
0
1
0
0
1
4
0
0
2
0
1

37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54

23
24
30
25
29
30
17
18
18
31

27
32

18

0
0
1
1
1
0
0
0
4
0
0
0
3
1
0
1
0
0

0
1
0
0
1
1

0
0
1
1
3
1
0
5
1
1
0
0

28
29
33
17

Hay xay dting bang phan phoi tan so theo tuoi va lln de,
- Lan de: 0 lln , 1, va 2 lan trd len
- T u o i: < 30 va tut 30 trd len

23
36
28
25
23
37

Bai 2. DO T H I. BIEU DO THONG KE Y TE
1. Y nghia , tac dung.
- Do thi thong ke bao gom cac con so, hinh ve, dUdng net hinh hoc, mau sac
de trinh bay khai quat, co ti'nh ch&'t quy u6c cac tai lieu thong ke nham so sanh, doi
chieu , phan tich cac moi quan he, tim ra cac quy luat dac trUng so' liidng cua hien
tUdng nghien ciiu.

- Dung phudng phap do thi doi hoi it cong doc, nhan thiic de , nhanh, co tinh
chat quin chung cao , hap dan, sinh dong, la phudng tien bieu dUdng tot.

2. Qui tac chung xay dvfng do thi thong ke.
Yeu clu cua do thi phai chi'nh xac, de hieu, de xem, trinh bay my thuat.
- Qui mo : To, nho tuy muc dich su dung. Ty le chieu cao , chieu dai la 1/1,5
hoac 3/3,5.
. -

Ky hieu hinh hoc : La cac cham , dUdng thang, dUdng cong, cot, hinh vuong,
hinh chii nhat, hinh tron .....

-

He toa do vuong goc :
True hoanh bieu thi cac dac tfnh nghien ciiu.
True tung ghi cac t i n so' (n ; ) hoac cac t in suat ( co,)

- Thang , ty le xich: Thang dUdng th&ng, thang dUdng cong, thang co khoang
cach deu dan hoac khong deu (thang logarit)
-

P h ln giai thich: Ten do thi, cac con so' ky hieu quy u6c.

3. Cac loai do thi thong ke.
a. Do thi dieting day (ditdng g a p kh u c) :
Bieu dien tinh hinh phat trien cua hien tUdng nghien ciiu. Tren trUdng cua
he thong toa do vuong goc ta ghi cac gia tri cua x, hoac cac dac ti'nh nghien ciiu
tiidng ling vdi true hoanh va cac tin so' hoac tin suat tUdng ling v6i true tung. Noi
cac diem nay lai v6i nhau ta se dudc dUdng bieu dien.
b. Do thi h in h cot:
La nhiing hinh chii nhat xep lien tiep nhau (con goi la to chiic do ) . Day cac
hinh chii nhat bang be rong cua cac to. Chieu cao bang tin so hoac tin suat tUdng
ting. Day cua cac hinh chii nhat blng nhau khi khoang cach to blng nhau.

7 8G

13


Khi khoang cach to khong bang nhau thi chieu cao cua cac hinh chii nhat bang :
h, : Chieu cao cua to i
nj : Tan so' cua to i
k, : Khoang cach cua to i
Do thi hinh cot bieu hien cac chi tieu cUdng do noi len mtic do pho bien cua
hien tUdng nghien ctiu, dung cho cac phan phoi co ghep to.

c. Do thi h in h trd n :
Bieu hien ket cau cua hien tUdng nghien ciiu (thudng dung de mieu ta cac dac
tfnh dinh tinh bieu hien bang phan tram) ngUdi ta thudng doi phan tram thanh
do, cii 1% = 3" 6 (chu vi hoac dien tich hinh tron la 360 0 ). Chu vi hinh tron dtfdc
chia ty le vcii tinh hinh phan phoi cua hien tUdng nghien ciiu.

14


PHUONG PHAP TRINH BAY VA DIEN GIAI C>
LIEN Q UAN DEN SUC KHOE

BANG DO THI VA BIEU DO
I.

BANG

Mac du khong co nhiing quy tac nghiem ngat va i
cach xay dung bang, song cung co mot so nguyen tac chi
nhan nhu chuEin.

1. Bang phai cang don gian cang tot.
Lam hai hoac ba bang nho con tot hcin la mot bang l<3n <
tiet hoac bien so. Thudng ba bien so la so toi da (*o the doc du<

2. Bang phai de hieu.
a. Cac ma so, chu viet tat hoac ky hieu phai co giai t]
thich 0 cuoi trang.
b. Moi hang va moi cot phai ghi tieu de chinh xac va r
c. Cac ddn vi do lUdng dac biet dung cho so lieu phai c
d. Tieu de phai ro rang, chinh xac va dung vao van de
Cai gi" Khi nao? d dau?

3. Thong thifcfng dau de phai cach phan than ban mot
Hoac khoang trong. Trong nhiing bang nho, co the
dUdng ke doc de phan cach cac cotv

4. Neu cac so lieu khong phai la goc thi phai cho bi
chu thich.
5. Vi du dac trifng.


Hoc van cua cha

So trUdng hdp de song

Tot nghiep cao hoc

50.684

Dudi 12 nam hoc

31.774

Cong

82.458

Nguon: "Thong ke sinh tit cua my" 1968. Tap ltr81
Bang 1 co the md rong ra de bao gom phan loai dudi nGa, nhu ndi de va

b.

ngUdi dd de, trong bang 2.
B an g 2

Phan loai cac trtfdng hop de song theo I19C van cua ngvfofi cha, nOi d e
va ngtfdi dof de, bat ky bang nao, 1968.
So trUdng hdp dd bdi
Hoc van

NgUdi

T h ly thuoc
Trong

Ngoai

benh vien

benh vien

Tot nghiep cao hoc

46.606

3014

910

Dudi 12 nam hoc

14.334

3094

13.930

60.940

6.108

14.840

cua ngUdi cha

Cong

Ba dd

khac va

Cong

khong ro

570

82.458

Nguon: "Thong ke sinh tit cua My", 1968. Tap l,tr81.
c.

Viec tom tat tong ket so lieu se difdc xuc tien va ddn gian hoa bang cach

chuan bi trudc mot bang chu yeu. Trong bang nay, tat ca cac so lieu san co phai

dudc xep loai dly du. Khi viec xep loai dly du da xong, cac so lieu lien quan den
mot bien so duy nhat hoac den bat cti phoi hdp nao cua bien so' cung co the co dudc
ma khong phai clu vien den cac so lieu goc.
Tuf khuon kho bang chu yeu nhu bang 3, chung ta co the xac dinh dudc bao
nhieu ngUdi thanh thi (A), bao nhieu ngUdi nam gidi (B) va bao nhieu nam gidi

thanh pho d nhom tuoi qui dinh (C) da dudc nhap vien, v.v....
B an g 3

So ngtfdi vao bat cii benh vien nao trong hai nam 1968, xep loai theo
tuoi, ndi d va gidi tinh
16


Tuoi ti'nh
theo nam
< 1
1- 4
5 - 9
10 - 14

Cong

Nong thon
T h anh thi
Cong Nam
Nam m
Cong Nam m

Cong

Nut

Cong

C

A

B

II. DO THI

D inh n g h ia: Do thi la phudng phap trinh bay so' lieu clinh lUdng bang each
dung he thong toa do (vdi muc dich cua chung ta thudng la x va y).

Co nhieu kieu do thi khac nhau, trong do co vai kieu la toa do vuong goc, toa
do cUc, cac kieu v6i muc dich dac biet (3 chieu). v.v... Chung ta chi han che trong do
do thi co toa do vuong goc.

A. KHAI NIEM CHUNG
Do thi co toa do vuong goc la do thi gom hai true dudng vuong goc vdi nhau.
Tren moi true dudng co mot thang bac chia do de nhan dang. Hinh 1 gidi thieu cau
true chung cua do thi toa do vuong goc. Thong thudng, bien so an dinh cua true x
dudc coi la bien so doc lap (phudng phap phan loai), trong khi bien so an dinh cho
true y la bien so phu thuoc (tan so). Vi the. khi ve do thi, chung ta danh dau su
thay doi cua v theo x.
H inh I:
Do Thi D ai CtfcJng

17

PHUONG PHAP PHAN LOAI
B. NGUYEN TAC CHUNG
Khi do thi dudc ve mot cach dung dan, chung cho phep ngUdi doc nhanh
chong nAm dudc toan bo so lieu. Mot vai net quan trong nhat cua do thi la:
1. Do thi quan trong nhat la do thi co hieu qua nhat. Khong dung them
dtfdng ve hoac ky hieu trong mot do thi ma mat co the de dang theo
doi dudc.
2. Do thi phai de hieu, khong giai thich them.
3. Tieu de co dat tren dudi do thi.
A. Khi co hdn mot bien so dudc trinh bay tren do thi, moi bien so phai dudc
phan biet ro rang bang cac ghi chu hoac cac ky hieu.
5: Khong ve them dudng toa do ngoai cai can thiet de de nhin thay.
6. Cac dudng cua ban than do thi phai dam hdn cac dudng toa do khac.
7. Thudng thudng, tin so' dudc bieu thi tren thang do cua true tung va
phudng phap phan loai tren thang do cua true hoanh.
8. Tren thang do so' hoc, cac ltfdng gia bang nhau tren thang de phai dai dien
cho cac ddn vi bang nhau.
9. Khoang chia tren thang do phai dudc vach ra ro rang cung nhu cac ddn vi
trong do thang do dudc phan chia ra.

C. NHUNG VI DU DAC TRUNG
1. Do thi hinh day theo thang so hoc.
La do thi trong do mot quang bang nhau bieu thi mot so ltfdng bang nhau bat
cii d cho nao tren true, nhung khong nhat thiet phai blng nhau giiia cac true. C ln
phai chu y trong viec lua chon hoac dung nhung khoang each bang nhau tren ea 2
true hoac nhiing khoang each rong tren true x lien quan vdi true y hoac ngUdc lai.
Cac thang do phai dudc xac dinh the nao de san pham cuoi eung phai dep mat. Mot
thang do dirt quang co the dUdc dung vdi mot do thi day, nhung neu dung, phai cln

than de khong giai thich sai llm do thi. Hinh 2 la mot wi du do thi hinh day theo
thang so hoc.

18


H inh 2

Ty le rubeon difote bao cao trong 13 ky 4 tuan d My nam 1968

Thai ky ket thuc
Nguon: Dctn vi g iam sat Rubeon.
2. Do thi hinh day theo thang ban logarit.
Do thi hinh day theo thang ban logarit cua ddn vi, trong do true kia dudc do
ltfdng theo don vi so' hoc. Do thi nay co l'ch 6 cho khi xem xet chuoi so' lieu theo mot
giai doan thdi gian, chung ta thudng chu y den su thay doi tUdng doi (hoac ty le
thay doi) hdn la cai tuyet doi (hoac so' luong hien tai). Ldi diem cua do thi ban
logarit la:
a. Duong thang chi mot ty le bien doi hang dinh,
b. Do doc chi ty le tang len hoac giam xuo'ng,
c. Hai dudng (hoac nhieu hdn) theo cac dtfdng song song cho thay cac ty le gia
tang (hoac thuyen giam) nhu nhau.
Minh hoa cho do thi nay dtfdc trinh bay d hinh 3.

19