際際滷

際際滷Share a Scribd company logo
???????????????????????????? 
???????????????????????????? ??????????????????? 
???????????? ????????????????????????????????????? ???????? 
???????????????????????????????? ?????? 
1. ?????????????? (Arithmetic mean) ???? ????????? 
???????????? X 
?????????? ????? X ???????? 
SX ; ?????????????????? 
??????? 1 X = N 
??????????????????? 
????? X ??? ????????????????? 
SX ??????????????????????? (SX = X1 + X2 
+ X3 + Xn) 
N ????????????????????? 
??????? ? ???????????????????????????? 10 ?????????? 
?????? 
5 7 9 12 20 8 3 7 11 15 ????????????????????? 
??????????????? 
SX 
X = N 
[5 + 7 + 9 +12 + 20 + 8 + 3 + 7 +11+15] = 
= 9.7 
10 
SX ; ???????????????????? 
??????? 2 X = N 
???????????????? 
????? X ??? ?????????????? 
?fx ??? ???????????????????????????? 
?????????????????????? 
N ??? ?????????????????? (N = ?f)
???????? ????????????????????????????????????????? 
????? ?????? 
????? 
(X) 
2 
4 
2 
3 
2 
2 
2 
1 
2 
0 
1 
9 
1 
8 
1 
7 
1 
6 
1 
5 
1 
4 
??????? 
(f) 
3 3 2 3 6 4 1 2 8 4 4 
SfX 
??????? X = N 
N = ?f = 40 
?fx = 740 
X = 740/40 = 18.5 
????? 
(X) 
? ? ? ? 
??? (f) 
fX 
24 
23 
22 
21 
20 
19 
18 
17 
16 
15 
14 
3 
3 
2 
3 
6 
4 
1 
2 
8 
4 
4 
72 
69 
44 
63 
120 
76 
18 
34 
128 
60 
56 
?f 
= 40 
? fx 
=740
??????????????????????? 
1. ??????????????? ? ??????????????????????????? 
? ????????????????????? (Norm) ???? ??? ??????? ???????? 
2. ?????????????????????????????????????????????? 
???? ? ?????????? ???? 
??????????????????????????? ??????????????? ??????????? 
??????? ??? 
3. ??????????????????????????????????????? 
2. ??????? (Median) ????????????????????????????????? 
????????????????????????????? Med ???? Mdn ??????????????? 
???????????????????????????????????? ???????????????? ???? 
????????????????????? ???????????????????? ? ??????????????? 
??????????????? 
??????? 1 ????????????????????????? ?????????????????? 
???? ??????????????? 
1. ?????????????????????? 
2. ????????????????????????????? 2 
(N +1) ????????? 
?????????? 
???????? ??????????????? 7 ????????? 14 13 18 16 15 19 20 
?????????? 13 14 15 16 18 19 20 
????????????????? = (N +1)/2 = (7+1)/2 = 4 
??????????? 4 ??????????? 16 
?????????? ???????????? 16
???????? ??????????????? 6 ?????????8 2 4 9 3 5 
?????????? 2 3 4 5 8 9 
????????????????? = (N +1)/2 = (6+1)/2 = 3.5 
??????????? 3.5 ???????????????????????????????? 3 ??? 4 
?????????? = (4+5)/2 = 4.5 
??????? 2 ?????????????????????????????????? ????????? 
????????????????? 
Mdn = 
L +i[(N / 2 - f )] 
o C 
m 
f 
????? Mdn??? ?????????? 
LO ??? ????????????????????????????????????? 
N ??? ??????????????????? 
I ??? ??????????? 
fC ??? ??????????????????????????????????????? 
fm ??? ????????????????????? 
???????? ?????????????????????? 30 ?? ??????????? 
??????? ?????????????? 
X 2 
5 
2 
4 
2 
6 
2 
3 
2 
1 
2 
0 
1 
9 
1 
8 
1 
7 
1 
6 
1 
5 
1 1 2 4 - 6 3 4 4 2 3
??????? 
1. ??????????????????????????? 
2. ???????????????? = N/2 ????????????????? 
???? 
?????? 
3. ?????????? 
Mdn = 
L +i[(N / 2 - f )] 
O C 
M 
f 
???????? LO = 18.5 
i = 1 
N/2 = 15 
fC = 13 
X F C 
f 
2 
5 
2 
4 
2 
3 
2 
2 
2 
1 
2 
0 
1 
1 
2 
4 
- 
6 
3 
0 
2 
9 
2 
8 
2 
6 
- 
2 
2 
1 
9 
3 1 
6 
1 
8 
1 
7 
1 
6 
1 
5 
4 
4 
2 
3 
1 
3 
9 
5 
3 
15
fM = 3 
1[(15-13)] 
Mdn = 18.5 + 3 
= 18.5 + .67 
??????? = 19.17 
???????????????? 
1. ?????????????????? ? ???????????????????? 
??????? ??????????????????????????????????? ? ???????????? 
??????????????????????????????????? 
2. ?????????????????????????????? 2 ????? ?????? 
??????????????????????? 
3. ??????? (Mode) ??????? ?????????????????????????? 
???????????? Mo ?????????????????????????????????????????? 
????? ? ??????? ???? ??????????????????????????????????? 
???? ? 
??????? ? ??????????????????????????? 12 15 13 14 14 13 
13 18? 
????????????????????? 13 ?????????? 13 ????????? 
????????? 
?????? ??? ???????????????????????? 2 ??? (Bimodel) 
???? 
2 1 4 8 5 8 3 5 7 5 8 15 
????????????????????????? ??? 5 ??? 8 
????????????????????????????????????????????????????????? 
?????????????? 
1. ?????????????? ???????????????????????????????? 
2. ????????? ???????????? 
3. ??????????? ?????????????????????????????????? 
?????? ???????????????????????????????????????????????????? 
?? 
??????? 
1. ?????????????? ????????????????????????????????? 
??????????? 
2. ???????????????? ??????????????????????????
3. ??????????? ?????????????????????????????? ???? 
??????????????????????????????? ???? ????????? ???????????? 
????????????????????? 
??????? 
1. ?????????????? ?????????????????????????????? 
????????? ???????????? 
2. ???????????????? ?????????????????????????????? 
?????????????? ? 
3. ??????????? ???????????????????????????? 
??????? ???????????????????????????????????????????

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  • 1. ???????????????????????????? ???????????????????????????? ??????????????????? ???????????? ????????????????????????????????????? ???????? ???????????????????????????????? ?????? 1. ?????????????? (Arithmetic mean) ???? ????????? ???????????? X ?????????? ????? X ???????? SX ; ?????????????????? ??????? 1 X = N ??????????????????? ????? X ??? ????????????????? SX ??????????????????????? (SX = X1 + X2 + X3 + Xn) N ????????????????????? ??????? ? ???????????????????????????? 10 ?????????? ?????? 5 7 9 12 20 8 3 7 11 15 ????????????????????? ??????????????? SX X = N [5 + 7 + 9 +12 + 20 + 8 + 3 + 7 +11+15] = = 9.7 10 SX ; ???????????????????? ??????? 2 X = N ???????????????? ????? X ??? ?????????????? ?fx ??? ???????????????????????????? ?????????????????????? N ??? ?????????????????? (N = ?f)
  • 2. ???????? ????????????????????????????????????????? ????? ?????? ????? (X) 2 4 2 3 2 2 2 1 2 0 1 9 1 8 1 7 1 6 1 5 1 4 ??????? (f) 3 3 2 3 6 4 1 2 8 4 4 SfX ??????? X = N N = ?f = 40 ?fx = 740 X = 740/40 = 18.5 ????? (X) ? ? ? ? ??? (f) fX 24 23 22 21 20 19 18 17 16 15 14 3 3 2 3 6 4 1 2 8 4 4 72 69 44 63 120 76 18 34 128 60 56 ?f = 40 ? fx =740
  • 3. ??????????????????????? 1. ??????????????? ? ??????????????????????????? ? ????????????????????? (Norm) ???? ??? ??????? ???????? 2. ?????????????????????????????????????????????? ???? ? ?????????? ???? ??????????????????????????? ??????????????? ??????????? ??????? ??? 3. ??????????????????????????????????????? 2. ??????? (Median) ????????????????????????????????? ????????????????????????????? Med ???? Mdn ??????????????? ???????????????????????????????????? ???????????????? ???? ????????????????????? ???????????????????? ? ??????????????? ??????????????? ??????? 1 ????????????????????????? ?????????????????? ???? ??????????????? 1. ?????????????????????? 2. ????????????????????????????? 2 (N +1) ????????? ?????????? ???????? ??????????????? 7 ????????? 14 13 18 16 15 19 20 ?????????? 13 14 15 16 18 19 20 ????????????????? = (N +1)/2 = (7+1)/2 = 4 ??????????? 4 ??????????? 16 ?????????? ???????????? 16
  • 4. ???????? ??????????????? 6 ?????????8 2 4 9 3 5 ?????????? 2 3 4 5 8 9 ????????????????? = (N +1)/2 = (6+1)/2 = 3.5 ??????????? 3.5 ???????????????????????????????? 3 ??? 4 ?????????? = (4+5)/2 = 4.5 ??????? 2 ?????????????????????????????????? ????????? ????????????????? Mdn = L +i[(N / 2 - f )] o C m f ????? Mdn??? ?????????? LO ??? ????????????????????????????????????? N ??? ??????????????????? I ??? ??????????? fC ??? ??????????????????????????????????????? fm ??? ????????????????????? ???????? ?????????????????????? 30 ?? ??????????? ??????? ?????????????? X 2 5 2 4 2 6 2 3 2 1 2 0 1 9 1 8 1 7 1 6 1 5 1 1 2 4 - 6 3 4 4 2 3
  • 5. ??????? 1. ??????????????????????????? 2. ???????????????? = N/2 ????????????????? ???? ?????? 3. ?????????? Mdn = L +i[(N / 2 - f )] O C M f ???????? LO = 18.5 i = 1 N/2 = 15 fC = 13 X F C f 2 5 2 4 2 3 2 2 2 1 2 0 1 1 2 4 - 6 3 0 2 9 2 8 2 6 - 2 2 1 9 3 1 6 1 8 1 7 1 6 1 5 4 4 2 3 1 3 9 5 3 15
  • 6. fM = 3 1[(15-13)] Mdn = 18.5 + 3 = 18.5 + .67 ??????? = 19.17 ???????????????? 1. ?????????????????? ? ???????????????????? ??????? ??????????????????????????????????? ? ???????????? ??????????????????????????????????? 2. ?????????????????????????????? 2 ????? ?????? ??????????????????????? 3. ??????? (Mode) ??????? ?????????????????????????? ???????????? Mo ?????????????????????????????????????????? ????? ? ??????? ???? ??????????????????????????????????? ???? ? ??????? ? ??????????????????????????? 12 15 13 14 14 13 13 18? ????????????????????? 13 ?????????? 13 ????????? ????????? ?????? ??? ???????????????????????? 2 ??? (Bimodel) ???? 2 1 4 8 5 8 3 5 7 5 8 15 ????????????????????????? ??? 5 ??? 8 ????????????????????????????????????????????????????????? ?????????????? 1. ?????????????? ???????????????????????????????? 2. ????????? ???????????? 3. ??????????? ?????????????????????????????????? ?????? ???????????????????????????????????????????????????? ?? ??????? 1. ?????????????? ????????????????????????????????? ??????????? 2. ???????????????? ??????????????????????????
  • 7. 3. ??????????? ?????????????????????????????? ???? ??????????????????????????????? ???? ????????? ???????????? ????????????????????? ??????? 1. ?????????????? ?????????????????????????????? ????????? ???????????? 2. ???????????????? ?????????????????????????????? ?????????????? ? 3. ??????????? ???????????????????????????? ??????? ???????????????????????????????????????????