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Download ʶԵͧ.pdf

  Ѵҡҧͧ

 Ѵҡҧͧ

Ҥҡҧͧŷ繵᷹ͧŷͤдǡ㹡ػͧǡѺŹ Ъ·ԴŶ١ͧբ ҤҡҧͧԸԸ ԸբʹТ դ㹡ù͹ѹ ѺѡɳТѵػʧͧŹ

ҡҧͧŷӤѭ 3 Դ

1.        ŢԵ (Arithmetic mean)

2.       Ѹ°ҹ (Median)

3.       ҹ (Mode)

   1.   ŢԵ (Arithmetic mean)
         ѭѡɳ   http://www.thaigoodview.com/library/teachershow/bangkok/pisamorn_s/pictures/x.JPG

1.1 ҤŢԵͧŷᨡᨧ

x 1 , x 2 , x 3 , , x N 繢 N

http://www.thaigoodview.com/library/teachershow/bangkok/pisamorn_s/pictures/21.JPG

ҧ ҡͺآͧѡ¹˹繴ѧ 14 , 16 , 14 , 17 , 16 , 14 , 18 , 17

1) ҤŢԵͧعѡ¹

2) չѡ¹ա 1 17 ŢԵ

3) 3 շ ŢԵͧعѡ¹

1) Ըշ

http://www.thaigoodview.com/library/teachershow/bangkok/pisamorn_s/pictures/22.JPGhttp://www.thaigoodview.com/library/teachershow/bangkok/pisamorn_s/pictures/23.JPG

       ŢԵͧѡ¹ 15.75

2) Ըշ
     չѡ¹ 8 չѡ¹ա 1 չѡ¹ 9

http://www.thaigoodview.com/library/teachershow/bangkok/pisamorn_s/pictures/24.JPG

        ŢԵ 15.89

3) Ըշ
3 շ 11 13 11 14 13 11 15 14
      ػѨغѹ 14 16 14 17 16 14 18 17

http://www.thaigoodview.com/library/teachershow/bangkok/pisamorn_s/pictures/25.JPG
3 շ ŢԵͧآͧѡ¹ 12.75

1.2 ŢԵͧŷᨡᨧ

f 1 , f 2 , f 3 , , f k 繤ͧҨҡѧࡵ x 1 , x 2 , x 3 ,. , x k

http://www.thaigoodview.com/library/teachershow/bangkok/pisamorn_s/pictures/26.JPG

  http://www.thaigoodview.com/library/teachershow/bangkok/pisamorn_s/pictures/27.JPG

ҧ ҡҧᨡᨧͧṹͺͧѡ¹ 40 ѧ ҤŢԵ

ӹǹѡ¹ (f 1)

x 1

f 1x 1

11 12

21 30

31 40

41 50

51 - 60

7

6

8

15

4

15.5

25.5

35.5

45.5

55.5

108.5

153

284

682.5

222

http://www.thaigoodview.com/library/teachershow/bangkok/pisamorn_s/pictures/28.JPG

 

http://www.thaigoodview.com/library/teachershow/bangkok/pisamorn_s/pictures/29.JPG

Ըշ

http://www.thaigoodview.com/library/teachershow/bangkok/pisamorn_s/pictures/x.JPG  =   http://www.thaigoodview.com/library/teachershow/bangkok/pisamorn_s/pictures/30.JPG

        =   http://www.thaigoodview.com/library/teachershow/bangkok/pisamorn_s/pictures/31.JPG

        =   34

    ŢԵ = 34

ѵԷӤѭͧŢԵ

1. http://www.thaigoodview.com/library/teachershow/bangkok/pisamorn_s/pictures/32.JPG = http://www.thaigoodview.com/library/teachershow/bangkok/pisamorn_s/pictures/33.JPG

2. http://www.thaigoodview.com/library/teachershow/bangkok/pisamorn_s/pictures/34.JPG = 0

3. http://www.thaigoodview.com/library/teachershow/bangkok/pisamorn_s/pictures/35.JPG ·ش   M = http://www.thaigoodview.com/library/teachershow/bangkok/pisamorn_s/pictures/x.JPG    http://www.thaigoodview.com/library/teachershow/bangkok/pisamorn_s/pictures/36.JPGhttp://www.thaigoodview.com/library/teachershow/bangkok/pisamorn_s/pictures/37.JPGhttp://www.thaigoodview.com/library/teachershow/bangkok/pisamorn_s/pictures/38.JPG

       M 繨ӹǹԧ

 4. http://www.thaigoodview.com/library/teachershow/bangkok/pisamorn_s/pictures/39.JPG

5. y 1 = a xi + b , I = 1, 2, 3, ., N a , b 繤Ҥ

http://www.thaigoodview.com/library/teachershow/bangkok/pisamorn_s/pictures/40.JPG = a http://www.thaigoodview.com/library/teachershow/bangkok/pisamorn_s/pictures/x.JPG + b

ŢԵ ( Combined Mean )

http://www.thaigoodview.com/library/teachershow/bangkok/pisamorn_s/pictures/41.JPG 繤ŢԵͧŪش 1 , 2 , , k ӴѺ

N 1 , N 2 , , N k 繨ӹǹҨҡѧࡵ㹢Ūش 1 , 2 , , k ӴѺ

      http://www.thaigoodview.com/library/teachershow/bangkok/pisamorn_s/pictures/42.JPG  =   http://www.thaigoodview.com/library/teachershow/bangkok/pisamorn_s/pictures/43.JPG
      ҧ 㹡ͺԪʶԵԢͧѡ¹ç¹ҳԷ ҡҹѡ¹ .6/1 ӹǹ 40 ŢԵͧṹͺҡѺ 70 ṹ ѡ¹ .6/2 ӹǹ 35 ŢԵͧṹͺҡѺ 68 ṹ ѡ¹ .6/3 ӹǹ 38 ŢԵͧṹͺҡѺ 72 ṹ ҤŢԵͧṹͺͧѡ¹ 3 ͧѹ

Ըշhttp://www.thaigoodview.com/library/teachershow/bangkok/pisamorn_s/pictures/x.JPG =    http://www.thaigoodview.com/library/teachershow/bangkok/pisamorn_s/pictures/44.JPG

                                                                                          =     http://www.thaigoodview.com/library/teachershow/bangkok/pisamorn_s/pictures/45.JPG

                                                                                          =  70.05

2 .  Ѹ°ҹ (Median)
   
ѭѡɳ Med ҷյ˹觡ҧͧŷ §ŵӴѺ Ҩҡҡ ͨҡҡ仹

   Ѹ°ҹͧŷᨡᨧ
   ѡäԴ
  
1 ) §ŷҡҡ ҡ仹¡
    2) ˹Ѹ°ҹ ˹觡觡ҧ ѧ鹵˹觢ͧѸ°ҹ = http://www.thaigoodview.com/library/teachershow/bangkok/pisamorn_s/pictures/46.JPG

        N ӹǹŷ

    3) Ѹ°ҹ ҷյ˹觡ҧͧŷ

  ͤʹ
1. ͧҡ˹觡觡ҧ繵˹觷ҨѸ°ҹ ѧ Ҩ¡˹觹 ˹觢ͧѸ°ҹ
  2. öҵ˹觡觡ҧԸաõҧҧ еͧ 㹡ùӤҨҡѧࡵ¹§ѹ        е˹ ѧ ҨԸաäӹdz ѧࡵѧ
       ˹Ѹ°ҹ = http://www.thaigoodview.com/library/teachershow/bangkok/pisamorn_s/pictures/52.JPG
3. 㹡Ѹ°ҹ Ӥѭ ѡ¹ͧҵ˹觢ͧѸ°ҹ ¡͹Ǩ֧ҤҢͧ ˹觹

ҧ ˹Ҩҡѧࡵ㹢Ūش˹ մѧ
                      5, 9, 16, 15, 2, 6, 1, 4, 3, 4, 12, 20, 14, 10, 9, 8, 6, 4, 5, 13
                       Ѹ°ҹ
    Ըշ § 1 , 2 , 3 , 4 , 4 , 4 , 5 , 5 , 6 , 6 , 8 , 9 , 9 , 10 , 12 , 13 , 14 , 15 , 16 , 20

   ˹Ѹ°ҹ = http://www.thaigoodview.com/library/teachershow/bangkok/pisamorn_s/pictures/52.JPG

= http://www.thaigoodview.com/library/teachershow/bangkok/pisamorn_s/pictures/53.JPG

= 10.5

       Ѹ°ҹ = http://www.thaigoodview.com/library/teachershow/bangkok/pisamorn_s/pictures/54.JPG = 7

Ѹ°ҹͧŷѴѹҤ
   鹵͹㹡Ѹ°ҹմѧ
   (1)     ҧҧ
   (2)ҵ˹觢ͧѸ°ҹ http://www.thaigoodview.com/library/teachershow/bangkok/pisamorn_s/pictures/55.JPG

        N 繨ӹǹͧŷ
   (3)   http://www.thaigoodview.com/library/teachershow/bangkok/pisamorn_s/pictures/55.JPG ҡѺͧѹҤ ѹҤ鹹繪 Ѹ°ҹ Ѹ°ҹҡѺͺ

        ͧѹҤ鹹 http://www.thaigoodview.com/library/teachershow/bangkok/pisamorn_s/pictures/55.JPG ҤͧѹҤ ѹҤáդҡ   http://www.thaigoodview.com/library/teachershow/bangkok/pisamorn_s/pictures/55.JPG

        繪鹢ͧѸ°ҹ Ѹ°ҹҡºѭѵҧ ٵôѧ
        ҡŷ N ӹǹ ˹觢ͧѸ°ҹ http://www.thaigoodview.com/library/teachershow/bangkok/pisamorn_s/pictures/55.JPG

        Med = http://www.thaigoodview.com/library/teachershow/bangkok/pisamorn_s/pictures/56.JPG

          L ͺҧͧѹҤ鹷Ѹ°ҹ

http://www.thaigoodview.com/library/teachershow/bangkok/pisamorn_s/pictures/57.JPG     ͧͧءѹҤ鹷Ѹ°ҹ

      f M ͧ鹷Ѹ°ҹ

         I ҧͧѹҤ鹷Ѹ°ҹ

       N ӹǹŷ

ҧժẺԴ http://www.thaigoodview.com/library/teachershow/bangkok/pisamorn_s/pictures/x.JPG Ѹ°ҹаҹ ҵ˹
ҡѺ ( 繵ش¢ͧ ) ͺͺͧ鹹

3.  ҹ (Mode)

  Ұҹͧŷᨡᨧ
  ѡäԴ
- Ң㹢ŷ աëӡѹҡش( ٧ش) Ź繰ҹͧŪش
   ˵
- ҹҨ ҡ 1 ҡ

  觷ͧ
1. ҢФҷᵡҧѹ դҡѹ ŷСͺ 2 , 7 , 9 , 11 , 13 о ФҢͧŷᵡҧѹ դҡѺ 1 ͹ѹ 㹷ʴ Ңͧŵ㴵˹繾  ѧ Ҷ ѡɳдѧǹ հҹ
  2. ҢФҷᵡҧѹ դ٧شҡѹ 2 ŷ Сͺ 2, 4, 4, 7, 7, 9, 8, 5 о 4 7 繢ŷդ٧شҡѺ 2 ҡѹ ѡɳ蹹 Ҷ Ŵѧհҹ 2 4 7
   3. ҡ 1, 2, еҧ ʴ ҹͧ Ҩա Ҩҡ 1 ҡ

ҰҹͧŷաᨡᨧѹҤ
   ûҳҧ

   ҹ ش觡ҧ鹷դ٧ش

   ҧ ҡҧᨡᨧ仹 Ұҹ»ҳҧ

20-29

30-39

40-49

50-59

60-69

2

10

15

13

5

ѹҤ鹷դ٧ش 40-49

                                                شҧ http://www.thaigoodview.com/library/teachershow/bangkok/pisamorn_s/pictures/58.JPG

ѧ ҹ»ҳ 44.5

سѵԷӤѭͧҹ
1.     ҹöҡ駢ͧ
2.    㹢Ъش Ҩհҹա Ҩ§ ¤ҡ
3.   X 1, X 2, X 3, .., X N 繢Ūش˹觷հҹҡѺ Mo
       k 繤Ҥ X 1+k, X 2+k, X 3+k, ., X N+k 繢ŷհҹҡѺ Mo + k
4.   X 1, X 2, X 3, ., X N 繢Ūش˹觷հҹҡѺ Mo
       k 繤Ҥ k =/= 0 kX 1, kX 2, kX 3, , kX N 繢ŷհҹҡѺ kMo
       سѵԢͷ 3 4 ǡѺŢԵ Ѹ°ҹ Ǥ ҹӤҤ仺ǡ ͤٳѺҨҡѧࡵء㹢Ūش˹ ҹͧŪش ҡѺ ҹͧŪش ǡͤٳѺҤǴѧ ӴѺ ( ! 繡äٳ ҤǷ令ٳҡѺٹ)