Ejercicio Dispersion

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Velocidad (rpm) %impureza 20 8.4 a) trace un diagrama de dispersión 22 9.5 24 11.8 %impureza 26 10.4 20 28 13.3 18 f(x) = 0.4566433566x - 0.2892773893 30 14.8 R² = 0.93383197 32 13.2 16 34 14.7 36 16.4 14 38 16.5 12 40 18.9 42 18.5 10 8 6 20

25

30

35

40

45

b) ajuste una recta de mínimos cuadrados, para determinar si existe una relación lineal entre las variables a estudiar �=(∑▒ 〖��−��   ̅�  ̅  〗 )/(∑▒ 〖� ^2− 〗 �� 〗 �� ^   2 ) Y= a+bx a- ordenada de la recta (punto donde corta al eje y) �=�  ̅−��   b.- pendiente de la recta (tipo de inclinación x.-variable independiente (causa) y.- variable dependiente (efecto o problema) Coeficiente de correlación �^2=(�∑▒𝑌+�∑▒𝑋𝑌−�𝑌  ̅^2)/(∑▒ 〖𝑌 ^2−��  ^2�  ^2 〗 )) �=√( X 20 22 24 26 28 30 32 34 36 38 40 42

Y XY 8.4 9.5 11.8 10.4 13.3 14.8 13.2 14.7 16.4 16.5 18.9 18.5 372 166.4 31 13.8666667

X^2

168 209 283.2 270.4 372.4 444 422.4 499.8 590.4 627 756 777 5419.6

400 484 576 676 784 900 1024 1156 1296 1444 1600 1764 12104

Y^2

�=(∑▒ 〖��−��   ̅�  ̅  〗 )/(∑▒ 〖� ^2− 〗 ���=�  ̅  ^2 ) −��   70.56 90.25 139.24 108.16 176.89 219.04 174.24 216.09 268.96 272.25 357.21 342.25 2435.14

b= a=

0.45664336 -0.2892774

Y= -0.2892774+0.4566434X

^2− 〗 ���=�  ̅  ^2 ) −��  

+0.4566434X

17 12 16 13 7

20 14 18 7 10

10 6 8 18 5

n= Max= Min= Rango= # clases=

50 32 3 29 8 3.625

9 9 3 7 14 Desde

Paso 1) Paso 2) Paso 3) Paso 4)

ancho clase=

23 13 3 10 15 Hasta

3 7 11 15 19 23 27

13 12 6 7 32 9 4 27 10 9 Frecuencia Marca Clase F.MC 7 14 5 11 13 9 15 10 13 19 8 17 23 2 21 27 2 25 32 1 29.5

Frecuencia 16 14 12 10 8 6 4 2 0

7

11

15

19

23

27

32

19 10 7 19 6 70 117 130 136 42 50 29.5 574.5

18 24 13 7 10 11 16 8 7 15 F(MC-X)^2 �  ̅=(∑▒ 〖� .𝑀� 〗 )/� 589.6814 11.49 80.6013 22.801 242.8808 �=√((∑▒ 〖� (��−�   ) 〗 ^2 )/(�−1)) 180.8802 365.0402 324.3601 6.07142017 1806.245

Velocidad (rpm) %impureza 20 8.4 22 9.5 24 11.8 26 10.4 28 13.3 30 14.8 32 13.2 34 14.7 36 16.4 38 16.5 40 18.9 42 18.5

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