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Media, Varianza, Desviación Muestral, entre otros

Media muestral, varianza muestral y desviación muestral, moda, mediana, valor mínimo y valor máximo de cada variable.

Sumatoria ∑

X_1 〖(X_1-μ)〗^2 〖X_1〗^2

1149.93 3671.18222 7504.0489

Sumatoria ∑

X_2 〖(X_2-μ)〗^2 〖X_2〗^2

5529746048 1.52113E+18 1.60976E+18

Sumatoria ∑

Y 〖(Y-μ)〗^2 Y^2

5.16417E+12 2.78189E+23 3.55489E+23

Media Muestral Variable X_1

μ=(∑▒X_1 )/n=1149.93/345=3.33313043

Media Muestral Variable X_2

μ=(∑▒X_2 )/n=5529746048/345=16028249.41

Media Muestral Variable Y

μ=(∑▒Y)/n=(5.16417E+12)/345=1.4969E+10

Varianza Muestral Variable X_1

〖(S_(X_1 ))〗^2=(∑▒〖(X_1-μ)〗^2 )/(n-1)=3671.18222/344=10.67204133

〖(S_(X_1 ))〗^2=(∑▒〖〖X_1〗^2-1/n 〖(∑X_1)〗^2 〗)/(n-1)=(7504.0489-1/345(〖1149.93〗^2))/344=10.67204133

Varianza Muestral Variable X_2

〖(S_(X_2 ))〗^2=(∑▒〖(X_2-μ)〗^2 )/(n-1)=(1.52113E+18)/344=4.4219E+15

〖(S_(X_2 ))〗^2=(∑▒〖〖X_2〗^2-1/n 〖(∑X_2)〗^2 〗)/(n-1)=((1.60976E+18)-1/345(〖5529746048〗^2))/344=4.4219E+15

Varianza Muestral Variable Y

〖(S_Y)〗^2=(∑▒〖(Y-μ)〗^2 )/(n-1)=(2.78189E+23)/344=8.08688E+20

〖(S_Y)〗^2=(∑▒〖Y^2-1/n 〖(∑Y)〗^2 〗)/(n-1)=(3.55489E+23-1/345(〖(25.16417E+12)〗^2))/344=8.08688E+20

Desviación Muestral Variable X_1

S_(X1_ )=√(2&〖(S_(X_1 ))〗^2 )=3.26680945

Desviación Muestral Variable X_2

S_(X_2 )=√(2&〖(S_(X_2 ))〗^2 )=66497341.47

Desviación Muestral Variable Y

S_Y=√(2&〖(S_Y)〗^2 )=28437433339

Variable X_1 Variable X_2 Variable Y

Moda 1.81 0 No hay moda

Mediana 2.16 21580 2782279234

Valor Mínimo 0 0 94849009

Valor Máximo 23.56 964313000 161781114362

Representaciones Gráficas

Graficar cada variable

Construir diagrama de rama y hoja para cada variable

Porcentaje de Hogares que reciben remesas de Estados Unidos (X_1)

Rama Hoja N

0 .00 , .00 , .00 , .04 , .05 , .08 , .13 , .14 , .15 , .18 , .22 , .27 , .31 , .32 , .35 , .37 , .38 , .38, .40 , .42 , .45 , .47 , .49 , .51 , .53 , .53 , .55 , .56 , .56 , .58 , .59 , .60 , .62 , .64 , .65 , .66 , .66 , .69 , .70 , .70 , .71 , .72 , .74 , .77 , .78 , .80 , .81 , .85 , .85 , .88 , .89 , .89 , .89 , .91 , .91 , .91 , .92 , .94 , .94 , .95 , .95 , .99 , .99 63

1 .01 , .04 , .04 , .06 , .07 , .12 , .12 , .12 , .13 , .14 , .15 , .15 , .15 , .15 , .17 , .19 , .20 , .23 , .24 , .26 , .27 , .28 , .28 , .29 , .29 , .31 , .32 , .32 , .33 , .33 , .34 , .36 , .37 , .38 , .38 , .39 , .39 , .40 , .42 , .43 , .44 , .46 , .48 , .48 , .49 , .51 , .51 , .52 , .54 , .54 , .55 , .57 , .58 , .59 , .59 , .59 , .59 , .61 , .61 , .64 , .65 , .65 , .65 , .66 , .66 , .67 , .68 , .69 , .71 , .71 , .73 , .73 , .73 , .74 , .76 , .76 , .77 , .78 , .79 , .81 , .81 , .81 , .81 , .81 , .82 , .83 , .83 , .84 , .87 , .88 , .90 , .94 , .97 , .98 , .99 95

2 .00 , .01 , .03 , .03 , .04 , .04 , .05 , .07 , .07 , .07 , .09 , .11 , .12 , .13 , .16 , .19 , .22 , .28 , .29 , .31 , .32 , .34 , .34 , .40 , .41 , .41 , .44 , .46 , .47 , .48 , .48 , .50 , .52 , .57 , .59 , .59 , .60 , .61 , .64 , .67 , .67 , .69 , .77 , .80 , .81 , .86 , .86 , .87 , .88 , .90 , .90 51

3 .02 , .02 , .03 , .06 , .07 , .10 , .10 , .12 , .13 , .13 , .19 , .22 , .26 , .26 , .28 , .36 , .36 , .37 , .39 , .40 , .42 , .43 , .45 , .46 , .48 , .50 , .54 , .54 , .56 , .58 , .59 , .60 , .64 , .72 , .72 , .75 , .88 ,.90 , .91 , .93 , .98 41

4 .00 , .07 , .14 , .15 , .17 , .17 , .18 , .21 , .22 , .24 , .28 , .40 , .44 , .45 , .51 , .54 , .58 , .64 , .72 , .97 , .98 , .99 , .99 23

5 .00 , .11 , .17 , .17 , .17 , .37 , .38 , .45 , .47 , .53 , .57 , .57 , .70 , .81 , .85 , .87 , .95 17

6 .10 , .18 , .20 , .23 , .29 , .30 , .39 , .41 , .47 , .47 , .55 , .62 , .69 , .72 , .83 15

7 .02 , .06 , .07 , .11 , .13 , .36 , .39 , .64 , .70 , .82 , .95 11

8 .05 , .20 , .63 , .77 , .83 , .86 , .97 7

9 .05 , .18 , .37 , .50 , .81 , .94 6

10 .00 , .19 , .30 , .35 , .55 5

11 .04 ,.08 , .08 , .96 4

12 .89 1

13 .58 1

14 .79 1

15 0

16 0

17 .11 , .47 2

18 0

19 0

20 0

21 .48 1

22 0

23 .56 1

Deuda Pública (X_2)

Rama Hoja n

0 00000000 , 00000000 , 00000000 , 00000000 ,00000000 , 00000000 ,00000000 ,00000000 ,00000000 ,00000000 ,00000000 ,00000000 ,00000000 ,00000000 ,00000000 ,00000000 ,00000000

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