Medidas De Tendencia Central Y Medidas De Dispersión.

Alturas de 40 estudiantes del plantel.

Cintia 1.48m

Blanca 1.49m

Samantha 1.52m

Karla 1.54m

Ana 1.54m

Karen 1.55m

Gabriela 1.56m

Rosario 1.57m

Brenda 1.57m

Gloria 1.57m

Angela 1.59m

Marcela 1.59m

Wendy 1.59m

Miranda 1.59m

Adriana 1.59

Sandra 1.59

Vanessa 1.59m

Jennifer 1.60 m

Yazmin 1.60m

Yesica 1.61m

Deisy 1.61m

Dalia 1.62m

Judith 1.64m

San Juana 1.64m

Adam 1.65m

Sara 1.65m

Jose Guadalupe 1.66m

Evelyn 1.66m

Ana 1.66m

Silvestre 1.67m

Dulce 1.67m

Belen 1.68m

Jair 1.72m

Irad 1.73m

Fernanda 1.74m

Ana Karen 1.74m

Ricardo 1.76m

Adrian 1.86m

Rogelio 1.86m

Juan Francisco 1.88m

Estaturas Número de alumnos 4103

1.48m 1

1.49m 1

1.52m 1

1.54m 2

1.55m 1

1.56m 1

1.57m 3

1.59m 7

1.60 m 2

1.61m 2

1.62m 1

1.64m 2

1.65m 2

1.66m 3

1.67m 2

1.68m 1

1.72m 1

1.73m 1

1.74m 2

1.76m 1

1.86m 2

1.88m 1

TOTAL 40

Medidas de tendencia central.

Media aritmética.

Estaturas

x f Xn.Fn

1.48m 1 (1.48)(1)=1.48

1.49m 1 (1.49)(1)=1.49

1.52m 1 (1.52)(1)=1.52

1.54m 2 (1.54)(2)=3.08

1.55m 1 (1.55)(1)=1.55

1.56m 1 (1.56)(1)=1.56

1.57m 3 (1.57)(3)=4.71

1.59m 7 (1.59)(7)=11.13

1.60 m 2 (1.60)(2)=3.2

1.61m 2 (1.61)(2)=3.22

1.62m 1 (1.62)(1)=1.62

1.64m 2 (1.64)(2)=3.28

1.65m 2 (1.65)(2)=3.3

1.66m 3 (1.66)(3)=4.98

1.67m 2 (1.67)(2)=3.34

1.68m 1 (1.68)(1)=1.68

1.72m 1 (1.72)(1)=1.72

1.73m 1 (1.73)(1)=1.73

1.74m 2 (1.74)(2)=3.48

1.76m 1 (1.76)(1)=1.76

1.86m 2 (1.86)(2)=3.72

1.88m 1 (1.88)(1)=1.88

TOTAL 40 65.43

x= 65.43 = 1.63

40

Media geométrica.

x= √(n&X1•X2•X3…..Xn)

x= √(40&(1.48(1) )(1.49(1) )(1.52(1) )(1.54(2) )(1.55(1) )(1.56(1) )(1.57(3) )(1.59(7)))

(1.60(2))(1.61(2))(1.62(1))(1.64(2))(1.65(2))(1.66(3))(1.67(2))

(1.68(1))(1.72(1))(1.73(1))(1.74(2))(1.76(1))(1.86(2))(1.88(1))

X= √(40&(1.48)(1.49)(1.52)(3.08)(1.55)(1.56)(4.71)(11.3)(3.2)(3.22)(1.62)(3.28)(3.3) )

(4.98)(3.34)(1.68)(1.72)(1.73)(3.48)(1.76)(3.72)(1.88)

X=√(40&152371941.4)

X= 1.60

Mediana

Me = n + 1

2

Me= 22 = 11 + 1 = 12

2

Me= 1.62 + 1.64 = 3.26 = 1.63m

2 2

Moda

Alturas Alumnos

1.44m – 1.52m 3

1.53m – 1.61m 18

1.62m – 1.70m 11

1.71m – 1.79m 5

1.80m – 1.88m 3

Total 40

Mo= Li + (F1 – F2) .

(F1 – F2) + (F1 + F3)

Mo = 153 + (18 – 3) .

(18 – 3) + (18 – 11)

Mo= 153 + 15 .

15 + 7

Mo= 153 + 15

22

Mo= 153 + 0.68 (3)

Mo= 153 + 2.04

Mo= 155.04 = 1.55m

Cuartiles

Alturas

x Alumnos

f Frecuencia

Acumulada

F

1.49m - 1.56m 7 7

☺ ♥ 1.57m - 1.64m 17 24

♣ 1.65m - 1.72m 9 33

1.73m - 1.80m 4 37

1.81m - 1.88m 3 40

TOTAL 40

Cuartil 1

Qk = k . N Q1= 157 + 10 – 7

4 17

Q1= 1 (40) Q1= 157 + 3

4 17

Q1 = 40 Q1= 157 + 0.176 (8)

4

Q1= 157 + 1.408

Q1 = 10 → Posición Q1= 158.408 ÷ 100 = 1.58m

Cuartil 2

Qk= k . N Q2= 157 + 20 - 7

4 17

Q2= 2 (40) Q2= 157 + 13

4 17

Q2= 80 Q2= 157 + 0.76 (8)

4

Q2= 157 + 6.08

Q2= 20 → Posición Q2= 163.08 ÷ 100= 1.63m

Cuartil 3

Qk= k . N Q3= 165 + 30 - 24

4 9

Q3= 3 (40) Q3= 165 + 6

4 9

Q3= 120 Q3= 165 + 0.66 (8)

4

Q3= 165 + 5.28

Q3= 30 → Posición Q3= 170.28 ÷ 100= 1.70m

Deciles

Alturas

x Alumnos

f Frecuencia

Acumulada

F

☺ ♣ 1.49m - 1.56m 7 7

♥ 1.57m - 1.64m 17 24

1.65m - 1.72m 9 33

1.73m - 1.80m 4 37

1.81m - 1.88m 3 40

TOTAL 40

Decil 1

D1= k . n D1= 149 + 4 – 0

10 8

D1= 1 (40) D1= 149 + 4

10 8

D1= 40 D1= 149 + 0.5 (8)

10

D1= 149 + 4

D1= 4 → Posición D1= 153 ÷ 100 = 1.53m

...