Ejercicio distribucion de frecuencias

Para los siguientes tres ejercicios siguientes, preparar una tabla de distribución de frecuencias, frecuencias acumuladas, frecuencias relativas y frecuencia relativa acumulada, un diagrama de tallo y hojas y una gráfica de caja.

N= 80
Rango: dato mayor – dato menor= 245 – 76= 169
Numero de clases: 1 + 3.322 log 80 = 7.322 ≈ 8
Ancho de clase: (dato sup. – dato inf.)/no. Clases =(245-76)/8= 21.125

Tabla de distribución de frecuencias
| f (frecuencia absoluta) | fa (frecuencia acumulada) | fr (frecuencia relativa) | fra (frecuencia relativa acumulada) | fra % |
76-97 | 3 | 3 | 0.0375 | 0.0375 | 3.75% |
98-119 | 5 | 8 | 0.0625 | 0.1 | 10% |
120-141 | 10 | 18 | 0.125 | 0.225 | 22.5% |
142-163 | 24 | 42 | 0.3 | 0.525 | 52.5% |
164-185 | 21 | 63 | 0.2625 | 0.7875 |78.75% |
186-207 | 10 | 73 | 0.125 | 0.9125 | 91.25% |
208-229 | 5 | 78 | 0.0625 | 0.975 | 97.5% |
230-251 | 2 | 80 | 0.025 | 1 | 100% |

Diagrama de tallo y hojas
7 | 6 |
8 | 7 |
9 | 7 |
10 | 1 5 |
11 | 0 5 8 |
12 | 0 1 3 |
13 | 1 3 3 4 5 5 |
14 | 1 2 3 5 6 8 9 9 |
15 | 0 0 1 3 4 4 6 7 8 8 8 8 |
16 | 0 00 3 3 5 7 7 8 9 |
17 | 0 1 1 2 4 4 5 6 6 8 |
18 | 0 0 1 1 3 4 6 |
19 | 0 3 4 6 9 9 |
20 | 0 1 7 8 |
21 | 8 |
22 | 1 8 9 |
23 | 7 |
24 | 5 |

Mediana: (160 +163)/2=161.5
Q1=(n+1)/4= (80+1)/4= posición 20.25= (143+145)/2=144
Q2=mediana=161.5
Q3=[3(n+1)]/4=posición 60.75=181

Rango Intercuartílico: 181-144= 37LBI: 144-(1.5 x 37)=88.5
LBS: 181+(1.5 x 37)=236.5

Nº de piezas aceptables producidas por 110 trabajadores.
64 | 35 | 80 | 48 | 29 | 63 | 83 | 66 | 38 | 55 |
77 | 66 | 21 | 41 | 36 | 55 | 44 | 81 | 73 | 60 |
34 | 53 | 65 | 35 | 73 | 79 | 33 | 51 | 62 | 58 |
59 | 37 | 49 | 40 | 76 | 81 | 24 | 71 | 37 | 48 |
44 | 32 | 54 | 69 | 53 | 69 | 55 | 66 | 46 | 40 |
88 | 61 | 56 | 66 | 74 | 52 |44 | 58 | 40 | 54 |
75 | 41 | 44 | 58 | 75 | 68 | 50 | 73 | 46 | 57 |
47 | 52 | 34 | 44 | 46 | 52 | 51 | 56 | 77 | 61 |
84 | 58 | 77 | 66 | 44 | 22 | 63 | 37 | 63 | 35 |
48 | 62 | 40 | 61 | 66 | 55 | 61 | 56 | 71 | 53 |
62 | 50 | 52 | 53 | 57 | 60 | 51 | 62 | 55 | 52 |

N= 110
Rango: dato mayor – dato menor= 88 – 21= 67
Numero de clases: 1 + 3.322 log 110 = 7.7 ≈ 8
Ancho de clase:(dato sup. – dato inf.)/no. Clases = (88-21)/8= 8.375

Tabla de distribución de frecuencias
| f | fa | fr | fra |
20-24 | 3 | 3 | 2.72% | 2.72% |
25-29 | 1 | 4 | 0.90% | 3.63% |
30-34 | 4 | 8 | 3.63% | 7.25% |
35-39 | 8 | 16 | 7.27% | 14.52% |
40-44 | 12 | 28 | 10.90% | 25.42% |
45-49 | 8 | 36 | 7.27% | 32.69% |
50-54 | 16 | 52 | 14.54% | 47.23% |
55-59 | 15 | 67 | 13.63% |60.86% |
60-64 | 14 | 81 | 12.72% | 73.58% |
65-69 | 10 | 91 | 9.09% | 82.67% |
70-74 | 6 | 97 | 5.45% | 88.12% |
75-79 | 7 | 104 | 6.36% | 94.48% |
80-84 | 5 | 109 | 4.54% | 99.02% |
85-89 | 1 | 110 | 0.90% | 99.92% |

Diagrama de tallo y hojas
2 | 1 2 4 9 |
3 | 2 3 4 4 5 5 5 6 7 7 7 8 |
4 | 0 0 0 0 1 1 4 4 4 4 4 4 6 6 6 7 8 8 8 9 |
5 | 0 0 1 1 1 2 2 2 2 2 3 3 3 3 4 4 5 5 5 55 6 6 6 7 7 8 8 8 8 9 |
6 | 0 0 1 1 1 1 2 2 2 2 3 3 3 4 5 6 6 6 6 6 6 8 9 9 |
7 | 1 1 3 3 3 4 5 5 6 7 7 7 9 |
8 | 0 1 1 3 4 8 |

Mediana: 110/2=55
Q1=110/4 = posición 27= 44
Q2=mediana=55
Q3=110/4=posición 82=66
Rango Intercuartílico: 66-44= 22
LBI: 44-(1.5 x 22)=11
LBS: 66+(1.5 x 22)=99

Toneladas de maíz cosechadas en un campo experimental
2.73 | 1.62 | 2.58 | 1.65 | 0.96 |1.33 | 0.75 | 0.69 |
2.84 | 1.46 | 0.57 | 1.34 | 2.05 | 1.46 | 1.21 | 1.69 |
2.13 | 2.06 | 2.03 | 2.21 | 1.36 | 0.45 | 1.97 | 1.27 |
0.89 | 2.17 | 1.62 | 1.82 | 1.37 | 2.39 | 2.21 | 0.96 |
N= 32
Rango: dato mayor – dato menor= 2.84 – 0.45= 2.39
Numero de clases: 1 + 3.322 log 32 = 6
Ancho de clase: (dato sup. – dato inf.)/no. Clases = (2.84-0.45)/6= 0.398 ≈ 0.4

N=32 | f | fa | fr |...