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DESCRIPCIÓN DEL PROBLEMA
• UNA CARACTERÍSTICA DE CALIDAD EN LAS TIENDAS DE CONVENIENCIA ES EL TIEMPO DE ATENCIÓN AL CLIENTE EN LA CAJA. LA TABLA ADJUNTA CONTIENE LOS TIEMPOS DE ATENCIÓN, EN MINUTOS, DE 300 CLIENTES, REDONDEADAS A DÉCIMAS DE MINUTO.
DATOS A EMPLEAR
Según las especificaciones del problema estos son nuestros datos aleatorios a usar
16 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 301 2.6 2.8 3.1 2.8 2.9 2.7 3.2 2.1 2.7 3.3 3.0 2.4 2.9 2.7 2.4 2.7 2.9 2.8 2.6 3.2 3.0 2.9 2.9 2.5 3.1 2.7 3.2 2.7 3.1 2.8
2 2.5 2.4 2.7 2.7 3.0 2.9 2.8 2.8 3.0 3.4 2.5 2.6 3.4 2.6 2.7 3.4 2.8 2.6 2.4 2.6 3.1 2.6 2.7 2.6 3.1 2.7 2.9 2.6 2.7 3.2
3 2.9 2.4 3.1 2.7 3.2 2.5 3.2 2.0 2.2 2.7 2.8 2.6 3.0 2.9 2.8 2.8 2.5 2.3 2.6 2.9 2.4 2.9 3.3 3.1 3.1 3.2 3.0 2.8 2.8 3.0
4 2.7 2.8 3.2 2.4 3.0 2.7 2.2 2.6 3.0 3.0 2.5 2.5 3.0 3.4 2.8 2.3 2.7 3.0 2.6 2.4 3.1 2.9 3.0 2.9 2.9 2.5 3.0 3.2 2.4 2.7
5 2.9 2.6 2.4 2.8 2.8 3.3 3.0 2.7 2.7 2.9 2.4 2.6 2.7 2.6 2.7 2.6 3.1 2.7 3.3 3.1 2.9 2.7 2.8 3.1 2.6 2.8 2.8 3.0 2.2 3.2
6 3.1 2.9 3.3 2.5 2.8 2.5 3.2 2.7 2.3 2.6 3.1 2.3 2.6 2.6 2.8 3.4 2.7 2.7 3.1 2.9 2.7 2.8 2.8 3.0 3.0 2.8 2.5 2.7 2.6 2.7
7 2.5 3.1 3.3 2.5 2.7 2.3 3.3 2.5 2.6 2.9 2.7 2.9 3.0 2.2 2.6 2.7 3.5 2.8 2.6 2.8 2.7 3.1 2.9 2.9 2.3 3.1 2.6 2.8 2.9 2.8
8 3.4 3.0 2.9 2.6 2.6 2.8 2.6 3.0 2.6 2.7 2.7 2.8 2.4 2.8 2.6 3.1 3.1 2.5 2.5 2.3 2.5 2.9 3.2 2.9 3.0 2.8 2.6 2.9 3.2 3.1
9 3.0 3.0 2.0 2.5 3.1 3.0 2.9 2.9 2.8 2.6 3.2 2.6 2.5 2.8 2.6 3.0 2.6 2.8 2.9 3.0 3.3 2.9 2.7 2.7 3.1 2.5 2.7 2.2 3.0 2.5
10 2.9 3.1 3.8 3.0 2.9 2.7 2.7 2.5 2.5 3.1 2.9 3.5 2.3 2.5 2.5 2.5 2.6 2.7 2.7 2.7 3.0 3.1 2.5 2.9 2.4 2.4 2.5 2.9 2.9 2.8
PREGUNTAS.
• 1. CON BASE EN LA INFORMACIÓN, EXPLICA CUÁL ES LA POBLACIÓN.
• ES EL CONJUNTO DE CLIENTES DE LA TIENDA
• 2. ¿SE ESTUDIÓ LA POBLACIÓN COMPLETA? ¿O SE TRATA SÓLO DE UNA MUESTRA?
• SOLO SE TRATA DE UNA MUESTRA, POR QUE SE TOMA COMO REFERENCIA LOS CLIENTES DE UNA SOLA TIENDA.
• 3. ¿CUÁL ES LA VARIABLE DE INTERÉS?
• EL NUMERO DE CLIENTES QUE FUERON ATENDIDOS EN LA TIENDA Y SUS TIEMPOS EN CAJA.
• 4. DETERMINA EL TIPO DE VARIABLE Y SU ESCALA DE MEDICIÓN.
• VARIABLE CUANTITATIVA DISCRETA
x i fi fai fri frai fix i |xi-x|fi (x i-x)2 fi
2.0 2 2 0.0067 0.67% 4 1.59 1.262.1 1 3 0.0033 1.00% 2.1 0.69 0.482.2 5 8 0.0167 2.67% 11 2.97 1.762.3 8 16 0.0267 5.33% 18.4 3.95 1.952.4 14 30 0.0467 10.00% 33.6 5.51 2.172.5 28 58 0.0933 19.33% 70 8.22 2.412.6 37 95 0.1233 31.67% 96.2 7.17 1.392.7 44 139 0.1467 46.33% 118.8 4.12 0.392.8 36 175 0.1200 58.33% 100.8 0.23 0.002.9 38 213 0.1267 71.00% 110.2 4.04 0.433.0 30 243 0.1000 81.00% 90 6.19 1.283.1 26 269 0.0867 89.67% 80.6 7.96 2.443.2 14 283 0.0467 94.33% 44.8 5.69 2.313.3 8 291 0.0267 97.00% 26.4 4.05 2.053.4 6 297 0.0200 99.00% 20.4 3.64 2.213.5 2 299 0.0067 99.67% 7 1.41 1.003.6 0 299 0.0000 99.67% 0 0.00 0.003.7 0 299 0.0000 99.67% 0 0.00 0.003.8 1 300 0.0033 100.00% 3.8 1.01 1.01
Totales 838.1 68.44 24.54x= 2.79
0.22813110.0817932220.285995144Desviación=
Categorias o clasesFrecuencias Medidas de tendencia central
y dispersion
Desviación Media=Varianza=
PREGUNTAS.• ELABORA LA
TABLA DE DISTRIBUCIÓN DE FRECUENCIAS E INTERPRETA LOS RESULTADOS
• DETERMINAR:
• MEDIA ARITMÉTICA.
• MEDIANA
• MODA
• DESVIACIÓN MEDIA
• VARIANZA
• DESVIACIÓN ESTÁNDAR
Media Aritmética
Moda
Mediana
Desviación Media
Desviación Estándar
Varianza
x i fi fai fri frai fix i |xi-x|fi (x i-x)2 fi
2.0 2 2 0.0067 0.67% 4 1.59 1.262.1 1 3 0.0033 1.00% 2.1 0.69 0.482.2 5 8 0.0167 2.67% 11 2.97 1.762.3 8 16 0.0267 5.33% 18.4 3.95 1.952.4 14 30 0.0467 10.00% 33.6 5.51 2.172.5 28 58 0.0933 19.33% 70 8.22 2.412.6 37 95 0.1233 31.67% 96.2 7.17 1.392.7 44 139 0.1467 46.33% 118.8 4.12 0.392.8 36 175 0.1200 58.33% 100.8 0.23 0.002.9 38 213 0.1267 71.00% 110.2 4.04 0.433.0 30 243 0.1000 81.00% 90 6.19 1.283.1 26 269 0.0867 89.67% 80.6 7.96 2.443.2 14 283 0.0467 94.33% 44.8 5.69 2.313.3 8 291 0.0267 97.00% 26.4 4.05 2.053.4 6 297 0.0200 99.00% 20.4 3.64 2.213.5 2 299 0.0067 99.67% 7 1.41 1.003.6 0 299 0.0000 99.67% 0 0.00 0.003.7 0 299 0.0000 99.67% 0 0.00 0.003.8 1 300 0.0033 100.00% 3.8 1.01 1.01
Totales 838.1 68.44 24.54x= 2.79
0.22813110.0817932220.285995144
Categorias o clasesFrecuencias
GRÁFICA DE BARRAS• UNA GRÁFICA DE BARRAS
CON LA FRECUENCIA ABSOLUTA
Frecuencia Absoluta
x i fi fai fri frai fix i |xi-x|fi (x i-x)2 fi
2.0 2 2 0.0067 0.67% 4 1.59 1.262.1 1 3 0.0033 1.00% 2.1 0.69 0.482.2 5 8 0.0167 2.67% 11 2.97 1.762.3 8 16 0.0267 5.33% 18.4 3.95 1.952.4 14 30 0.0467 10.00% 33.6 5.51 2.172.5 28 58 0.0933 19.33% 70 8.22 2.412.6 37 95 0.1233 31.67% 96.2 7.17 1.392.7 44 139 0.1467 46.33% 118.8 4.12 0.392.8 36 175 0.1200 58.33% 100.8 0.23 0.002.9 38 213 0.1267 71.00% 110.2 4.04 0.433.0 30 243 0.1000 81.00% 90 6.19 1.283.1 26 269 0.0867 89.67% 80.6 7.96 2.443.2 14 283 0.0467 94.33% 44.8 5.69 2.313.3 8 291 0.0267 97.00% 26.4 4.05 2.053.4 6 297 0.0200 99.00% 20.4 3.64 2.213.5 2 299 0.0067 99.67% 7 1.41 1.003.6 0 299 0.0000 99.67% 0 0.00 0.003.7 0 299 0.0000 99.67% 0 0.00 0.003.8 1 300 0.0033 100.00% 3.8 1.01 1.01
Totales 838.1 68.44 24.54x= 2.79
0.22813110.0817932220.285995144
Categorias o clasesFrecuencias
x i fi fai fri frai fix i |xi-x|fi (x i-x)2 fi
2.0 2 2 0.0067 0.67% 4 1.59 1.262.1 1 3 0.0033 1.00% 2.1 0.69 0.482.2 5 8 0.0167 2.67% 11 2.97 1.762.3 8 16 0.0267 5.33% 18.4 3.95 1.952.4 14 30 0.0467 10.00% 33.6 5.51 2.172.5 28 58 0.0933 19.33% 70 8.22 2.412.6 37 95 0.1233 31.67% 96.2 7.17 1.392.7 44 139 0.1467 46.33% 118.8 4.12 0.392.8 36 175 0.1200 58.33% 100.8 0.23 0.002.9 38 213 0.1267 71.00% 110.2 4.04 0.433.0 30 243 0.1000 81.00% 90 6.19 1.283.1 26 269 0.0867 89.67% 80.6 7.96 2.443.2 14 283 0.0467 94.33% 44.8 5.69 2.313.3 8 291 0.0267 97.00% 26.4 4.05 2.053.4 6 297 0.0200 99.00% 20.4 3.64 2.213.5 2 299 0.0067 99.67% 7 1.41 1.003.6 0 299 0.0000 99.67% 0 0.00 0.003.7 0 299 0.0000 99.67% 0 0.00 0.003.8 1 300 0.0033 100.00% 3.8 1.01 1.01
Totales 838.1 68.44 24.54x= 2.79
0.22813110.0817932220.285995144
Frecuencias
GRAFICA CIRCULAR• UNA GRÁFICA
CIRCULAR CON LA FRECUENCIA RELATIVA
Frecuencia Relativa
xi fi fai fri frai fixi |xi-x|fi (x i-x)2 fi
2.0 2 2 0.0067 0.67% 4 1.59 1.262.1 1 3 0.0033 1.00% 2.1 0.69 0.482.2 5 8 0.0167 2.67% 11 2.97 1.762.3 8 16 0.0267 5.33% 18.4 3.95 1.952.4 14 30 0.0467 10.00% 33.6 5.51 2.172.5 28 58 0.0933 19.33% 70 8.22 2.412.6 37 95 0.1233 31.67% 96.2 7.17 1.392.7 44 139 0.1467 46.33% 118.8 4.12 0.392.8 36 175 0.1200 58.33% 100.8 0.23 0.002.9 38 213 0.1267 71.00% 110.2 4.04 0.433.0 30 243 0.1000 81.00% 90 6.19 1.283.1 26 269 0.0867 89.67% 80.6 7.96 2.443.2 14 283 0.0467 94.33% 44.8 5.69 2.313.3 8 291 0.0267 97.00% 26.4 4.05 2.053.4 6 297 0.0200 99.00% 20.4 3.64 2.213.5 2 299 0.0067 99.67% 7 1.41 1.003.6 0 299 0.0000 99.67% 0 0.00 0.003.7 0 299 0.0000 99.67% 0 0.00 0.003.8 1 300 0.0033 100.00% 3.8 1.01 1.01
Totales 838.1 68.44 24.54x= 2.79
0.22813110.0817932220.285995144
Categorias o clasesFrecuencias
xi fi fai fri frai fixi |xi-x|fi (x i-x)2 fi
2.0 2 2 0.0067 0.67% 4 1.59 1.262.1 1 3 0.0033 1.00% 2.1 0.69 0.482.2 5 8 0.0167 2.67% 11 2.97 1.762.3 8 16 0.0267 5.33% 18.4 3.95 1.952.4 14 30 0.0467 10.00% 33.6 5.51 2.172.5 28 58 0.0933 19.33% 70 8.22 2.412.6 37 95 0.1233 31.67% 96.2 7.17 1.392.7 44 139 0.1467 46.33% 118.8 4.12 0.392.8 36 175 0.1200 58.33% 100.8 0.23 0.002.9 38 213 0.1267 71.00% 110.2 4.04 0.433.0 30 243 0.1000 81.00% 90 6.19 1.283.1 26 269 0.0867 89.67% 80.6 7.96 2.443.2 14 283 0.0467 94.33% 44.8 5.69 2.313.3 8 291 0.0267 97.00% 26.4 4.05 2.053.4 6 297 0.0200 99.00% 20.4 3.64 2.213.5 2 299 0.0067 99.67% 7 1.41 1.003.6 0 299 0.0000 99.67% 0 0.00 0.003.7 0 299 0.0000 99.67% 0 0.00 0.003.8 1 300 0.0033 100.00% 3.8 1.01 1.01
Totales 838.1 68.44 24.54x= 2.79
0.22813110.0817932220.285995144
Frecuencias
GRAFICA DE POLÍGONOS• UNA GRÁFICA DE POLÍGONO CON LA FRECUENCIA RELATIVA
ACUMULADA
Frecuencia R. Acumulada
xi fi fai fri frai fixi |xi-x|fi (x i-x)2 fi
2.0 2 2 0.0067 0.67% 4 1.59 1.262.1 1 3 0.0033 1.00% 2.1 0.69 0.482.2 5 8 0.0167 2.67% 11 2.97 1.762.3 8 16 0.0267 5.33% 18.4 3.95 1.952.4 14 30 0.0467 10.00% 33.6 5.51 2.172.5 28 58 0.0933 19.33% 70 8.22 2.412.6 37 95 0.1233 31.67% 96.2 7.17 1.392.7 44 139 0.1467 46.33% 118.8 4.12 0.392.8 36 175 0.1200 58.33% 100.8 0.23 0.002.9 38 213 0.1267 71.00% 110.2 4.04 0.433.0 30 243 0.1000 81.00% 90 6.19 1.283.1 26 269 0.0867 89.67% 80.6 7.96 2.443.2 14 283 0.0467 94.33% 44.8 5.69 2.313.3 8 291 0.0267 97.00% 26.4 4.05 2.053.4 6 297 0.0200 99.00% 20.4 3.64 2.213.5 2 299 0.0067 99.67% 7 1.41 1.003.6 0 299 0.0000 99.67% 0 0.00 0.003.7 0 299 0.0000 99.67% 0 0.00 0.003.8 1 300 0.0033 100.00% 3.8 1.01 1.01
Totales 838.1 68.44 24.54x= 2.79
0.22813110.0817932220.285995144
Categorias o clasesFrecuencias
GRAFICA DE RADIANES• UNA GRÁFICA RADIAL CON LOS DATOS QUE CONSIDERES APROPIADOS.
Frecuencia Absoluta
xi fi fai fri frai fixi |xi-x|fi (x i-x)2 fi
2.0 2 2 0.0067 0.67% 4 1.59 1.262.1 1 3 0.0033 1.00% 2.1 0.69 0.482.2 5 8 0.0167 2.67% 11 2.97 1.762.3 8 16 0.0267 5.33% 18.4 3.95 1.952.4 14 30 0.0467 10.00% 33.6 5.51 2.172.5 28 58 0.0933 19.33% 70 8.22 2.412.6 37 95 0.1233 31.67% 96.2 7.17 1.392.7 44 139 0.1467 46.33% 118.8 4.12 0.392.8 36 175 0.1200 58.33% 100.8 0.23 0.002.9 38 213 0.1267 71.00% 110.2 4.04 0.433.0 30 243 0.1000 81.00% 90 6.19 1.283.1 26 269 0.0867 89.67% 80.6 7.96 2.443.2 14 283 0.0467 94.33% 44.8 5.69 2.313.3 8 291 0.0267 97.00% 26.4 4.05 2.053.4 6 297 0.0200 99.00% 20.4 3.64 2.213.5 2 299 0.0067 99.67% 7 1.41 1.003.6 0 299 0.0000 99.67% 0 0.00 0.003.7 0 299 0.0000 99.67% 0 0.00 0.003.8 1 300 0.0033 100.00% 3.8 1.01 1.01
Totales 838.1 68.44 24.54x= 2.79
0.22813110.0817932220.285995144
Categorias o clasesFrecuencias
GRAFICA DE CAJAS• UNA GRÁFICA DE CAJAS Y
BIGOTES.
Mínimo = 2.0Cuartil 1 = 2.45Cuartil 2 = 2.90Cuartil 3 = 3.35Máximo = 3.8
𝑄1=𝑛4∗1
𝑄2=𝑛4∗2
𝑄3=𝑛4∗3
Valores Atípicos𝑓 1=𝑄1−1.5𝑅𝐼𝑓 3=𝑄3+1.5𝑅𝐼
Rango Inter-cuartilico (RI)𝑅𝐼=𝑄1−𝑄3
Q1
Q3
Q2