ESTADISTICA DESCRIPTIVA PASÓ 3
UNIVERSIDAD NACIONAL ABIERTA Y A DISTANCIA UNAD Escuela de Ciencias Básicas, Tecnología e Ingeniería
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INTRODUCCION
Por medio de este trabajo se pretende dar a conocer los dif erentes métodos de análisis estadísticos, estadíst icos, en este informe se encontrarán con tablas de frecuencias, imágenes y graficas que demuestran el análisis de datos recopilados por medio de una tabla en Excel los cuales son resumidos por las diferentes técnicas estadísticas
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OBJETIVOS
Objetivo general
Analizar Analizar por medio de técnicas técnicas estadísticas estadísticas el el problema planteado planteado en Excel Excel
Objetivos específicos
Clasificar las variables cuantitativas y cualitativas del problema Realizar tabla de frecuencias para identificar datos Realizar graficas de datos seleccionados Calcular medidas de tendencia central y medidas de de posición Realizar histogramas y polígonos de frecuencias
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Actividad 1. Mapa Mental.
Resumir mediante un mapa mental las medidas estadísticas univariantes, describiendo ampliamente una de ellas, ya sean las medidas de tendencia central, de posición o de dispersión.
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Actividad 2. Medidas Univariantes -variable Discreta A partir de la base de datos “ Encuesta_ Instituciones_ Educativas 2019 (16-1)”, encontrada en el entorno de aprendizaje Colaborativo, cada estudiante deberá elegir una variable cuantitativa discreta distinta, manifestarlo en el foro paso 3 Análisis de la Información y calcular las medidas de tendencia central y de dispersión.
Variable elegida: Numero de materias con desempeño bajo Posterior a la consulta de las referencias, resolver los siguientes incisos:
a. Tabla de frecuencia datos no agrupados. Cada estudiante deberá elegir una variable cuantitativa discreta y diseñar una tabla de frecuencia para datos no agrupados, a partir de ella elaborar un diagrama de barras y un diagrama de líneas.
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b. Medidas de tendencias central y de Posición. Para la variable cuantitativa discreta elegida, cada estudiante deberá calcular las medidas de tendencia central (media, mediana, moda), medidas de posición: cuartiles, Decil 5 y percentil 50, determinar el tipo de asimetría y curtosis e interpretar los resultados y asociarlos con la problemática: Bajo rendimiento académico en “
estudiantes de educación básica primaria Colombia
”
Medidas de posición Cuartiles
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=
1 ∗ 110 4
=
110 4
= 27,5 27,5 ≈ 28 28
=
El 25% de los estudiantes tienen cero materias con bajo desempeño
Q2: =
=
=
2 ∗ 110 4
=
55 + 56 2
220 4
=
= 55
1+1 2
=
El 50% de los estudiantes tienen 1 materia con bajo desempeño
Q3: =
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Deciles D5: D5: =
Donde: L: indica la posición donde se ubicara el decil k: indica el decil que se desea encontrar ya sea el 1, el 2 o el 3 n: indica el valor de la muestra o la cantidad de datos seleccionada
=
5 ∗ 110 10
=
550 10
= 55
=
El 50% de los estudiantes tienen 1 materia con bajo desempeño
D7: =
=
7 ∗ 110 10
=
770 10
= 77
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Percentiles P25: P25: =
Donde: L: indica la posición donde se ubicara el percentil k: indica el percentil que se desea encontrar ya sea el 1, el 2 o el 3 n: indica el valor de la muestra o la cantidad de datos seleccionada
=
25 ∗ 110 100
=
2750 = 27,5 ≈ 28 100
=
El 25% de los estudiantes tienen 0 materias con bajo desempeño
P50: =
=
50 ∗ 110 100
=
5500 100
= 55
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c. Medidas de Dispersión. Para la variable cuantitativa discreta elegida calcular: Rango, varianza, desviación típica, coeficiente de variación, posteriormente interpretar los resultados y asociarlos con la problemática: Bajo rendimiento académico en estudiantes de educación “
básica primaria Colombia
”
Actividad 3. Medidas Univariantes -variable Continua A partir de la base de datos “ Encuesta_ Instituciones_ Educativas 2019 (16-1)”, encontrada en el entorno de aprendizaje Colaborativo, cada estudiante deberá elegir una variable cuantitativa continua distinta, manifestarlo en el foro paso 3 Análisis de la Información y calcular las medidas
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a. Tabla de frecuencia datos agrupados. Cada estudiante deberá elegir una variable cuantitativa continua y diseñar una tabla de frecuencia para datos agrupados identificando rango, número de intervalos, amplitud y a partir de ella elaborar un histograma de frecuencias y un polígono de frecuencias. Finalmente, interpretar los resultados y asociarlos con la problemática:
Bajo rendimiento académico en estudiantes de educación básica primaria Colombia
“
Variable elegida: Peso
”
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b. Medidas de tendencias central y de Posición. Para la variable cuantitativa continúa elegida, cada estudiante deberá calcular las medidas de tendencia central (media, mediana, moda), medidas de posición: cuartiles, Decil 5 y percentil 50, determinar el tipo de asimetría y curtosis e interpretar los resultados y asociarlos con la problemática: Bajo rendimiento académico en “
estudiantes de educación básica primaria Colombia
”
Columna1
Media
31,36909091
Error típico
0,563787303
Mediana
30,6
Moda
35,2
Desviación estándar
5,913051114
Varianza de la muestra 34,96417348 Curtosis 0,383741452 Coeficiente de asimetría 0,328382643
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c. Medidas de Dispersión. Para la variable cuantitativa continúa elegida calcular: Rango, varianza, desviación típica, coeficiente de variación, posteriormente interpretar los resultados y asociarlos con la problemática: Bajo rendimiento académico en estudiantes de educación “
básica primaria Colombia
”
Columna1
Media
31,36909091
Error típico
0,563787303
Mediana
30,6
Moda
35,2
Desviación estándar
5,913051114
Varianza de la muestra 34,96417348 Curtosis 0,383741452 Coeficiente de asimetría 0,328382643 Rango
28,1
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CONCLUSIONES
Se pueden emplear análisis de frecuencias cuando los datos de una encuesta son amplios y resumirlos de manera fácil y concreta Las medidas de posición permiten desglosar por segmentos los datos datos cuando son muy numerosos y analizarlos de manera sencilla Se puede emplear programas especializados para realizar los análisis estadísticos o bien el programa Excel en el cual se aprende de manera más específica de donde salen los cálculos estadísticos
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REFERENCIAS BIBLIOGRAFICAS
García, J. E (2005). Análisis de Datos Unidimensionales.et al. Madrid: Paraninfo. Página 26 -42
Montero, J. M. (2007). Características de Una Distribución de Frecuencias. Statistical Descriptive. Cengage Learning Paraninfo, S.A. Paginas 41-50
MMLugoLopez. (2011). Medidas de tendencia central. 10 de Abril De 2019, de YouTube Sitio web: https://www.youtube.com/watch?v=jstpOsLt_YI
Marco Martinez. (2012). Tablas de distribucion de frecuencias. 10 de Abril de 2019, de YouTube Sitio web: https://www.youtube.com/watch?v=bKK0kXzwpgs