Transporte de petróleo mediante oleoductos en Ecuador
Variable: Eficiencia operativa (%) (cuantitativa continua)
*
2026-11-14
1 Carga de librerias
library(readxl)
library(dplyr)
library(gt)
library(e1071)2 Carga de datos
setwd("C:/Users/HP/Desktop/tabla_petro")
archivo <- list.files(pattern = "^tabla_transporte_petroleo.*\\.xlsx$")[1]
if (is.na(archivo)) stop("No se encontró el archivo .xlsx dentro de la carpeta tabla_petro")
datos <- as.data.frame(read_excel(archivo, sheet = "Datos_10000"))
dim(datos)## [1] 10000 203 Selección de la variable
Variable <- as.numeric(na.omit(datos$Eficiencia_operativa_estimada_pct))
if (length(Variable) == 0) {
stop("ERROR: No hay datos válidos para la variable seleccionada.")
}4 Frecuencia
Se agrupan los datos en K clases con la regla de Sturges.
N <- length(Variable)
K <- floor(1 + 3.322 * log10(N))
breaks_table <- seq(min(Variable), max(Variable), length.out = K + 1)
ni <- as.vector(table(cut(Variable, breaks = breaks_table, include.lowest = TRUE, right = FALSE)))
hi <- (ni / sum(ni)) * 100
Ni_asc <- cumsum(ni)
Ni_desc <- rev(cumsum(rev(ni)))
Hi_asc <- cumsum(hi)
Hi_desc <- rev(cumsum(rev(hi)))5 Tabla de Distribución de Frecuencia
A continuación se presenta la tabla de distribución de frecuencias obtenida.
5.1 Tabla General
TDF_General <- data.frame(
Li = round(breaks_table[1:K], 2),
Ls = round(breaks_table[2:(K + 1)], 2),
MC = round((breaks_table[1:K] + breaks_table[2:(K + 1)]) / 2, 2),
ni = ni,
hi = hi,
Ni_asc = Ni_asc,
Ni_desc = Ni_desc,
Hi_asc = Hi_asc,
Hi_desc = Hi_desc
)
TDF_General %>%
gt(rowname_col = "Li") %>%
tab_header(
title = md("**DISTRIBUCIÓN DE FRECUENCIAS: Eficiencia operativa (%)**"),
subtitle = md("Variable: **Eficiencia operativa**")
) %>%
tab_source_note(source_note = "Autor: *") %>%
grand_summary_rows(
columns = c(ni, hi),
fns = list("TOTAL" = ~sum(., na.rm = TRUE))
) %>%
fmt_number(
columns = c(ni, Ni_asc, Ni_desc),
decimals = 0,
use_seps = TRUE
) %>%
fmt_number(
columns = c(hi, Hi_asc, Hi_desc),
decimals = 2
) %>%
cols_label(
Ls = "Lím. Sup", MC = "Marca Clase (Xi)",
ni = "ni", hi = "hi (%)",
Ni_asc = "Ni (Asc)", Ni_desc = "Ni (Desc)",
Hi_asc = "Hi (Asc)", Hi_desc = "Hi (Desc)"
) %>%
tab_stubhead(label = "Lím. Inf") %>%
cols_align(align = "center", columns = everything()) %>%
tab_style(
style = cell_text(align = "center"),
locations = cells_stub()
) %>%
tab_style(
style = list(cell_fill(color = "#235347"), cell_text(color = "white", weight = "bold")),
locations = list(cells_title(), cells_column_labels(), cells_stubhead())
) %>%
tab_options(
table.border.top.style = "none",
table.border.bottom.color = "#235347",
column_labels.border.bottom.color = "#235347",
data_row.padding = px(6)
)| DISTRIBUCIÓN DE FRECUENCIAS: Eficiencia operativa (%) | ||||||||
| Variable: Eficiencia operativa | ||||||||
| Lím. Inf | Lím. Sup | Marca Clase (Xi) | ni | hi (%) | Ni (Asc) | Ni (Desc) | Hi (Asc) | Hi (Desc) |
|---|---|---|---|---|---|---|---|---|
| 69.09 | 71.30 | 70.19 | 1 | 0.01 | 1 | 10,000 | 0.01 | 100.00 |
| 71.30 | 73.51 | 72.40 | 6 | 0.06 | 7 | 9,999 | 0.07 | 99.99 |
| 73.51 | 75.71 | 74.61 | 16 | 0.16 | 23 | 9,993 | 0.23 | 99.93 |
| 75.71 | 77.92 | 76.82 | 31 | 0.31 | 54 | 9,977 | 0.54 | 99.77 |
| 77.92 | 80.13 | 79.03 | 96 | 0.96 | 150 | 9,946 | 1.50 | 99.46 |
| 80.13 | 82.34 | 81.23 | 144 | 1.44 | 294 | 9,850 | 2.94 | 98.50 |
| 82.34 | 84.54 | 83.44 | 271 | 2.71 | 565 | 9,706 | 5.65 | 97.06 |
| 84.54 | 86.75 | 85.65 | 424 | 4.24 | 989 | 9,435 | 9.89 | 94.35 |
| 86.75 | 88.96 | 87.86 | 552 | 5.52 | 1,541 | 9,011 | 15.41 | 90.11 |
| 88.96 | 91.17 | 90.06 | 850 | 8.50 | 2,391 | 8,459 | 23.91 | 84.59 |
| 91.17 | 93.38 | 92.27 | 975 | 9.75 | 3,366 | 7,609 | 33.66 | 76.09 |
| 93.38 | 95.58 | 94.48 | 1,107 | 11.07 | 4,473 | 6,634 | 44.73 | 66.34 |
| 95.58 | 97.79 | 96.69 | 1,221 | 12.21 | 5,694 | 5,527 | 56.94 | 55.27 |
| 97.79 | 100.00 | 98.90 | 4,306 | 43.06 | 10,000 | 4,306 | 100.00 | 43.06 |
| TOTAL | — | — | 10000 | 100 | — | — | — | — |
| Autor: * | ||||||||
5.2 Tabla Simplificada
Se redefinen las clases con límites redondeados y una amplitud constante.
breaks_table <- pretty(Variable, n = K)
amplitud <- breaks_table[2] - breaks_table[1]
K <- length(breaks_table) - 1
ni <- as.vector(table(cut(Variable, breaks = breaks_table, include.lowest = TRUE, right = FALSE)))
hi <- (ni / sum(ni)) * 100
Ni_asc <- cumsum(ni)
Ni_desc <- rev(cumsum(rev(ni)))
Hi_asc <- cumsum(hi)
Hi_desc <- rev(cumsum(rev(hi)))
TDF_Simple <- data.frame(
Li = round(breaks_table[1:K], 2),
Ls = round(breaks_table[2:(K + 1)], 2),
MC = round((breaks_table[1:K] + breaks_table[2:(K + 1)]) / 2, 2),
ni = ni,
hi = hi,
Ni_asc = Ni_asc,
Ni_desc = Ni_desc,
Hi_asc = Hi_asc,
Hi_desc = Hi_desc
)
TDF_Simple %>%
gt(rowname_col = "Li") %>%
tab_header(
title = md("**DISTRIBUCIÓN DE FRECUENCIAS SIMPLIFICADA: Eficiencia operativa (%)**"),
subtitle = md(paste0("Variable: **Eficiencia operativa** (Amplitud = ", round(amplitud, 2), ")"))
) %>%
tab_source_note(source_note = "Autor: *") %>%
grand_summary_rows(
columns = c(ni, hi),
fns = list("TOTAL" = ~sum(., na.rm = TRUE))
) %>%
fmt_number(
columns = c(ni, Ni_asc, Ni_desc),
decimals = 0,
use_seps = TRUE
) %>%
fmt_number(
columns = c(hi, Hi_asc, Hi_desc),
decimals = 2
) %>%
cols_label(
Ls = "Lím. Sup", MC = "Marca Clase (Xi)",
ni = "ni", hi = "hi (%)",
Ni_asc = "Ni (Asc)", Ni_desc = "Ni (Desc)",
Hi_asc = "Hi (Asc)", Hi_desc = "Hi (Desc)"
) %>%
tab_stubhead(label = "Lím. Inf") %>%
cols_align(align = "center", columns = everything()) %>%
tab_style(
style = cell_text(align = "center"),
locations = cells_stub()
) %>%
tab_style(
style = list(cell_fill(color = "#235347"), cell_text(color = "white", weight = "bold")),
locations = list(cells_title(), cells_column_labels(), cells_stubhead())
) %>%
tab_options(
table.border.top.style = "none",
table.border.bottom.color = "#235347",
column_labels.border.bottom.color = "#235347",
data_row.padding = px(6)
)| DISTRIBUCIÓN DE FRECUENCIAS SIMPLIFICADA: Eficiencia operativa (%) | ||||||||
| Variable: Eficiencia operativa (Amplitud = 2) | ||||||||
| Lím. Inf | Lím. Sup | Marca Clase (Xi) | ni | hi (%) | Ni (Asc) | Ni (Desc) | Hi (Asc) | Hi (Desc) |
|---|---|---|---|---|---|---|---|---|
| 68 | 70 | 69 | 1 | 0.01 | 1 | 10,000 | 0.01 | 100.00 |
| 70 | 72 | 71 | 1 | 0.01 | 2 | 9,999 | 0.02 | 99.99 |
| 72 | 74 | 73 | 8 | 0.08 | 10 | 9,998 | 0.10 | 99.98 |
| 74 | 76 | 75 | 18 | 0.18 | 28 | 9,990 | 0.28 | 99.90 |
| 76 | 78 | 77 | 26 | 0.26 | 54 | 9,972 | 0.54 | 99.72 |
| 78 | 80 | 79 | 86 | 0.86 | 140 | 9,946 | 1.40 | 99.46 |
| 80 | 82 | 81 | 131 | 1.31 | 271 | 9,860 | 2.71 | 98.60 |
| 82 | 84 | 83 | 211 | 2.11 | 482 | 9,729 | 4.82 | 97.29 |
| 84 | 86 | 85 | 326 | 3.26 | 808 | 9,518 | 8.08 | 95.18 |
| 86 | 88 | 87 | 461 | 4.61 | 1,269 | 9,192 | 12.69 | 91.92 |
| 88 | 90 | 89 | 655 | 6.55 | 1,924 | 8,731 | 19.24 | 87.31 |
| 90 | 92 | 91 | 802 | 8.02 | 2,726 | 8,076 | 27.26 | 80.76 |
| 92 | 94 | 93 | 944 | 9.44 | 3,670 | 7,274 | 36.70 | 72.74 |
| 94 | 96 | 95 | 1,029 | 10.29 | 4,699 | 6,330 | 46.99 | 63.30 |
| 96 | 98 | 97 | 1,096 | 10.96 | 5,795 | 5,301 | 57.95 | 53.01 |
| 98 | 100 | 99 | 4,205 | 42.05 | 10,000 | 4,205 | 100.00 | 42.05 |
| TOTAL | — | — | 10000 | 100 | — | — | — | — |
| Autor: * | ||||||||
6 Gráficas De Distribución De Frecuencias
Esta sección presenta la visualización de la distribución de los datos.
6.1 Histogramas de Frecuencia
col_barras <- "#235347"
col_ejes <- "#163832"
col_claro <- "#8EB69B"
h_base <- hist(Variable, breaks = breaks_table, right = FALSE, include.lowest = TRUE, plot = FALSE)
limite_x <- range(breaks_table)
etiquetas_x <- format(breaks_table, scientific = FALSE, trim = TRUE)6.2 GRÁFICO 1: Histograma Absoluto (Local)
par(mar = c(8, 5, 4, 2))
plot(h_base,
main = "Gráfica N°1: Distribución de Eficiencia operativa",
xlab = "Eficiencia operativa (%)", ylab = "Frecuencia absoluta",
col = col_barras, border = "white", axes = FALSE,
ylim = c(0, max(h_base$counts) * 1.1),
xlim = limite_x, cex.main = 1)
axis(1, at = breaks_table, labels = etiquetas_x, las = 2, cex.axis = 0.7)
axis(2)
grid(nx = NA, ny = NULL, col = "#D7DBDD", lty = "dotted")
6.3 GRÁFICO 2: Histograma Absoluto (Global)
par(mar = c(8, 5, 4, 2))
plot(h_base,
main = "Gráfica N°2: Distribución de Eficiencia operativa",
xlab = "Eficiencia operativa (%)", ylab = "Total registros",
col = col_barras, border = "white", axes = FALSE,
ylim = c(0, sum(h_base$counts)),
xlim = limite_x, cex.main = 1)
axis(1, at = breaks_table, labels = etiquetas_x, las = 2, cex.axis = 0.7)
axis(2)
grid(nx = NA, ny = NULL, col = "#D7DBDD", lty = "dotted")
6.4 Gráficos Porcentuales
h_porc <- h_base
h_porc$counts <- (h_porc$counts / sum(h_porc$counts)) * 1006.5 GRÁFICO 3: Porcentajes (Local)
par(mar = c(8, 5, 4, 2))
plot(h_porc,
main = "Gráfica N°3: Distribución porcentual de Eficiencia operativa",
xlab = "Eficiencia operativa (%)", ylab = "Porcentaje (%)",
col = col_barras, border = "white", axes = FALSE, freq = TRUE,
ylim = c(0, max(h_porc$counts) * 1.2),
xlim = limite_x, cex.main = 1)
axis(1, at = breaks_table, labels = etiquetas_x, las = 2, cex.axis = 0.7)
axis(2)
text(x = h_base$mids, y = h_porc$counts,
labels = paste0(round(h_porc$counts, 1), "%"),
pos = 3, cex = 0.6, col = col_ejes)
6.6 GRÁFICO 4: Porcentajes (Global)
par(mar = c(8, 5, 4, 2))
plot(h_porc,
main = "Gráfica N°4: Distribución porcentual de Eficiencia operativa",
xlab = "Eficiencia operativa (%)", ylab = "% del total",
col = col_barras, border = "white", axes = FALSE, freq = TRUE,
ylim = c(0, 100),
xlim = limite_x, cex.main = 1)
axis(1, at = breaks_table, labels = etiquetas_x, las = 2, cex.axis = 0.7)
axis(2)
text(x = h_base$mids, y = h_porc$counts,
labels = paste0(round(h_porc$counts, 1), "%"),
pos = 3, cex = 0.6, col = col_ejes)
6.7 GRÁFICO 5: Boxplot
par(mar = c(8, 5, 4, 2))
boxplot(Variable, horizontal = TRUE, col = col_barras,
main = "Gráfica N°5: Diagrama de caja de Eficiencia operativa",
xlab = "Eficiencia operativa (%)", outline = TRUE, outpch = 19,
outcol = col_claro, axes = FALSE, xlim = c(0.7, 1.3),
ylim = limite_x, cex.main = 1)
axis(1, at = breaks_table, labels = etiquetas_x, las = 2, cex.axis = 0.7)
box()
6.8 GRÁFICO 6: Ojivas
par(mar = c(8, 5, 4, 8), xpd = TRUE)
plot(breaks_table, c(0, Ni_asc), type = "o", col = col_barras,
lwd = 2, pch = 19, axes = FALSE,
main = "Gráfica N°6: Ojivas ascendente y descendente de Eficiencia operativa",
xlab = "Eficiencia operativa (%)", ylab = "Frecuencia acumulada", cex.main = 1)
lines(breaks_table, c(Ni_desc, 0), type = "o", col = col_claro,
lwd = 2, pch = 19)
axis(1, at = breaks_table, labels = etiquetas_x, las = 2, cex.axis = 0.6)
axis(2)
legend("right", legend = c("Ascendente", "Descendente"),
col = c(col_barras, col_claro),
lty = 1, pch = 19, cex = 0.7, lwd = 2,
inset = c(-0.2, 0), bty = "n")
par(xpd = FALSE)7 Indicadores Estadísticos
media_val <- mean(Variable)
mediana_val <- median(Variable)
sd_val <- sd(Variable)
cv_val <- (sd_val / abs(media_val)) * 100
asimetria_val <- skewness(Variable, type = 2)
curtosis_val <- kurtosis(Variable, type = 2)
atipicos <- boxplot.stats(Variable)$out
status_atipicos <- if (length(atipicos) > 0) {
paste0(length(atipicos), " [ ", round(min(atipicos), 2), " ; ", round(max(atipicos), 2), " ]")
} else {
"0 (Sin atípicos)"
}
df_resumen <- data.frame(
Variable = "Eficiencia operativa",
Rango = paste0("[", round(min(Variable), 2), " ; ", round(max(Variable), 2), "]"),
X = media_val,
Me = mediana_val,
Mo = paste(round(TDF_Simple$MC[TDF_Simple$hi == max(TDF_Simple$hi)], 2), collapse = ", "),
Varianza = var(Variable),
sd = sd_val,
CV = cv_val,
As = asimetria_val,
K = curtosis_val,
Atipicos = status_atipicos
)
df_resumen %>%
gt() %>%
tab_header(title = md("**CONCLUSIONES Y ESTADÍSTICOS**"), subtitle = "Variable: Eficiencia operativa") %>%
tab_source_note(source_note = "Autor: *") %>%
cols_label(
X = "X",
Me = "Me",
Mo = "Mo",
sd = "sd",
CV = "CV",
As = "As",
K = "K",
Atipicos = "Valores atípicos"
) %>%
fmt_number(columns = c(X, Me, sd), decimals = 2) %>%
fmt_number(columns = Varianza, decimals = 2) %>%
fmt_number(columns = c(CV, K), decimals = 2) %>%
fmt_number(columns = As, decimals = 4) %>%
cols_width(
Variable ~ px(140),
Rango ~ px(150),
Mo ~ px(100),
Atipicos ~ px(220),
everything() ~ px(85)
) %>%
tab_options(
column_labels.background.color = "#235347",
table.border.top.style = "solid",
table.border.bottom.style = "solid",
heading.border.bottom.style = "solid",
column_labels.border.top.style = "solid",
column_labels.border.bottom.style = "solid",
data_row.padding = px(8)
) %>%
tab_style(
style = list(
cell_text(weight = "bold", color = "white"),
cell_borders(sides = c("left", "right"), color = "#D3D3D3", weight = px(1))
),
locations = cells_column_labels()
) %>%
tab_style(
style = cell_borders(sides = c("left", "right"), color = "#D3D3D3", weight = px(1)),
locations = cells_body()
)| CONCLUSIONES Y ESTADÍSTICOS | ||||||||||
| Variable: Eficiencia operativa | ||||||||||
| Variable | Rango | X | Me | Mo | Varianza | sd | CV | As | K | Valores atípicos |
|---|---|---|---|---|---|---|---|---|---|---|
| Eficiencia operativa | [69.09 ; 100] | 94.93 | 96.57 | 99 | 29.93 | 5.47 | 5.76 | −1.0508 | 0.48 | 79 [ 69.09 ; 78.72 ] |
| Autor: * | ||||||||||
txt_cv <- if (cv_val < 15) "homogéneo" else if (cv_val <= 30) "moderadamente heterogéneo" else "heterogéneo"
txt_ubic <- if (asimetria_val > 0.5) "se agrupan en la parte baja de la variable" else if (asimetria_val < -0.5) "se agrupan en la parte alta de la variable" else "se reparten de forma equilibrada alrededor de la media"
txt_asim <- if (abs(asimetria_val) < 0.5) "aproximadamente simétrica" else if (asimetria_val > 0) "asimétrica positiva (sesgo a la derecha)" else "asimétrica negativa (sesgo a la izquierda)"
txt_curt <- if (abs(curtosis_val) < 0.5) "mesocúrtica (similar a la normal)" else if (curtosis_val > 0) "leptocúrtica (más concentrada y con colas más pesadas)" else "platicúrtica (más aplanada)"
txt_atip <- if (length(atipicos) > 0) {
paste0("Se identificaron ", length(atipicos), " valores atípicos, en el rango de ", round(min(atipicos), 2), " a ", round(max(atipicos), 2), ".")
} else {
"No se identificaron valores atípicos."
}8 Conclusiones
Los valores de Eficiencia operativa fluctúan entre 69.09 y 100 y giran en torno a la media de 94.93 (mediana de 96.57), con una desviación estándar de 5.47. Con un coeficiente de variación de 5.76 %, el conjunto de datos es homogéneo y sus valores se agrupan en la parte alta de la variable. La distribución es asimétrica negativa (sesgo a la izquierda) (As = -1.0508) y mesocúrtica (similar a la normal) (K = 0.48). Se identificaron 79 valores atípicos, en el rango de 69.09 a 78.72.