LATITUDE
MARTIN SARMIENTO
2025-12-01
1 Configuración y Carga de Datos
##### UNIVERSIDAD CENTRAL DEL ECUADOR #####
#### AUTOR: MARTIN SARMIENTO ####
### CARRERA: INGENIERÍA EN PETRÓLEOS #####
#### VARIABLE LATITUD ####
## DATASET ##
setwd("~/R/LATITUD")
# Cargar dataset
Datos <- read.csv("DataSet_.csv", sep = ";", fileEncoding = "latin1")
# Estructura de los datos
str(Datos)## 'data.frame': 7142 obs. of 26 variables:
## $ fid : int 1 2 3 4 5 6 7 8 9 10 ...
## $ objectid : int 127 128 129 130 131 132 133 134 135 136 ...
## $ code : chr "Arg-00001" "Arg-00002" "Arg-00003" "Arg-00004" ...
## $ country : chr "Argentina" "Argentina" "Argentina" "Argentina" ...
## $ plant_name : chr "Aconcagua solar farm" "Aconcagua solar farm" "Altiplano 200 Solar Power Plant" "Altiplano 200 Solar Power Plant" ...
## $ operational_status : chr "announced" "announced" "operating" "operating" ...
## $ longitude : num -68.9 -68.9 -66.9 -66.9 -68.9 ...
## $ latitude : num -33 -33 -24.1 -24.1 -33.3 ...
## $ elevation : int 929 929 4000 4000 937 865 858 858 858 858 ...
## $ area : num 0 0 4397290 5774 0 ...
## $ slope : num 0.574 0.574 1.603 6.243 0.903 ...
## $ slope_type : chr "Plano o casi plano" "Plano o casi plano" "Plano o casi plano" "Moderado" ...
## $ curvature : num 0.000795 0.000795 -0.002781 -0.043699 0.002781 ...
## $ curvature_type : chr "Superficies planas o intermedias" "Superficies planas o intermedias" "Superficies planas o intermedias" "Superficies cóncavas / Valles" ...
## $ aspect : num 55.1 55.1 188.7 270.9 108.4 ...
## $ aspect_type : chr "Northeast" "Northeast" "South" "West" ...
## $ ghi : num 6.11 6.11 8.01 7.88 6.12 ...
## $ solar_aptitude : num 0.746 0.746 0.8 0.727 0.595 ...
## $ solar_aptittude_class: chr "Alta" "Alta" "Alta" "Alta" ...
## $ humidity : num 0 0 53.7 53.7 0 ...
## $ wind_speed : num 3.78 3.78 7.02 8.33 3.87 ...
## $ wind_direction : num 0 0 55.1 55.1 0 ...
## $ ambient_temperature : num 12.6 12.6 6.8 6.8 13.1 ...
## $ optimal_tilt : int 31 31 26 26 31 33 30 30 30 30 ...
## $ peak_power_per_hour : num 4.98 4.98 6.39 6.39 4.97 ...
## $ total_power : num 25 66.2 101 107 180 ...##
## Adjuntando el paquete: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union2 Cálculo de Intervalos y Frecuencias
#Extraer variable
Variable <- na.omit(Datos$latitude)
N <- length(Variable)
# Cálculo Límites Decimales #
# Cálculos básicos
min_dec <- min(Variable)
max_dec <- max(Variable)
k_dec <- floor(1 + 3.322 * log10(N))
rango_dec <- max(Variable) - min(Variable)
amplitud_dec <- rango_dec / k_dec
# Generamos los cortes exactos
cortes_dec <- seq(min(Variable), max(Variable), length.out = k_dec + 1)
cortes_dec[length(cortes_dec)] <- max(Variable) + 0.0001
# Frecuencias
inter_dec <- cut(Variable, breaks = cortes_dec, include.lowest = TRUE, right = FALSE)
ni_dec <- as.vector(table(inter_dec))
hi_dec <- (ni_dec/N)*100
# Cálculos de Frecuencias
sum_ni <- sum(ni_dec)
hi_dec <- (ni_dec / sum_ni) * 100
Ni_asc_dec <- cumsum(ni_dec)
Hi_asc_dec <- cumsum(hi_dec)
Ni_desc_dec <- rev(cumsum(rev(ni_dec)))
Hi_desc_dec <- rev(cumsum(rev(hi_dec)))
# Construcción del Dataframe Decimal
TDF_Decimal <- data.frame(
Li = round(cortes_dec[1:k_dec], 2),
Ls = round(cortes_dec[2:(k_dec+1)], 2),
MC = round((cortes_dec[1:k_dec] + cortes_dec[2:(k_dec+1)]) / 2, 2),
ni = ni_dec,
hi = round(hi_dec, 2),
Ni_asc = cumsum(ni_dec),
Ni_desc = rev(cumsum(rev(ni_dec))),
Hi_asc = cumsum(round(hi_dec, 2)),
Hi_desc = rev(cumsum(rev(round(hi_dec, 2)))))
# Cálculo Límites Enteros #
BASE <- 10
# Cálculos básicos
min_int <- floor(min(Variable) / BASE) * BASE
max_int <- ceiling(max(Variable) / BASE) * BASE
k_int_sug <- floor(1 + 3.322 * log10(N))
Rango_int <- max_int - min_int
Amplitud_raw <- Rango_int / k_int_sug
Amplitud_int <- ceiling(Amplitud_raw / 10) * 10
if(Amplitud_int == 0) Amplitud_int <- 10
# Generar cortes enteros
cortes_int <- seq(from = min_int, by = Amplitud_int, length.out = k_int_sug + 2)
cortes_int <- cortes_int[cortes_int <= (max_int + Amplitud_int)]
# Asegurar cobertura del máximo
while(max(cortes_int) < max(Variable)) {
cortes_int <- c(cortes_int, max(cortes_int) + Amplitud_int)
}
K_real <- length(cortes_int) - 1
lim_inf_int <- cortes_int[1:K_real]
lim_sup_int <- cortes_int[2:(K_real+1)]
# Frecuencias
inter_int <- cut(Variable, breaks = cortes_int, include.lowest = TRUE, right = FALSE)
ni_int <- as.vector(table(inter_int))
# Cálculos de Frecuencias
hi_int <- (ni_int / N) * 100
Ni_asc_int <- cumsum(ni_int)
Ni_desc_int <- rev(cumsum(rev(ni_int)))
Hi_asc_int <- cumsum(hi_int)
Hi_desc_int <- rev(cumsum(rev(hi_int)))
# Construcción del Dataframe Entero
TDF_Enteros <- data.frame(
Li = lim_inf_int,
Ls = lim_sup_int,
MC = (lim_inf_int + lim_sup_int) / 2,
ni = ni_int,
hi = round(hi_int, 2),
Ni_asc = Ni_asc_int,
Ni_desc = Ni_desc_int,
Hi_asc = round(Hi_asc_int, 2),
Hi_desc = round(Hi_desc_int, 2))3 Tabla de Distribución de Frecuencias
3.1 Tabla con Límites Decimales
#### Crear de fila de totales ####
totales_dec <- c("TOTAL", "-", "-", sum(TDF_Decimal$ni), 100, "-", "-", "-", "-")
TDF_Dec_Final <- rbind(mutate(TDF_Decimal, across(everything(), as.character)), totales_dec)
# Generar GT Decimal
TDF_Dec_Final %>%
gt() %>%
tab_header(title = md("**Tabla N°1 de Distribución de Frecuencias de Latitud (°)**")) %>%
cols_label(
Li = "Lim. Inf",
Ls = "Lim. Sup",
MC = "Marca Clase",
ni = "Frec. Abs (ni)",
hi = "Frec. Rel (%)",
Ni_asc = "Ni (Asc)",
Ni_desc = "Ni (Desc)",
Hi_asc = "Hi Asc (%)",
Hi_desc = "Hi Desc (%)"
) %>%
tab_options(heading.title.font.size = px(14), column_labels.background.color = "#F0F0F0")| Tabla N°1 de Distribución de Frecuencias de Latitud (°) | ||||||||
| Lim. Inf | Lim. Sup | Marca Clase | Frec. Abs (ni) | Frec. Rel (%) | Ni (Asc) | Ni (Desc) | Hi Asc (%) | Hi Desc (%) |
|---|---|---|---|---|---|---|---|---|
| -53.15 | -48.16 | -50.66 | 3 | 0.04 | 3 | 7141 | 0.04 | 99.99 |
| -48.16 | -43.17 | -45.67 | 0 | 0 | 3 | 7138 | 0.04 | 99.95 |
| -43.17 | -38.18 | -40.68 | 1 | 0.01 | 4 | 7138 | 0.05 | 99.95 |
| -38.18 | -33.19 | -35.69 | 166 | 2.32 | 170 | 7137 | 2.37 | 99.94 |
| -33.19 | -28.2 | -30.7 | 201 | 2.81 | 371 | 6971 | 5.18 | 97.62 |
| -28.2 | -23.21 | -25.71 | 319 | 4.47 | 690 | 6770 | 9.65 | 94.81 |
| -23.21 | -18.22 | -20.72 | 1247 | 17.46 | 1937 | 6451 | 27.11 | 90.34 |
| -18.22 | -13.23 | -15.73 | 1899 | 26.59 | 3836 | 5204 | 53.7 | 72.88 |
| -13.23 | -8.24 | -10.74 | 1073 | 15.03 | 4909 | 3305 | 68.73 | 46.29 |
| -8.24 | -3.25 | -5.75 | 1363 | 19.09 | 6272 | 2232 | 87.82 | 31.26 |
| -3.25 | 1.74 | -0.76 | 159 | 2.23 | 6431 | 869 | 90.05 | 12.17 |
| 1.74 | 6.73 | 4.23 | 368 | 5.15 | 6799 | 710 | 95.2 | 9.94 |
| 6.73 | 11.71 | 9.22 | 342 | 4.79 | 7141 | 342 | 99.99 | 4.79 |
| TOTAL | - | - | 7141 | 100 | - | - | - | - |
3.2 Tabla con Límites Enteros
#### Crear de fila de totales ####
totales_int <- c("TOTAL", "-", "-", sum(TDF_Enteros$ni), 100, "-", "-", "-", "-")
TDF_Int_Final <- rbind(mutate(TDF_Enteros, across(everything(), as.character)), totales_int)
# Generar GT Enteros
TDF_Int_Final %>%
gt() %>%
tab_header(
title = md("**Tabla N°2 de Distribución de Frecuencias de Latitud (°)**")) %>%
cols_label(
Li = "Lim. Inf",
Ls = "Lim. Sup",
MC = "Marca Clase",
ni = "Frec. Abs (ni)",
hi = "Frec. Rel (%)",
Ni_asc = "Ni (Asc)",
Ni_desc = "Ni (Desc)",
Hi_asc = "Hi Asc (%)",
Hi_desc = "Hi Desc (%)"
) %>%
fmt_number(columns = c(Li, Ls), decimals = 0) %>%
fmt_number(columns = c(hi, Hi_asc, Hi_desc), decimals = 2) %>%
tab_options(heading.title.font.size = px(14), column_labels.background.color = "#F0F0F0")| Tabla N°2 de Distribución de Frecuencias de Latitud (°) | ||||||||
| Lim. Inf | Lim. Sup | Marca Clase | Frec. Abs (ni) | Frec. Rel (%) | Ni (Asc) | Ni (Desc) | Hi Asc (%) | Hi Desc (%) |
|---|---|---|---|---|---|---|---|---|
| -60 | -50 | -55 | 3 | 0.04 | 3 | 7141 | 0.04 | 100 |
| -50 | -40 | -45 | 0 | 0 | 3 | 7138 | 0.04 | 99.96 |
| -40 | -30 | -35 | 300 | 4.2 | 303 | 7138 | 4.24 | 99.96 |
| -30 | -20 | -25 | 1216 | 17.03 | 1519 | 6838 | 21.27 | 95.76 |
| -20 | -10 | -15 | 2821 | 39.5 | 4340 | 5622 | 60.78 | 78.73 |
| -10 | 0 | -5 | 2064 | 28.9 | 6404 | 2801 | 89.68 | 39.22 |
| 0 | 10 | 5 | 604 | 8.46 | 7008 | 737 | 98.14 | 10.32 |
| 10 | 20 | 15 | 133 | 1.86 | 7141 | 133 | 100 | 1.86 |
| 20 | 30 | 25 | 0 | 0 | 7141 | 0 | 100 | 0 |
| TOTAL | - | - | 7141 | 100 | - | - | - | - |
4 Gráficos
4.1 Gráfico 1 – Frecuencia Local
color_sutil <- "#B0C4DE"
par(mar = c(8, 5, 4, 2))
barplot(TDF_Enteros$ni,
names.arg = TDF_Enteros$MC,
main = "Gráfica N°1: Distribución de Cantidad de Plantas Solares por Latitud",
cex.main = 1,
xlab = "",
ylab = "Cantidad",
col = color_sutil,
space = 0,
las = 2,
cex.names = 0.7)
mtext("Latitud (°)", side = 1, line = 4)
4.2 Gráfico 2 – Frecuencia Global
color_grafico <- "#B0C4DE"
par(mar = c(8, 5, 4, 2))
barplot(TDF_Enteros$ni,
main="Gráfica N°2: Distribución de Cantidades Globales de las Plantas Solares por Latitud",
cex.main = 0.9,
xlab = "",
ylab = "Cantidad",
names.arg = TDF_Enteros$MC,
col = color_sutil,
space = 0,
cex.names = 0.7,
las = 2,
ylim = c(0, sum(TDF_Enteros$ni)))
mtext("Latitud (°)", side = 1, line = 4)
4.3 Gráfico 3 – Porcentaje Local
color_grafico <- "#B0C4DE"
par(mar = c(8, 5, 4, 2))
barplot(TDF_Enteros$hi,
main="Gráfica N°3: Distribución Porcentual de las Plantas Solares por Latitud",
cex.main = 1,
xlab = "",
ylab = "Porcentaje (%)",
col = color_sutil,
space = 0,
names.arg = TDF_Enteros$MC,
cex.names = 0.7,
las = 2,
ylim = c(0, max(TDF_Enteros$hi) * 1.1))
mtext("Latitud (°)", side = 1, line = 4)
4.4 Gráfico 4 – Porcentaje Global
color_grafico <- "#B0C4DE"
par(mar = c(8, 5, 4, 2))
barplot(TDF_Enteros$hi,
main="Gráfica N°4: Distribución Porcentual Global de las Plantas Solares por Latitud",
cex.main = 1,
xlab = "",
ylab = "Porcentaje (%)",
col = color_sutil,
space = 0,
names.arg = TDF_Enteros$MC,
las = 2,
cex.names = 0.7,
ylim = c(0, 100))
mtext("Latitud (°)", side = 1, line = 4)
4.5 Gráfico 5 – Diagrama de Cajas (Boxplot)
par(mar = c(5, 5, 4, 2))
boxplot(Variable,
horizontal = TRUE,
col = color_sutil,
xlab = "Latitud (°)",
cex.main = 0.9,
main = "Gráfica N°5: Distribución de la Latitud en las Plantas Solares")
4.6 Gráfico 6 – Ojivas de Frecuencia Acumulada
par(mar = c(5, 5, 4, 10), xpd = TRUE)
# Coordenadas
x_asc <- TDF_Enteros$Ls
x_desc <- TDF_Enteros$Li
y_asc <- TDF_Enteros$Ni_asc
y_desc <- TDF_Enteros$Ni_desc
# 1. Dibujar la Ascendente
plot(x_asc, y_asc,
type = "b",
main = "Gráfica N°6: Ojivas Ascendentes y Descendentes de la Distribución de la Latitud en las Plantas Solares",
cex.main = 0.7,
xlab = "Latitud (°)",
ylab = "Frecuencia Acumulada",
col = "black",
pch = 19,
xlim = c(min(x_desc), max(x_asc)),
ylim = c(0, sum(TDF_Enteros$ni))
)
# 2. Agregar la Descendente
lines(x_desc, y_desc, col = "blue", type = "b", pch = 19)
grid()
legend("right",
legend = c("Ascendente", "Descendente"),
col = c("black", "blue"),
lty = 1,
pch = 1,
cex = 0.6,
inset = c(0.05, 0.05),
bty = "n")
5 Indicadores Estadísticos
## INDICADORES DE TENDENCIA CENTRAL
# Media aritmética
media <- round(mean(Variable), 2)
# Mediana
mediana <- round(median(Variable), 2)
# Moda
max_frecuencia <- max(TDF_Enteros$ni)
moda_vals <- TDF_Enteros$MC[TDF_Enteros$ni == max_frecuencia]
moda_txt <- paste(round(moda_vals, 2), collapse = ", ")
## INDICADORES DE DISPERSIÓN
# Varianza
varianza <- var(Variable)
# Desviación Estándar
sd_val <- sd(Variable)
# Coeficiente de Variación
cv <- round((sd_val / abs(media)) * 100, 2)
## INDICADORES DE FORMA
# Coeficiente de Asimetría
asimetria <- skewness(Variable, type = 2)
# Curtosis
curtosis <- kurtosis(Variable)
# Outliers
outliers_data <- boxplot.stats(Variable)$out
if(length(outliers_data) > 0) {
num_out <- length(outliers_data)
min_out <- round(min(outliers_data), 2)
max_out <- round(max(outliers_data), 2)
# Formato Total [Min; Max]
msg_atipicos <- paste0(" ", num_out, " [", min_out, " ; ", max_out, "]")
} else {
msg_atipicos <- "No hay presencia de valores atípicos"
}
tabla_indicadores <- data.frame(
"Variable" = c("Latitud (°)"),
"Rango_MinMax" = paste0("[", round(min(Variable), 2), "; ", round(max(Variable), 2), "]"),
"X" = c(media),
"Me" = c(mediana),
"Mo" = c(moda_txt),
"V" = c(varianza),
"Sd" = c(sd_val),
"Cv" = c(cv),
"As" = c(asimetria),
"K" = c(curtosis),
"Outliers" = msg_atipicos
)
# Generar Tabla GT
tabla_conclusiones_gt <- tabla_indicadores %>%
gt() %>%
tab_header(title = md("**Tabla N°3 de Conclusiones**")) %>%
tab_source_note(source_note = "Autor: Martin Sarmiento") %>%
cols_label(
Variable = "Variable",
Rango_MinMax = "Rango",
X = "Media (X)",
Me = "Mediana (Me)",
Mo = "Moda (Mo)",
V = "Varianza (V)",
Sd = "Desv. Est. (Sd)",
Cv = "C.V. (%)",
As = "Asimetría (As)",
K = "Curtosis (K)",
Outliers = "Outliers"
) %>%
tab_options(
heading.title.font.size = px(16),
column_labels.background.color = "#f0f0f0"
)
tabla_conclusiones_gt| Tabla N°3 de Conclusiones | ||||||||||
| Variable | Rango | Media (X) | Mediana (Me) | Moda (Mo) | Varianza (V) | Desv. Est. (Sd) | C.V. (%) | Asimetría (As) | Curtosis (K) | Outliers |
|---|---|---|---|---|---|---|---|---|---|---|
| Latitud (°) | [-53.15; 11.71] | -12.73 | -14.82 | -15 | 95.67181 | 9.781197 | 76.84 | 0.2528149 | 0.1926481 | 4 [-53.15 ; -38.97] |
| Autor: Martin Sarmiento | ||||||||||
6 Conclusiones
La variable “Latitud” fluctúa entre -53.15° y 11.71° y sus valores se encuentran alrededor de -14.82°, con una desviación estándar de 9.781197, siendo una variable heterogénea, cuyos valores se concentran en la parte media alta de la variable con la agregación de valores atípicos de 4 outliers; por todo lo anterior, el comportamiento de la variable es regular.