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("Data_Mundial_Final.csv", sep = ";", dec = ",", fileEncoding = "latin1")
# Estructura de los datos
str(Datos)## 'data.frame': 58771 obs. of 29 variables:
## $ OBJECTID : int 127 129 131 132 133 137 138 139 140 145 ...
## $ code : chr "00127-ARG-P" "00129-ARG-G" "00131-ARG-P" "00132-ARG-P" ...
## $ plant_name : chr "Aconcagua solar farm" "Altiplano 200 Solar Power Plant" "Anchoris solar farm" "Antu Newen solar farm" ...
## $ country : chr "Argentina" "Argentina" "Argentina" "Argentina" ...
## $ operational_status : chr "announced" "operating" "construction" "cancelled - inferred 4 y" ...
## $ longitude : num -68.9 -66.9 -68.9 -70.3 -66.8 ...
## $ latitude : num -33 -24.1 -33.3 -37.4 -28.6 ...
## $ elevation : int 929 4000 937 865 858 570 1612 665 3989 2640 ...
## $ area : num 250 4397290 645 241 30 ...
## $ size : chr "Small" "Big" "Small" "Small" ...
## $ slope : num 0.574 1.603 0.903 1.791 1.872 ...
## $ slope_type : chr "Plano o casi plano" "Plano o casi plano" "Plano o casi plano" "Plano o casi plano" ...
## $ curvature : num 0.000795 -0.002781 0.002781 -0.002384 -0.009137 ...
## $ curvature_type : chr "Superficies planas o intermedias" "Superficies planas o intermedias" "Superficies planas o intermedias" "Superficies planas o intermedias" ...
## $ aspect : num 55.1 188.7 108.4 239.3 56.2 ...
## $ aspect_type : chr "Northeast" "South" "East" "Southwest" ...
## $ dist_to_road : num 127 56015 336 34 314 ...
## $ ambient_temperature : num 12.6 6.8 13.1 11.4 18.8 ...
## $ ghi : num 6.11 8.01 6.12 6.22 6.74 ...
## $ humidity : num 53.7 53.7 53.7 53.7 51.5 ...
## $ wind_speed : num 3.78 7.02 3.87 6.56 7.19 ...
## $ wind_direction : num 55.1 55.1 55.1 55.1 114.8 ...
## $ dt_wind : chr "Northeast" "Northeast" "Northeast" "Northeast" ...
## $ solar_aptitude : num 0.746 0.8 0.595 0.657 0.743 ...
## $ solar_aptitude_rounded: int 7 8 6 7 7 7 8 7 8 6 ...
## $ solar_aptittude_class : chr "Alta" "Alta" "Media" "Alta" ...
## $ capacity : num 25 101 180 20 50.4 ...
## $ optimal_tilt : num 31 26 31 33 30 31 29 31 27 32 ...
## $ pv_potential : num 4.98 6.39 4.97 5 5.37 ...##
## 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
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
# 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))
# CÁLCULOS MATEMÁTICOS
hi_dec <- (ni_dec / N) * 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)))
# Dataframe Decimal
TDF_Decimal <- data.frame(
Li = cortes_dec[1:k_dec],
Ls = cortes_dec[2:(k_dec+1)],
MC = (cortes_dec[1:k_dec] + cortes_dec[2:(k_dec+1)]) / 2,
ni = ni_dec,
hi = hi_dec,
Ni_asc = Ni_asc_dec,
Ni_desc = Ni_desc_dec,
Hi_asc = Hi_asc_dec,
Hi_desc = Hi_desc_dec)
# CÁLCULO LÍMITES ENTEROS
BASE <- 10
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
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)]
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 MATEMÁTICOS
hi_int <- (ni_int / N) * 100
Ni_asc_int <- cumsum(ni_int)
Hi_asc_int <- cumsum(hi_int)
Ni_desc_int <- rev(cumsum(rev(ni_int)))
Hi_desc_int <- rev(cumsum(rev(hi_int)))
# 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 = hi_int,
Ni_asc = Ni_asc_int,
Ni_desc = Ni_desc_int,
Hi_asc = Hi_asc_int,
Hi_desc = Hi_desc_int)3 Tabla de Distribución de Frecuencias
3.1 Tabla con Límites Decimales
# Crear Dataframe
TDF_Dec_Final <- data.frame(
Li = as.character(round(TDF_Decimal$Li, 2)),
Ls = as.character(round(TDF_Decimal$Ls, 2)),
MC = as.character(round(TDF_Decimal$MC, 2)),
ni = as.character(TDF_Decimal$ni),
hi = as.character(round(TDF_Decimal$hi, 2)),
Ni_asc = as.character(TDF_Decimal$Ni_asc),
Ni_desc = as.character(TDF_Decimal$Ni_desc),
Hi_asc = as.character(round(TDF_Decimal$Hi_asc, 2)),
Hi_desc = as.character(round(TDF_Decimal$Hi_desc, 2))
)
# Calcular Totales
totales_dec <- c("TOTAL", "-", "-", sum(TDF_Decimal$ni), round(sum(TDF_Decimal$hi), 2), "-", "-", "-", "-")
TDF_Dec_Final <- rbind(TDF_Dec_Final, totales_dec)
# Generar GT
TDF_Dec_Final %>%
gt() %>%
tab_header(title = md("**Tabla N°1 de Distribución de Frecuencias de Latitud (°) de las Plantas Solares**")) %>%
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 (%)"
) %>%
cols_align(align = "center", columns = everything()) %>%
tab_options(heading.title.font.size = px(14), column_labels.background.color = "#F0F0F0")| Tabla N°1 de Distribución de Frecuencias de Latitud (°) de las Plantas Solares | ||||||||
| Lim. Inf | Lim. Sup | Marca Clase | Frec. Abs (ni) | Frec. Rel (%) | Ni (Asc) | Ni (Desc) | Hi Asc (%) | Hi Desc (%) |
|---|---|---|---|---|---|---|---|---|
| -53.15 | -46.08 | -49.62 | 1 | 0 | 1 | 58771 | 0 | 100 |
| -46.08 | -39.01 | -42.55 | 0 | 0 | 1 | 58770 | 0 | 100 |
| -39.01 | -31.95 | -35.48 | 238 | 0.4 | 239 | 58770 | 0.41 | 100 |
| -31.95 | -24.88 | -28.41 | 361 | 0.61 | 600 | 58532 | 1.02 | 99.59 |
| -24.88 | -17.81 | -21.34 | 782 | 1.33 | 1382 | 58171 | 2.35 | 98.98 |
| -17.81 | -10.74 | -14.28 | 606 | 1.03 | 1988 | 57389 | 3.38 | 97.65 |
| -10.74 | -3.67 | -7.21 | 431 | 0.73 | 2419 | 56783 | 4.12 | 96.62 |
| -3.67 | 3.39 | -0.14 | 278 | 0.47 | 2697 | 56352 | 4.59 | 95.88 |
| 3.39 | 10.46 | 6.93 | 915 | 1.56 | 3612 | 56074 | 6.15 | 95.41 |
| 10.46 | 17.53 | 14 | 2432 | 4.14 | 6044 | 55159 | 10.28 | 93.85 |
| 17.53 | 24.6 | 21.06 | 2872 | 4.89 | 8916 | 52727 | 15.17 | 89.72 |
| 24.6 | 31.67 | 28.13 | 5633 | 9.58 | 14549 | 49855 | 24.76 | 84.83 |
| 31.67 | 38.73 | 35.2 | 19070 | 32.45 | 33619 | 44222 | 57.2 | 75.24 |
| 38.73 | 45.8 | 42.27 | 12087 | 20.57 | 45706 | 25152 | 77.77 | 42.8 |
| 45.8 | 52.87 | 49.34 | 10780 | 18.34 | 56486 | 13065 | 96.11 | 22.23 |
| 52.87 | 59.94 | 56.41 | 2285 | 3.89 | 58771 | 2285 | 100 | 3.89 |
| TOTAL | - | - | 58771 | 100 | - | - | - | - |
3.2 Tabla con Límites Enteros
# Crear Dataframe
TDF_Int_Final <- data.frame(
Li = as.character(TDF_Enteros$Li),
Ls = as.character(TDF_Enteros$Ls),
MC = as.character(TDF_Enteros$MC),
ni = as.character(TDF_Enteros$ni),
hi = as.character(round(TDF_Enteros$hi, 2)),
Ni_asc = as.character(TDF_Enteros$Ni_asc),
Ni_desc = as.character(TDF_Enteros$Ni_desc),
Hi_asc = as.character(round(TDF_Enteros$Hi_asc, 2)),
Hi_desc = as.character(round(TDF_Enteros$Hi_desc, 2))
)
# Calcular Totales
totales_int <- c("TOTAL", "-", "-", sum(TDF_Enteros$ni), round(sum(TDF_Enteros$hi), 2), "-", "-", "-", "-")
TDF_Int_Final <- rbind(TDF_Int_Final, totales_int)
# Generar GT
TDF_Int_Final %>%
gt() %>%
tab_header(title = md("**Tabla N°2 de Distribución de Frecuencias de Latitud (°) de las Plantas Solares**")) %>%
cols_label(
Li = "Lim. Inf",
Ls = "Lim. Sup",
MC = "Marca Clase",
ni = "Frec. Abs (ni)",
hi = "Frec. Rel (%)",
Ni_asc = "Ni (Asc)",
Ni_desc = "Ni (Desc)",
Hi_asc = "Hi Asc (%)",
Hi_desc = "Hi Desc (%)"
) %>%
cols_align(align = "center", columns = everything()) %>%
tab_options(heading.title.font.size = px(14), column_labels.background.color = "#F0F0F0")| Tabla N°2 de Distribución de Frecuencias de Latitud (°) de las Plantas Solares | ||||||||
| Lim. Inf | Lim. Sup | Marca Clase | Frec. Abs (ni) | Frec. Rel (%) | Ni (Asc) | Ni (Desc) | Hi Asc (%) | Hi Desc (%) |
|---|---|---|---|---|---|---|---|---|
| -60 | -50 | -55 | 1 | 0 | 1 | 58771 | 0 | 100 |
| -50 | -40 | -45 | 0 | 0 | 1 | 58770 | 0 | 100 |
| -40 | -30 | -35 | 308 | 0.52 | 309 | 58770 | 0.53 | 100 |
| -30 | -20 | -25 | 866 | 1.47 | 1175 | 58462 | 2 | 99.47 |
| -20 | -10 | -15 | 842 | 1.43 | 2017 | 57596 | 3.43 | 98 |
| -10 | 0 | -5 | 495 | 0.84 | 2512 | 56754 | 4.27 | 96.57 |
| 0 | 10 | 5 | 1019 | 1.73 | 3531 | 56259 | 6.01 | 95.73 |
| 10 | 20 | 15 | 3223 | 5.48 | 6754 | 55240 | 11.49 | 93.99 |
| 20 | 30 | 25 | 6087 | 10.36 | 12841 | 52017 | 21.85 | 88.51 |
| 30 | 40 | 35 | 23597 | 40.15 | 36438 | 45930 | 62 | 78.15 |
| 40 | 50 | 45 | 14351 | 24.42 | 50789 | 22333 | 86.42 | 38 |
| 50 | 60 | 55 | 7982 | 13.58 | 58771 | 7982 | 100 | 13.58 |
| 60 | 70 | 65 | 0 | 0 | 58771 | 0 | 100 | 0 |
| TOTAL | - | - | 58771 | 100 | - | - | - | - |
4 Análisis Gráfico
4.1 Histogramas de Cantidad
par(mar = c(8, 7, 5, 2))
barplot(TDF_Enteros$ni,
names.arg = TDF_Enteros$MC,
main = "",
xlab = "",
ylab = "",
col = "#B0C4DE",
ylim = c(0, max(TDF_Enteros$ni) * 1.2),
space = 0,
las = 2,
cex.names = 0.7)
mtext("Cantidad", side = 2, line = 4.5, cex = 1, font = 1)
mtext("Latitud (°)", side = 1, line = 4)
mtext("Gráfica N°1: Distribución de Cantidad de Plantas Solares por Latitud",
side = 3,
line = 2,
adj = 0.5,
cex = 0.9,
font = 2)
par(mar = c(8, 7, 5, 2))
barplot(TDF_Enteros$ni,
main="",
xlab = "",
ylab = "",
names.arg = TDF_Enteros$MC,
col = "#B0C4DE",
ylim = c(0, 58771),
space = 0,
cex.names = 0.7,
las = 2)
mtext("Cantidad", side = 2, line = 4.5, cex = 1, font = 1)
mtext("Latitud (°)", side = 1, line = 4)
mtext("Gráfica N°2: Distribución de Cantidad de Plantas Solares por Latitud",
side = 3,
line = 2,
adj = 0.5,
cex = 0.9,
font = 2)
4.2 Histogramas Porcentuales
par(mar = c(8, 5, 5, 2))
bp3 <- barplot(TDF_Enteros$hi,
main = "",
xlab = "",
ylab = "Porcentaje (%)",
col = "#B0C4DE",
ylim = c(0, max(TDF_Enteros$hi) * 1.3),
space = 0,
names.arg = TDF_Enteros$MC,
cex.names = 0.7,
las = 2)
mtext("Latitud (°)", side = 1, line = 4)
mtext("Gráfica N°3: Distribución Porcentual de las Plantas Solares por Latitud",
side = 3,
line = 2,
adj = 0.5,
cex = 0.9,
font = 2)
text(x = bp3,
y = TDF_Enteros$hi,
labels = paste0(round(TDF_Enteros$hi, 1), "%"),
pos = 3,
cex = 0.6,
col = "black")
par(mar = c(8, 5, 5, 2))
bp4 <- barplot(TDF_Enteros$hi,
main = "",
xlab = "",
ylab = "Porcentaje (%)",
col = "#B0C4DE",
space = 0,
names.arg = TDF_Enteros$MC,
las = 2,
cex.names = 0.7,
ylim = c(0, 100))
mtext("Latitud (°)", side = 1, line = 4)
mtext("Gráfica N°4: Distribución Porcentual de las Plantas Solares por Latitud",
side = 3,
line = 2,
adj = 0.5,
cex = 0.9,
font = 2)
text(x = bp4,
y = TDF_Enteros$hi,
labels = paste0(round(TDF_Enteros$hi, 1), "%"),
pos = 3,
cex = 0.6,
col = "black")
4.3 Diagrama de Cajas (Boxplot)
par(mar = c(5, 5, 4, 2))
boxplot(Variable,
horizontal = TRUE,
col = "#B0C4DE",
xlab = "Latitud (°)",
cex.main = 0.9,
main = "Gráfica N°5: Distribución de la Latitud en las Plantas Solares")
4.4 Ojivas
par(mar = c(5, 5, 7, 10), xpd = TRUE)
# Coordenadas
x_asc <- TDF_Enteros$Ls
x_desc <- TDF_Enteros$Li
y_asc <- TDF_Enteros$Ni_asc
y_desc <- TDF_Enteros$Ni_desc
# 1. Dibujar la Ascendente
plot(x_asc, y_asc,
type = "b",
main = "",
xlab = "Latitud (°)",
ylab = "Frecuencia Acumulada",
col = "black",
pch = 19,
xlim = c(min(x_desc), max(x_asc)),
ylim = c(0, sum(TDF_Enteros$ni)))
# 2. Agregar la Descendente
lines(x_desc, y_desc, col = "blue", type = "b", pch = 19)
grid()
mtext("Gráfica N°6: Ojivas Ascendentes y Descendentes de la\nDistribución de la Latitud en las Plantas Solares",
side = 3,
line = 3,
adj = 0.5,
cex = 0.9,
font = 2)
legend("left",
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
Q1 <- quantile(Variable, 0.25)
Q3 <- quantile(Variable, 0.75)
IQR_val <- Q3 - Q1
lim_inf <- Q1 - 1.5 * IQR_val
lim_sup <- Q3 + 1.5 * IQR_val
outliers_data <- Variable[Variable < lim_inf | Variable > lim_sup]
num_outliers <- length(outliers_data)
if(num_outliers > 0){
rango_outliers <- paste0(num_outliers, " [", round(min(outliers_data), 2), "; ", round(max(outliers_data), 2), "]")
} else {
rango_outliers <- "0 [Sin Outliers]"
}
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" = rango_outliers)
# Generar Tabla GT
tabla_conclusiones_gt <- tabla_indicadores %>%
gt() %>%
tab_header(title = md("**Tabla N°3 de Conclusiones de Latitud de las Plantas Solares**")) %>%
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 [Intervalo]"
) %>%
tab_options(
heading.title.font.size = px(16),
column_labels.background.color = "#F0F0F0"
)
tabla_conclusiones_gt| Tabla N°3 de Conclusiones de Latitud de las Plantas Solares | ||||||||||
| Variable | Rango | Media (X) | Mediana (Me) | Moda (Mo) | Varianza (V) | Desv. Est. (Sd) | C.V. (%) | Asimetría (As) | Curtosis (K) | Outliers [Intervalo] |
|---|---|---|---|---|---|---|---|---|---|---|
| Latitud (°) | [-53.15; 59.94] | 35.09 | 37.05 | 35 | 242.417 | 15.56975 | 44.37 | -1.922878 | 4.821545 | 4498 [-53.15; 12.94] |
| Autor: Martin Sarmiento | ||||||||||
6 Conclusiones
La variable “Latitud” fluctúa entre -53.15° y 59.94° y sus valores se encuentran alrededor de 37.05°, con una desviación estándar de 15.56975 , siendo una variable heterogénea, cuyos valores se concentran en la parte media alta de la variable con la agregación de valores atípicos de 4498 outliers; por todo lo anterior, el comportamiento de la variable es regular.