2 Cálculo de Intervalos y Frecuencias
# ── LÍMITES DECIMALES ──────────────────────────────────────────
min_dec <- min(Variable)
max_dec <- max(Variable)
k_dec <- floor(1 + 3.322 * log10(N))
rango_dec <- max_dec - min_dec
amplitud_dec <- rango_dec / k_dec
# Cortes exactos
cortes_dec <- seq(min_dec, max_dec, length.out = k_dec + 1)
cortes_dec[length(cortes_dec)] <- max_dec + 0.0001
# Frecuencias
inter_dec <- cut(Variable, breaks = cortes_dec, include.lowest = TRUE, right = FALSE)
ni_dec <- as.vector(table(inter_dec))
# Cálculos
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
)
# ── 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_int <- ceiling((Rango_int / k_int_sug) / 10) * 10
if (Amplitud_int == 0) Amplitud_int <- 10
cortes_int <- seq(from = min_int, by = Amplitud_int, length.out = k_int_sug + 1)
if (max(cortes_int) < max(Variable)) {
cortes_int <- c(cortes_int, max(cortes_int) + Amplitud_int)
}
while (length(cortes_int) > 2 && cortes_int[length(cortes_int)-1] >= max(Variable)) {
cortes_int <- cortes_int[-length(cortes_int)]
}
K_real <- length(cortes_int) - 1
lim_inf_int <- cortes_int[1:K_real]
lim_sup_int <- cortes_int[2:(K_real+1)]
inter_int <- cut(Variable, breaks = cortes_int, include.lowest = TRUE, right = FALSE)
ni_int <- as.vector(table(inter_int))
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)))
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
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$Hi_desc, 2))
)
totales_dec <- c("TOTAL", "-", "-", sum(TDF_Decimal$ni),
round(sum(TDF_Decimal$hi), 2), "-", "-", "-", "-")
TDF_Dec_Final <- rbind(TDF_Dec_Final, totales_dec)
TDF_Dec_Final %>%
gt() %>%
tab_header(title = md("**Tabla N°1 de Distribución de Frecuencias de Longitud (°) de las Unidades Petroleras**")) %>%
tab_source_note(source_note = "Autor: Tu Nombre") %>%
cols_label(
Li = "Lim. Inf",
Ls = "Lim. Sup",
MC = "Marca Clase",
ni = "Frec. Abs (ni)",
hi = "Frec. Rel (%)",
Ni_asc = "Ni (Asc)",
Ni_desc = "Ni (Desc)",
Hi_asc = "Hi Asc (%)",
Hi_desc = "Hi Desc (%)"
) %>%
cols_align(align = "center", columns = everything()) %>%
tab_options(heading.title.font.size = px(14),
column_labels.background.color = "#F0F0F0")
| Tabla N°1 de Distribución de Frecuencias de Longitud (°) de las Unidades Petroleras |
| Lim. Inf |
Lim. Sup |
Marca Clase |
Frec. Abs (ni) |
Frec. Rel (%) |
Ni (Asc) |
Ni (Desc) |
Hi Asc (%) |
Hi Desc (%) |
| -152.13 |
-127.01 |
-139.57 |
37 |
0.49 |
37 |
7537 |
0.49 |
100 |
| -127.01 |
-101.9 |
-114.46 |
2327 |
30.87 |
2364 |
7500 |
31.37 |
99.51 |
| -101.9 |
-76.79 |
-89.34 |
1991 |
26.42 |
4355 |
5173 |
57.78 |
68.63 |
| -76.79 |
-51.67 |
-64.23 |
719 |
9.54 |
5074 |
3182 |
67.32 |
42.22 |
| -51.67 |
-26.56 |
-39.11 |
105 |
1.39 |
5179 |
2463 |
68.71 |
32.68 |
| -26.56 |
-1.44 |
-14 |
66 |
0.88 |
5245 |
2358 |
69.59 |
31.29 |
| -1.44 |
23.67 |
11.12 |
1157 |
15.35 |
6402 |
2292 |
84.94 |
30.41 |
| 23.67 |
48.79 |
36.23 |
306 |
4.06 |
6708 |
1135 |
89 |
15.06 |
| 48.79 |
73.9 |
61.35 |
354 |
4.7 |
7062 |
829 |
93.7 |
11 |
| 73.9 |
99.02 |
86.46 |
148 |
1.96 |
7210 |
475 |
95.66 |
6.3 |
| 99.02 |
124.13 |
111.57 |
275 |
3.65 |
7485 |
327 |
99.31 |
4.34 |
| 124.13 |
149.25 |
136.69 |
41 |
0.54 |
7526 |
52 |
99.85 |
0.69 |
| 149.25 |
174.36 |
161.8 |
11 |
0.15 |
7537 |
11 |
100 |
0.15 |
| TOTAL |
- |
- |
7537 |
100 |
- |
- |
- |
- |
| Autor: Tu Nombre |
3.2 Tabla con Límites Enteros
TDF_Int_Final <- data.frame(
Li = as.character(TDF_Enteros$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))
)
totales_int <- c("TOTAL", "-", "-", sum(TDF_Enteros$ni),
round(sum(TDF_Enteros$hi), 2), "-", "-", "-", "-")
TDF_Int_Final <- rbind(TDF_Int_Final, totales_int)
TDF_Int_Final %>%
gt() %>%
tab_header(title = md("**Tabla N°2 de Distribución de Frecuencias de Longitud (°) de las Unidades Petroleras**")) %>%
tab_source_note(source_note = "Autor: Tu Nombre") %>%
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 Longitud (°) de las Unidades Petroleras |
| Lim. Inf |
Lim. Sup |
Marca Clase |
Frec. Abs (ni) |
Frec. Rel (%) |
Ni (Asc) |
Ni (Desc) |
Hi Asc (%) |
Hi Desc (%) |
| -160 |
-130 |
-145 |
37 |
0.49 |
37 |
7537 |
0.49 |
100 |
| -130 |
-100 |
-115 |
2689 |
35.68 |
2726 |
7500 |
36.17 |
99.51 |
| -100 |
-70 |
-85 |
2018 |
26.77 |
4744 |
4811 |
62.94 |
63.83 |
| -70 |
-40 |
-55 |
403 |
5.35 |
5147 |
2793 |
68.29 |
37.06 |
| -40 |
-10 |
-25 |
51 |
0.68 |
5198 |
2390 |
68.97 |
31.71 |
| -10 |
20 |
5 |
1130 |
14.99 |
6328 |
2339 |
83.96 |
31.03 |
| 20 |
50 |
35 |
431 |
5.72 |
6759 |
1209 |
89.68 |
16.04 |
| 50 |
80 |
65 |
384 |
5.09 |
7143 |
778 |
94.77 |
10.32 |
| 80 |
110 |
95 |
183 |
2.43 |
7326 |
394 |
97.2 |
5.23 |
| 110 |
140 |
125 |
178 |
2.36 |
7504 |
211 |
99.56 |
2.8 |
| 140 |
170 |
155 |
26 |
0.34 |
7530 |
33 |
99.91 |
0.44 |
| 170 |
200 |
185 |
7 |
0.09 |
7537 |
7 |
100 |
0.09 |
| TOTAL |
- |
- |
7537 |
100 |
- |
- |
- |
- |
| Autor: Tu Nombre |
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 = "#FF6961",
ylim = c(0, max(TDF_Enteros$ni) * 1.2),
space = 0,
las = 2,
cex.names = 0.7)
mtext("Cantidad", side = 2, line = 4.5, cex = 1, font = 1)
mtext("Longitud (\u00b0)", side = 1, line = 4, cex = 0.9)
mtext("Gráfica N\u00b01: Distribución de Cantidad de Unidades Petroleras por Longitud",
side = 3, line = 2, adj = 0.5, cex = 0.9, font = 2)
par(mar = c(8, 7, 5, 2))
barplot(TDF_Enteros$ni,
names.arg = TDF_Enteros$MC,
main = "",
xlab = "",
ylab = "",
col = "#FF6961",
ylim = c(0, max(TDF_Enteros$ni) * 1.2),
space = 0,
las = 2,
cex.names = 0.7)
mtext("Cantidad", side = 2, line = 4.5, cex = 1, font = 1)
mtext("Longitud (\u00b0)", side = 1, line = 4, cex = 0.9)
mtext("Gráfica N\u00b02: Distribución de Cantidad de Unidades Petroleras por Longitud",
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$hi,
main = "",
xlab = "",
ylab = "Porcentaje (%)",
col = "#FF6961",
ylim = c(0, max(TDF_Enteros$hi) * 1.3),
space = 0,
names.arg = TDF_Enteros$MC,
cex.names = 0.7,
las = 2)
mtext("Longitud (\u00b0)", side = 1, line = 4, cex = 0.9)
mtext("Gráfica N\u00b03: Distribución Porcentual de las Unidades Petroleras por Longitud",
side = 3, line = 2, adj = 0.5, cex = 0.9, font = 2)
text(x = bp3,
y = TDF_Enteros$hi,
labels = paste0(round(TDF_Enteros$hi, 2), "%"),
pos = 3,
cex = 0.6,
col = "black")
par(mar = c(8, 5, 5, 2))
bp4 <- barplot(TDF_Enteros$hi,
main = "",
xlab = "",
ylab = "Porcentaje (%)",
col = "#FF6961",
space = 0,
names.arg = TDF_Enteros$MC,
cex.names = 0.7,
las = 2,
ylim = c(0, 100))
mtext("Longitud (\u00b0)", side = 1, line = 4, cex = 0.9)
mtext("Gráfica N\u00b04: Distribución Porcentual de las Unidades Petroleras por Longitud",
side = 3, line = 2, adj = 0.5, cex = 0.9, font = 2)
text(x = bp4,
y = TDF_Enteros$hi,
labels = paste0(round(TDF_Enteros$hi, 2), "%"),
pos = 3,
cex = 0.6,
col = "black")
4.3 Diagrama de Cajas (Boxplot)
par(mar = c(5, 5, 4, 2))
boxplot(Variable,
horizontal = TRUE,
col = "#FF6961",
xlab = "Longitud (\u00b0)",
cex.main = 0.9,
main = "Gráfica N\u00b05: Distribución de la Longitud en las Unidades Petroleras")
4.4 Ojivas
par(mar = c(5, 5, 7, 10), xpd = TRUE)
x_asc <- TDF_Enteros$Ls
x_desc <- TDF_Enteros$Li
y_asc <- TDF_Enteros$Ni_asc
y_desc <- TDF_Enteros$Ni_desc
plot(x_asc, y_asc,
type = "b",
main = "",
xlab = "Longitud (\u00b0)",
ylab = "Frecuencia Acumulada",
col = "black",
pch = 19,
xlim = c(min(TDF_Enteros$Li), max(x_asc)),
ylim = c(0, sum(TDF_Enteros$ni)))
lines(x_desc, y_desc, col = "red", type = "b", pch = 19)
grid()
mtext("Gráfica N\u00b06: Ojivas Ascendentes y Descendentes de la\nDistribución de la Longitud en las Unidades Petroleras",
side = 3, line = 3, adj = 0.5, cex = 0.9, font = 2)
legend("right",
inset = c(-0.2, 0),
legend = c("Ascendente", "Descendente"),
col = c("black", "red"),
lty = 1,
pch = 1,
cex = 0.6,
bty = "n")
5 Indicadores Estadísticos
## TENDENCIA CENTRAL
media <- round(mean(Variable), 2)
mediana <- round(median(Variable), 2)
max_frecuencia <- max(TDF_Enteros$ni)
moda_vals <- TDF_Enteros$MC[TDF_Enteros$ni == max_frecuencia]
moda_txt <- paste(round(moda_vals, 2), collapse = ", ")
## DISPERSIÓN
varianza <- var(Variable)
sd_val <- sd(Variable)
cv <- round((sd_val / abs(media)) * 100, 2)
## FORMA
asimetria <- skewness(Variable, type = 2)
curtosis <- kurtosis(Variable)
## OUTLIERS
Q1 <- quantile(Variable, 0.25)
Q3 <- quantile(Variable, 0.75)
IQR_val <- Q3 - Q1
lim_inf_out <- Q1 - 1.5 * IQR_val
lim_sup_out <- Q3 + 1.5 * IQR_val
outliers_data <- Variable[Variable < lim_inf_out | Variable > lim_sup_out]
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 = "Longitud (\u00b0)",
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
)
tabla_indicadores %>%
gt() %>%
tab_header(title = md("**Tabla N°3 de Indicadores Estadísticos de Longitud (°) de las Unidades Petroleras**")) %>%
tab_source_note(source_note = "Autor: Tu Nombre") %>%
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]"
) %>%
cols_align(align = "center", columns = everything()) %>%
tab_options(
heading.title.font.size = px(14),
column_labels.background.color = "#F0F0F0"
)
| Tabla N°3 de Indicadores Estadísticos de Longitud (°) de las Unidades Petroleras |
| Variable |
Rango |
Media (X) |
Mediana (Me) |
Moda (Mo) |
Varianza (V) |
Desv. Est. (Sd) |
C.V. (%) |
Asimetría (As) |
Curtosis (K) |
Outliers [Intervalo] |
| Longitud (°) |
[-152.13; 174.36] |
-54.65 |
-93.4 |
-115 |
4610.381 |
67.89978 |
124.24 |
1.072274 |
-0.05216078 |
7 [173.31; 174.36] |
| Autor: Tu Nombre |