ESTUDIO ESTADÍSTICO DE LA CALIDAD DEL AIRE EN INDIA

UNIVERSIDAD CENTRAL DEL ECUADOR

PROYECTO:ESTUDIO ESTADÍSTICO DE LA CALIDAD DEL AIRE EN INDIA

FECHA: 21/11/2025

# Estadística Descriptiva
# 09/12/2025
# Ariana Viteri

# ======= CARGA DE PAQUETES =======
library(gt)
library(dplyr)

# ======= CARGAR DATOS =======
datos <- read.csv(
  "~/ariana tercer semestre/Estadistica/city_day.csv",
  header = TRUE,
  sep = ",",
  dec = "."
)

# ======= LIMPIEZA DE LA VARIABLE PM10 =======
PM10 <- datos$PM10[datos$PM10 != "-"]
PM10 <- as.numeric(PM10)

length(PM10)

## [1] 18391

# ======= MIN, MAX, RANGO =======
min_PM10 <- min(PM10)
max_PM10 <- max(PM10)
R <- max_PM10 - min_PM10

# ======= USAMOS k = 16 =======
k <- 16
A <- R / k

# ======= GENERACIÓN DE INTERVALOS =======
Li <- seq(from = min_PM10, to = max_PM10 - A, by = A)
Ls <- c(seq(from = min_PM10 + A, to = max_PM10 - A, by = A), max_PM10)

MC <- (Li + Ls) / 2

# ======= CÁLCULO DE FRECUENCIAS =======
PM10 <- round(PM10, 3)
Li <- round(Li, 3)
Ls <- round(Ls, 3)

ni <- numeric(length(Li))

for (i in 1:length(Li)) {
  if (i < length(Li)) {
    ni[i] <- sum(PM10 >= Li[i] & PM10 < Ls[i])
  } else {
    ni[i] <- sum(PM10 >= Li[i] & PM10 <= Ls[i])
  }
}

# ======= CÁLCULOS COMPLEMENTARIOS =======
N <- sum(ni)
hi <- (ni / N) * 100

Ni_asc <- cumsum(ni)
Ni_desc <- rev(cumsum(rev(ni)))
Hi_asc <- cumsum(hi)
Hi_desc <- rev(cumsum(rev(hi)))

# ======= FORMATO DE INTERVALOS =======
Intervalo <- paste0("[", round(Li,2), " - ", round(Ls,2), ")")
Intervalo[length(Intervalo)] <- paste0("[", round(Li[length(Li)],2), " - ",
                                       round(Ls[length(Ls)],2), "]")

# ======= TABLA FINAL =======
TDF_PM10 <- data.frame(
  Intervalo = Intervalo,
  MC = round(MC, 2),
  ni = ni,
  hi = round(hi, 2),
  Ni_ascendente = Ni_asc,
  Ni_descendente = Ni_desc,
  Hi_ascendente = round(Hi_asc, 2),
  Hi_descendente = round(Hi_desc, 2)
)

# ======= AGREGAR FILA DE TOTALES =======
totales <- data.frame(
  Intervalo = "Totales",
  MC = "-",
  ni = sum(ni),
  hi = sum(hi),
  Ni_ascendente = "-",
  Ni_descendente = "-",
  Hi_ascendente = "-",
  Hi_descendente = "-"
)

TDF_PM10 <- rbind(TDF_PM10, totales)

# ======= TABLA BONITA CON gt() =======
TDF_PM10 %>%
  gt() %>%
  tab_header(
    title = md("*Tabla Nro. 1*"),
    subtitle = md("**Distribución de frecuencia de la concentración de PM10, estudio de calidad del aire en India**")
  ) %>%
  tab_source_note(
    source_note = md("Fuente: Datos obtenidos y procesados por medio de https://www.kaggle.com/datasets/rohanrao/air-quality-data-in-india")
  ) %>%
  tab_style(
    style = cell_borders(sides = "left", color = "black", weight = px(2), style = "solid"),
    locations = cells_body()
  ) %>%
  tab_style(
    style = cell_borders(sides = "right", color = "black", weight = px(2), style = "solid"),
    locations = cells_body()
  ) %>%
  tab_style(
    style = cell_borders(sides = "left", color = "black", weight = px(2), style = "solid"),
    locations = cells_column_labels()
  ) %>%
  tab_style(
    style = cell_borders(sides = "right", color = "black", weight = px(2), style = "solid"),
    locations = cells_column_labels()
  ) %>%
  tab_options(
    table.border.top.color = "black",
    table.border.bottom.color = "black",
    table.border.top.style = "solid",
    table.border.bottom.style = "solid",
    column_labels.border.top.color = "black",
    column_labels.border.bottom.color = "black",
    column_labels.border.bottom.width = px(2),
    row.striping.include_table_body = TRUE,
    heading.border.bottom.color = "black",
    heading.border.bottom.width = px(2),
    table_body.hlines.color = "gray",
    table_body.border.bottom.color = "black"
  )

Tabla Nro. 1
Distribución de frecuencia de la concentración de PM10, estudio de calidad del aire en India
Intervalo	MC	ni	hi	Ni_ascendente	Ni_descendente	Hi_ascendente	Hi_descendente
[0.01 - 62.51)	31.26	5395	29.34	5395	18391	29.34	100
[62.51 - 125.01)	93.76	6760	36.76	12155	12996	66.09	70.66
[125.01 - 187.51)	156.26	3335	18.13	15490	6236	84.23	33.91
[187.51 - 250.01)	218.76	1346	7.32	16836	2901	91.54	15.77
[250.01 - 312.51)	281.26	700	3.81	17536	1555	95.35	8.46
[312.51 - 375.01)	343.76	425	2.31	17961	855	97.66	4.65
[375.01 - 437.51)	406.26	228	1.24	18189	430	98.9	2.34
[437.51 - 500)	468.76	112	0.61	18301	202	99.51	1.1
[500 - 562.5)	531.25	49	0.27	18350	90	99.78	0.49
[562.5 - 625)	593.75	18	0.10	18368	41	99.87	0.22
[625 - 687.5)	656.25	8	0.04	18376	23	99.92	0.13
[687.5 - 750)	718.75	5	0.03	18381	15	99.95	0.08
[750 - 812.5)	781.25	5	0.03	18386	10	99.97	0.05
[812.5 - 875)	843.75	1	0.01	18387	5	99.98	0.03
[875 - 937.5)	906.25	1	0.01	18388	4	99.98	0.02
[937.5 - 1000]	968.75	3	0.02	18391	3	100	0.02
Totales	-	18391	100.00	-	-	-	-
Fuente: Datos obtenidos y procesados por medio de https://www.kaggle.com/datasets/rohanrao/air-quality-data-in-india

# ============================================
# PROCESO DE SIMPLIFICACIÓN — VARIABLE PM10
# ============================================

library(gt)
library(dplyr)

PM10 <- datos$PM10[datos$PM10 != "-"]
PM10 <- as.numeric(PM10)

n <- length(PM10)

min_PM10 <- min(PM10)
max_PM10 <- max(PM10)
R <- max_PM10 - min_PM10

k <- 12
A <- R / k

Lis <- seq(from = min_PM10, to = max_PM10 - A, by = A)
Lss <- c(seq(from = min_PM10 + A, to = max_PM10 - A, by = A), max_PM10)

MCs <- (Lis + Lss) / 2

PM10 <- round(PM10, 3)
Lis <- round(Lis, 3)
Lss <- round(Lss, 3)

ni <- numeric(length(Lis))

for (i in 1:length(Lis)) {
  if (i < length(Lis)) {
    ni[i] <- sum(PM10 >= Lis[i] & PM10 < Lss[i])
  } else {
    ni[i] <- sum(PM10 >= Lis[i] & PM10 <= Lss[i])
  }
}

# FRECUENCIAS RELATIVAS
hi <- round((ni / sum(ni)) * 100, 2)
hi[length(hi)] <- 100 - sum(hi[-length(hi)])

Ni_asc <- cumsum(ni)
Hi_asc <- round(cumsum(hi), 2)
Ni_desc <- rev(cumsum(rev(ni)))
Hi_desc <- round(rev(cumsum(rev(hi))), 2)

# CREACIÓN DE TABLA
TDF_PM10 <- data.frame(
  Intervalo = paste0("[", Lis, " - ", Lss, ")"),
  MC = round(MCs, 3),
  ni = ni,
  `hi(%)` = hi,
  Ni_asc = Ni_asc,
  `Hi_asc (%)` = Hi_asc,
  Ni_desc = Ni_desc,
  `Hi_desc (%)` = Hi_desc
)

totales <- data.frame(
  Intervalo = "Totales",
  MC = "-",
  ni = sum(ni),
  `hi(%)` = sum(hi),
  Ni_asc = "-",
  `Hi_asc (%)` = "-",
  Ni_desc = "-",
  `Hi_desc (%)` = "-"
)
# Detectar nombre REAL de la columna hi
col_hi <- grep("^hi", colnames(TDF_PM10), value = TRUE)

# Convertir a numérico donde corresponda
TDF_PM10$MC <- suppressWarnings(as.numeric(TDF_PM10$MC))
TDF_PM10[[col_hi]] <- suppressWarnings(as.numeric(TDF_PM10[[col_hi]]))

TDF_PM10 <- rbind(TDF_PM10, totales)
#tabla 
TDF_PM10 %>%
  gt() %>%
  tab_header(
    title = md("*Tabla Nro. 2*"),
    subtitle = md("**Distribución de frecuencia simplificada de la concentración de PM10, estudio de calidad del aire en India**")
  ) %>%
  tab_source_note(
    source_note = md("Fuente: Datos obtenidos y procesados por medio de https://www.kaggle.com/datasets/rohanrao/air-quality-data-in-india")
  ) %>%
  tab_style(
    style = cell_borders(sides = "left", color = "black", weight = px(2), style = "solid"),
    locations = cells_body()
  ) %>%
  tab_style(
    style = cell_borders(sides = "right", color = "black", weight = px(2), style = "solid"),
    locations = cells_body()
  ) %>%
  tab_style(
    style = cell_borders(sides = "left", color = "black", weight = px(2), style = "solid"),
    locations = cells_column_labels()
  ) %>%
  tab_style(
    style = cell_borders(sides = "right", color = "black", weight = px(2), style = "solid"),
    locations = cells_column_labels()
  ) %>%
  tab_options(
    table.border.top.color = "black",
    table.border.bottom.color = "black",
    table.border.top.style = "solid",
    table.border.bottom.style = "solid",
    column_labels.border.top.color = "black",
    column_labels.border.bottom.color = "black",
    column_labels.border.bottom.width = px(2),
    row.striping.include_table_body = TRUE,
    heading.border.bottom.color = "black",
    heading.border.bottom.width = px(2),
    table_body.hlines.color = "gray",
    table_body.border.bottom.color = "black"
  )

Tabla Nro. 2
Distribución de frecuencia simplificada de la concentración de PM10, estudio de calidad del aire en India
Intervalo	MC	ni	hi...	Ni_asc	Hi_asc....	Ni_desc	Hi_desc....
[0.01 - 83.342)	41.676	7848	42.67	7848	42.67	18391	100
[83.342 - 166.675)	125.009	6850	37.25	14698	79.92	10543	57.33
[166.675 - 250.007)	208.341	2138	11.63	16836	91.55	3693	20.08
[250.007 - 333.34)	291.674	864	4.70	17700	96.25	1555	8.45
[333.34 - 416.672)	375.006	434	2.36	18134	98.61	691	3.75
[416.672 - 500.005)	458.339	167	0.91	18301	99.52	257	1.39
[500.005 - 583.338)	541.671	53	0.29	18354	99.81	90	0.48
[583.338 - 666.67)	625.004	21	0.11	18375	99.92	37	0.19
[666.67 - 750.002)	708.336	6	0.03	18381	99.95	16	0.08
[750.002 - 833.335)	791.669	5	0.03	18386	99.98	10	0.05
[833.335 - 916.667)	875.001	1	0.01	18387	99.99	5	0.02
[916.667 - 1000)	958.334	4	0.01	18391	100	4	0.01
Totales	-	18391	100.00	-	-	-	-
Fuente: Datos obtenidos y procesados por medio de https://www.kaggle.com/datasets/rohanrao/air-quality-data-in-india

# ========= CREAR HISTOGRAMA PARA OBTENER LOS BREAKS ==========
Histograma_PM10 <- hist(PM10, breaks = 11, plot = FALSE)

# ========= GRÁFICA — HISTOGRAMA DE PM10 =========
hist(PM10, breaks = 11,
     main = "Gráfica N°1: Distribución de la Concentración de PM10
     presente en el estudio sobre calidad del aire en India entre 2015-2020 ",
     xlab = "PM10 (µg/m3)",
     ylab = "Cantidad",
     ylim = c(0, max(ni)),
     col = "yellow",
     cex.main = 0.9,
     cex.lab = 1,
     cex.axis = 0.9,
     xaxt = "n")

axis(1, at = Histograma_PM10$breaks,
     labels = Histograma_PM10$breaks,
     las = 1,
     cex.axis = 0.9)

hist(PM10, breaks = 11,
     main = "Gráfica N°2: Distribución de la Concentración de PM10
     presente en el estudio sobre calidad del aire en India entre 2015-2020",
     xlab = "PM10 (µg/m3)",
     ylab = "Cantidad",
     ylim = c(0, length(PM10)),
     col = "orange",
     cex.main = 1,
     cex.lab = 1,
     cex.axis = 0.9,
     xaxt = "n")

axis(1, at = Histograma_PM10$breaks,
     labels = Histograma_PM10$breaks,
     las = 1,
     cex.axis = 0.9)

# --- Número de filas sin contar totales ---
n <- nrow(TDF_PM10) - 1

# --- Asegurar que MC sea numérico solo para filas de datos ---
MC_num <- as.numeric(TDF_PM10$MC[1:n])

# --- Detectar columna hi(%) automáticamente ---
col_hi <- grep("hi", names(TDF_PM10), value = TRUE)
hi_num <- as.numeric(TDF_PM10[[col_hi]][1:n])

# --- Crear la gráfica ---
bp <- barplot(
  height = hi_num,
  space = 0,
  col = "blue",
  main = "Gráfica N°3: Distribución de la concentración de PM10\nEstudio calidad del aire en India, 2015-2020",
  xlab = "PM10 (µg/m3)",
  ylab = "Porcentaje (%)",
  names.arg = rep("", n),   # temporal
  ylim = c(0, 100),
  las = 1
)

# --- Eje X con MC enteros ---
axis(
  side = 1,
  at = bp,
  labels = round(MC_num, 0),  # redondea a enteros
  las = 2,
  cex.axis = 0.8
)

# --- Número de filas sin contar totales ---
n <- nrow(TDF_PM10) - 1

# --- Asegurar que MC sea numérico solo para filas de datos ---
MC_num <- as.numeric(TDF_PM10$MC[1:n])

# --- Detectar columna hi(%) automáticamente ---
col_hi <- grep("hi", names(TDF_PM10), value = TRUE)
hi_num <- as.numeric(TDF_PM10[[col_hi]][1:n])

# --- Crear la Gráfica 4 ---
bp4 <- barplot(
  height = hi_num,
  space = 0,
  col = "skyblue",
  main = "Gráfica N°4: Distribución de la concentración de PM10\nEstudio calidad del aire en India, 2015-2020",
  xlab = "PM10 (µg/m3)",
  ylab = "Porcentaje (%)",
  names.arg = rep("", n),  # temporal
  las = 1
)

# --- Eje X con MC enteros ---
axis(
  side = 1,
  at = bp4,
  labels = round(MC_num, 0),  # redondea a enteros
  las = 2,
  cex.axis = 0.8
)

# --- Gráfica 5: Boxplot de PM10 ---
CajaPM10 <- boxplot(
  PM10,
  horizontal = TRUE,
  col = "turquoise",
  border = "black",
  main = "Gráfica No. 5: Distribución de la concentración de PM10\nEstudio calidad del aire en India 2015-2020",
  xlab = "PM10 (µg/m3)"
)

# --- Asegurarse de tener Lis, Lss, ni, hi (sin fila de totales) ---
# Recalcular acumuladas
Ni_asc  <- cumsum(ni)
Ni_desc <- rev(cumsum(rev(ni)))
Hi_asc  <- cumsum(hi)
Hi_desc <- rev(cumsum(rev(hi)))

k <- length(Lis)  # número de clases

# --- Gráfica 6: Ojiva (cantidad) para PM10 ---
plot(Lss, Ni_asc,
     type = "b",
     main = "Gráfica N°6: Ojiva ascendente y descendente (Cantidad) - PM10",
     xlab = "PM10 (µg/m3)",
     ylab = "Cantidad",
     pch = 19,
     col = "turquoise",
     ylim = c(0, max(Ni_asc))) 

lines(Lis, Ni_desc, type = "b", col = "red", pch = 19)

# --- Gráfica 7: Ojiva (porcentaje) para PM10 ---
plot(Lss, Hi_asc,
     type = "b",
     main = "Gráfica N°7: Ojiva ascendente y descendente (Porcentaje) - PM10",
     xlab = "PM10 (µg/m3)",
     ylab = "Porcentaje (%)",
     pch = 19,
     col = "blue",
     ylim = c(0, max(Hi_asc, Hi_desc))) 

lines(Lis, Hi_desc, type = "b", col = "red", pch = 19)