From ee581bdaa66309e88c8e37eb33916dc1dba8ce8c Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?F=C3=A9lix=20MARQUET?= Date: Fri, 28 Feb 2025 10:38:48 +0100 Subject: [PATCH] feat: add statistical analysis and visualization for conductor heights --- TP3/Exercice1.R | 120 ++++++++++++++++++++++ TP3/TP3-R-Statistiques Descriptives-1.pdf | Bin 0 -> 87130 bytes TP3/tp3datas.xlsx | Bin 0 -> 13147 bytes 3 files changed, 120 insertions(+) create mode 100644 TP3/Exercice1.R create mode 100644 TP3/TP3-R-Statistiques Descriptives-1.pdf create mode 100644 TP3/tp3datas.xlsx diff --git a/TP3/Exercice1.R b/TP3/Exercice1.R new file mode 100644 index 0000000..b28fb55 --- /dev/null +++ b/TP3/Exercice1.R @@ -0,0 +1,120 @@ +# Spécifier un miroir CRAN +options(repos = c(CRAN = "https://cran.rstudio.com/")) + +# Installer le package readxl +install.packages("readxl") + +# Charger le package readxl +library(readxl) + +# Spécifier le chemin vers votre fichier .xlsx +file_path <- "./TP3/tp3datas.xlsx" + +# Lire la feuille nommée "Exercice 1" +data <- read_excel(file_path, sheet = "Exercice 1") + +# 1. Quelle est la population statistique observée ? La taille de l’échantillon ? +tailles <- as.vector(as.matrix(data)) + +echantillon_taille <- length(tailles) + +print("Population observée: Tailles des conducteurs (en cm)") +cat("Taille de l'échantillon:", echantillon_taille, "observations\n") + +# 2. Quel est le caractère statistique observé et sa nature ? +print("Caractère statistique: Taille des conducteurs") +print("Nature: Quantitative continue (mesurée en cm)") + +# 3. Dépouiller les données suivant une distribution des fréquences dont la limite +# inférieure est 150 cm (inclus) et dont la largeur de chaque classe est de 5. On +# indiquera les fréquences de chaque classe et on représentera graphiquement +# l’histogramme associé à cette distribution + +# Créer les classes avec une largeur de 5cm +breaks <- seq(150, 190, by = 5) # De 150 à 190 pour couvrir toutes les données + +# Calculer la distribution des fréquences +freq_dist <- table(cut(tailles, breaks = breaks, include.lowest = TRUE, right = FALSE)) + +# Afficher le tableau des fréquences absolues +cat("Distribution des fréquences absolues:\n") +print(freq_dist) + +# Calculer et afficher les fréquences relatives +freq_rel <- prop.table(freq_dist) +cat("\nDistribution des fréquences relatives:\n") +print(freq_rel) + +# Créer l'histogramme +hist(tailles, + breaks = breaks, + main = "Distribution des tailles des conducteurs", + xlab = "Taille (cm)", + ylab = "Frequence", + col = "lightblue", + border = "black") + +# 4. Tracer la courbe de la fonction de répartition empirique (diagramme des +# fréquences cumulées) de la distribution de fréquences de la question précédente. + +# Calculer les fréquences cumulées +freq_cum <- cumsum(freq_dist) +freq_cum_rel <- cumsum(freq_rel) + +# Créer les points pour le graphique (milieu des classes) +points_x <- breaks[-length(breaks)] + 2.5 + +# Tracer la courbe des fréquences cumulées +plot(points_x, freq_cum_rel, + type = "s", # type "s" pour une courbe en escalier + main = "Fonction de repartition empirique", + xlab = "Taille (cm)", + ylab = "Frequences cumulees", + ylim = c(0, 1), + col = "blue") + +# Ajouter une grille +grid() + +# Ajouter les points +points(points_x, freq_cum_rel, pch = 16, col = "red") + +# 5. Calculer la médiane, l’intervalle interquartile et interdécile. + +# Calculer la médiane +mediane <- median(tailles) + +# Calculer les quartiles +Q1 <- quantile(tailles, 0.25) +Q3 <- quantile(tailles, 0.75) +IQR <- Q3 - Q1 + +# Calculer les déciles +D1 <- quantile(tailles, 0.1) +D9 <- quantile(tailles, 0.9) +IDR <- D9 - D1 + +# Afficher les résultats +cat("Médiane:", mediane, "cm\n") +cat("\nIntervalle interquartile (IQR):\n") +cat("Q1 (25%):", Q1, "cm\n") +cat("Q3 (75%):", Q3, "cm\n") +cat("IQR:", IQR, "cm\n") +cat("\nIntervalle interdécile (IDR):\n") +cat("D1 (10%):", D1, "cm\n") +cat("D9 (90%):", D9, "cm\n") +cat("IDR:", IDR, "cm\n") + +# 6. Si on élimine les 5% plus grands et les 5% les plus petits des conducteurs, quel +# intervalle de taille standard retiendra-t-on ? + +# Calculer les percentiles 5 et 95 +P5 <- quantile(tailles, 0.05) +P95 <- quantile(tailles, 0.95) +intervalle <- P95 - P5 + +# Afficher les résultats +cat("Intervalle standard (après élimination des 5% extrêmes):\n") +cat("Borne inférieure (5%):", P5, "cm\n") +cat("Borne supérieure (95%):", P95, "cm\n") +cat("Amplitude de l'intervalle:", intervalle, "cm\n") \ No newline at end of file diff --git a/TP3/TP3-R-Statistiques Descriptives-1.pdf b/TP3/TP3-R-Statistiques Descriptives-1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..b9345cad327320cde757ce8628d54af2c8f2d291 GIT binary patch literal 87130 zcmcG$1y~%**6%&I1qdD>z@R~b4THP84GzKGonQ&BA-D#2cZc8(fnWgwBzW*Z2o@l4 zn`}Az?0w#I-}^n!*UxmOySlo1ty=%8nOQ$7v?>x(%sblRbVm^^fL9xxl&(ZmK_ zK!8=j+QHn|#oF8449w1|0OsLl=U`)%(F1cqxgZcQJ137mt1=kE#wz(+39AyAgH;{O 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