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Catégorie :Category: nCreator TI-Nspire
Auteur Author: superkepo28
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 2.31 Ko KB
Mis en ligne Uploaded: 06/01/2025 - 12:25:07
Uploadeur Uploader: superkepo28 (Profil)
Téléchargements Downloads: 1
Visibilité Visibility: Archive publique
Shortlink : http://ti-pla.net/a4433802
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 2.31 Ko KB
Mis en ligne Uploaded: 06/01/2025 - 12:25:07
Uploadeur Uploader: superkepo28 (Profil)
Téléchargements Downloads: 1
Visibilité Visibility: Archive publique
Shortlink : http://ti-pla.net/a4433802
Description
Fichier Nspire généré sur TI-Planet.org.
Compatible OS 3.0 et ultérieurs.
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1. Moyenne arithmétique X É = 1 n Å i = 1 m C i Å m i bar{X} = frac{1}{n} cdot sum_{i=1}^{m} C_i cdot m_i X É = n 1 Å i = 1 m C i Å m i C i C_i C i : Centre de la classe i i i m i m_i m i : Effectif de la classe i i i n = m i n = sum m_i n = m i : Total des effectifs 2. Effectif corrigé Effectif corrig e Ê = m i a i text{Effectif corrigé} = frac{m_i}{a_i} Effectif corrig e Ê = a i m i m i m_i m i : Effectif de la classe i i i a i a_i a i : Amplitude de la classe i i i 3. Moyennes marginales Pour un tableau croisé entre X X X et Y Y Y : Moyenne marginale de X X X : X É = i = 1 m j = 1 n C i , X Å N i j N bar{X} = frac{sum_{i=1}^{m} sum_{j=1}^{n} C_{i,X} cdot N_{ij}}{N} X É = N i = 1 m j = 1 n C i , X Å N ij Moyenne marginale de Y Y Y : Y É = i = 1 m j = 1 n C j , Y Å N i j N bar{Y} = frac{sum_{i=1}^{m} sum_{j=1}^{n} C_{j,Y} cdot N_{ij}}{N} Y É = N i = 1 m j = 1 n C j , Y Å N ij C i , X C_{i,X} C i , X : Centre de la i e i^text{e} i e classe pour X X X C j , Y C_{j,Y} C j , Y : Centre de la j e j^text{e} j e classe pour Y Y Y N i j N_{ij} N ij : Effectif correspondant à la cellule ( i , j ) (i,j) ( i , j ) N = N i j N = sum N_{ij} N = N ij : Total des effectifs 4. Covariance (Forme factorisée) Cov ( X , Y ) = 1 n Å i = 1 n X i Å Y i X É Å Y É text{Cov}(X, Y) = frac{1}{n} cdot sum_{i=1}^{n} X_i cdot Y_i - bar{X} cdot bar{Y} Cov ( X , Y ) = n 1 Å i = 1 n X i Å Y i X É Å Y É 5. Coefficient de corrélation ( r r r ) r = Cov ( X , Y ) Ã X Å Ã Y r = frac{text{Cov}(X, Y)}{sigma_X cdot sigma_Y} r = Ã X Å Ã Y Cov ( X , Y ) Ã X = Var ( X ) sigma_X = sqrt{text{Var}(X)} Ã X = Var ( X ) Ã Y = Var ( Y ) sigma_Y = sqrt{text{Var}(Y)} Ã Y = Var ( Y ) 6. Variance Var ( X ) = 1 n Å i = 1 n m i Å ( C i X É ) 2 text{Var}(X) = frac{1}{n} cdot sum_{i=1}^{n} m_i cdot (C_i - bar{X})^2 Var ( X ) = n 1 Å i = 1 n m i Å ( C i X É ) 2 Made with nCreator - tiplanet.org
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Compatible OS 3.0 et ultérieurs.
<<
1. Moyenne arithmétique X É = 1 n Å i = 1 m C i Å m i bar{X} = frac{1}{n} cdot sum_{i=1}^{m} C_i cdot m_i X É = n 1 Å i = 1 m C i Å m i C i C_i C i : Centre de la classe i i i m i m_i m i : Effectif de la classe i i i n = m i n = sum m_i n = m i : Total des effectifs 2. Effectif corrigé Effectif corrig e Ê = m i a i text{Effectif corrigé} = frac{m_i}{a_i} Effectif corrig e Ê = a i m i m i m_i m i : Effectif de la classe i i i a i a_i a i : Amplitude de la classe i i i 3. Moyennes marginales Pour un tableau croisé entre X X X et Y Y Y : Moyenne marginale de X X X : X É = i = 1 m j = 1 n C i , X Å N i j N bar{X} = frac{sum_{i=1}^{m} sum_{j=1}^{n} C_{i,X} cdot N_{ij}}{N} X É = N i = 1 m j = 1 n C i , X Å N ij Moyenne marginale de Y Y Y : Y É = i = 1 m j = 1 n C j , Y Å N i j N bar{Y} = frac{sum_{i=1}^{m} sum_{j=1}^{n} C_{j,Y} cdot N_{ij}}{N} Y É = N i = 1 m j = 1 n C j , Y Å N ij C i , X C_{i,X} C i , X : Centre de la i e i^text{e} i e classe pour X X X C j , Y C_{j,Y} C j , Y : Centre de la j e j^text{e} j e classe pour Y Y Y N i j N_{ij} N ij : Effectif correspondant à la cellule ( i , j ) (i,j) ( i , j ) N = N i j N = sum N_{ij} N = N ij : Total des effectifs 4. Covariance (Forme factorisée) Cov ( X , Y ) = 1 n Å i = 1 n X i Å Y i X É Å Y É text{Cov}(X, Y) = frac{1}{n} cdot sum_{i=1}^{n} X_i cdot Y_i - bar{X} cdot bar{Y} Cov ( X , Y ) = n 1 Å i = 1 n X i Å Y i X É Å Y É 5. Coefficient de corrélation ( r r r ) r = Cov ( X , Y ) Ã X Å Ã Y r = frac{text{Cov}(X, Y)}{sigma_X cdot sigma_Y} r = Ã X Å Ã Y Cov ( X , Y ) Ã X = Var ( X ) sigma_X = sqrt{text{Var}(X)} Ã X = Var ( X ) Ã Y = Var ( Y ) sigma_Y = sqrt{text{Var}(Y)} Ã Y = Var ( Y ) 6. Variance Var ( X ) = 1 n Å i = 1 n m i Å ( C i X É ) 2 text{Var}(X) = frac{1}{n} cdot sum_{i=1}^{n} m_i cdot (C_i - bar{X})^2 Var ( X ) = n 1 Å i = 1 n m i Å ( C i X É ) 2 Made with nCreator - tiplanet.org
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