Cours de distribution statistique

Résumé du document

- Dispersion : donne un indice sur la façon dont se répartissent les individus autour de la tendance.

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Extraits

[...] Fréquences cumulées Pour les variables ordinales discrètes et continues, on peut expliciter la relation d'ordre sur les valeurs. On définit alors les distributions cumulées. X n if iEffectifs cumulésFréquences cumuléesx 1n 1f 1n 1f 1x 2n 2f 2n 1 + n 2 f 1 + f 2x kn kf kn 1 + . + n k f 1 + . [...]

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0000fc020000000080000000040000002d01040005000000010200008000040000000201 02000e00000024030500f2004000f5004200f2004400f0004200f2004000050000000102 ffffff000400000002010100040000002e01180009000000320a4500ff00010000004600 0400040000002e010000040000002d010500040000002d010600040000002d0101000400 00002701ffff030000001e00040000002d010000040000002d010400040000002d010200 050000000102ffffff0005000000090200000000040000002c0100000700000016044900 07013b00e600040000002d010500040000002d010600040000002d010100040000002701 ffff030000001e00040000002d010000040000002d010400040000002d01020005000000 0102ffffff0005000000090200000000040000002c01000007000000160490000d010000 000007000000fc020000000000000000040000002d01080004000000f001040004000000 2d01050004000000f0010200040000002d010100040000002701ffff030000001e000500 00000102ffffff0005000000090200000000040000002701ffff030000001e0005000000 0102ffffff0005000000090200000000040000002701ffff q 0.25 ª [18,24[ q 0.25 = 18 + - 18) . ( 0.25 - 0.196 ) / ( 0.326 - 0.196 = 20.5 Mé ª [30,36[ Mé = 30 + 30) . ( 0.5 0.473 ) / ( 0.635 0.473 = 31 q 0.75 ª [36,42[ q 0.75 = 36 + 36) . ( 0.75 0.635 ) / ( 0.77 0.75 = Ecart interquartile : 41.11 20.5 = 20.61 Il y a 20.61 Km de dispersion de 50% autour de la médiane. [...]

[...] Box-plot : q 0.25 q 0.75 Ex 15 : Distance parcourueNbr de livraisonsf iC if i C iF[0,6[ [12,18[ .196[18,24[ [24,30[ [30,36[ .635[36,42[ [42,48[ [48,54[ [54,60[ Distance moyenne parcourue pour une livraison ? 2. Fonction de répartition ? 3. [...]

[...] Définition générale et á sont des cas particuliers de moments. On appelle moment général d'ordre par rapport à une valeur quelconque a : aM n = n i i a)ⁿ / n = f i i a)ⁿ picscalex1080100090000039b00000000003d000000000004000000030108000500000 00b0200000000050000000c020d000e00030000001e003d000000410b8600ee000c000d0 0000000000c000d0000000000280000000d0000000c00000001000100000000000000000 00000000000000000000000000000000000000000ffffff003300c530120000000a00494 c0400ffff0400a402060011001d80000000000100000000003ff00000000000000000000 03d000000410bc60088000c000d00000000000c000d0000000000280000000d0000000c0 000000100010000000000000000000000000000000000000000000000000000000000fff fff00ccf80000edf80000f5f80101fbf82644fbf80100f9f80001e2780101fff82644fff 80101c0080001fff80101fff82644040000002701ffff030000000000 = f i x i = 0M 1 = f i i picscalex1080100090000039b00000000003d0000000000040000000301080005000000 0b0200000000050000000c020d000e00030000001e003d000000410b8600ee000c000d00 000000000c000d0000000000280000000d0000000c000000010001000000000000000000 0000000000000000000000000000000000000000ffffff003300c530120000000a00494c 0400ffff0400a402060011001d80000000000100000000003ff000000000000000000000 3d000000410bc60088000c000d00000000000c000d0000000000280000000d0000000c00 00000100010000000000000000000000000000000000000000000000000000000000ffff ff00ccf80000edf80000f5f80101fbf82644fbf80100f9f80001e2780101fff82644fff8 0101c0080001fff80101fff82644040000002701ffff030000000000)² = picscalex1080100090000039b00000000003d0000000000040000000301080005000000 0b0200000000050000000c020d000e00030000001e003d000000410b8600ee000c000d00 000000000c000d0000000000280000000d0000000c000000010001000000000000000000 0000000000000000000000000000000000000000ffffff003300c530120000000a00494c 0400ffff0400a402060011001d80000000000100000000003ff000000000000000000000 3d000000410bc60088000c000d00000000000c000d0000000000280000000d0000000c00 00000100010000000000000000000000000000000000000000000000000000000000ffff ff00ccf80000edf80000f5f80101fbf82644fbf80100f9f80001e2780101fff82644fff8 0101c0080001fff80101fff82644040000002701ffff030000000000M Moments simples On appelle moment simple un moment pour a = 0 M = f i x i 3. [...]

[...] Moyenne arithmétique Elle est définie pour les variables quantitatives uniquement. Cas discret : picscalex1080100090000039b00000000003d0000000000040000000301080005000000 0b0200000000050000000c020d000e00030000001e003d000000410b8600ee000c000d00 000000000c000d0000000000280000000d0000000c000000010001000000000000000000 0000000000000000000000000000000000000000ffffff003300c530120000000a00494c 0400ffff0400a402060011001d80000000000100000000003ff000000000000000000000 3d000000410bc60088000c000d00000000000c000d0000000000280000000d0000000c00 00000100010000000000000000000000000000000000000000000000000000000000ffff ff00ccf80000edf80000f5f80101fbf82644fbf80100f9f80001e2780101fff82644fff8 0101c0080001fff80101fff82644040000002701ffff030000000000 = (Ó n i x i ) / n = Ó f i x i Cas continu : picscalex1080100090000039b00000000003d0000000000040000000301080005000000 0b0200000000050000000c020d000e00030000001e003d000000410b8600ee000c000d00 000000000c000d0000000000280000000d0000000c000000010001000000000000000000 0000000000000000000000000000000000000000ffffff003300c530120000000a00494c 0400ffff0400a402060011001d80000000000100000000003ff000000000000000000000 3d000000410bc60088000c000d00000000000c000d0000000000280000000d0000000c00 00000100010000000000000000000000000000000000000000000000000000000000ffff ff00ccf80000edf80000f5f80101fbf82644fbf80100f9f80001e2780101fff82644fff8 0101c0080001fff80101fff82644040000002701ffff030000000000 = Ó f i x i Avec x i = i i+1 le centre de i i+1 [ Ex 10 : picscalex1080100090000039b00000000003d0000000000040000000301080005000000 0b0200000000050000000c020d000e00030000001e003d000000410b8600ee000c000d00 000000000c000d0000000000280000000d0000000c000000010001000000000000000000 0000000000000000000000000000000000000000ffffff003300c530120000000a00494c 0400ffff0400a402060011001d80000000000100000000003ff000000000000000000000 3d000000410bc60088000c000d00000000000c000d0000000000280000000d0000000c00 00000100010000000000000000000000000000000000000000000000000000000000ffff ff00ccf80000edf80000f5f80101fbf82644fbf80100f9f80001e2780101fff82644fff8 0101c0080001fff80101fff82644040000002701ffff030000000000 = 2510 E. [...]