Estadistica

E S T A D I S T I C A B A S I C A

Medidas de dispersión, Actividad 4,5 y 6.

Recorrido, Varianza y Desviación Típica.

Datos no agrupados.

816 810 856 888 833 839 853 837 881 873 889 836 815 860 830 888 830844 830 831 840 844 840 858 810 888 883 835 884 849 856 888 833 869 835 835 884 849 844 840 858 853 837 881 873 889 836 815

Recorrido

Re = max xi – max xi 889- 810= 79.

Varianza

Donde media es igual a

(810x2)+(815x2)+816+(830x3)+831+(833x2)+(835x3)+(836x2)+(837x2)+839+ (840x3)+(844x3)+(849x2)+(853x2)+(856x2)+(858x2)+860+869+(873x2)+ (881x2)+883+(884x2)+(888x4)+(889x2) / 48 = 40 845 / 48 = 850.9375

= (816-850.9375)2+(810-850.9375)2+( 856-850.9375)2+ (888-850.9375)2+(833-850.9375)2+(839-850.9375)2+(853-850.9375)2+(837-850.9375)2+ (881-850.9375)2+(873-850.9375)2+(889-850.9375)2+(836-850.9375)2+(815-850.9375)2+ (860-850.9375)2+(830-850.9375)2+(888-850.9375)2+(830-850.9375)2+(844-850.9375)2+ (830-850.9375)2+(831-850.9375)2+(840-850.9375)2+(844-850.9375)2+(840-850.9375)2+ (858-850.9375)2+(810-850.9375)2+(888-850.9375)2+(883-850.9375)2+(835-850.9375)2+ (884-850.9375)2+(849-850.9375)2+(856-850.9375)2+(888-850.9375)2+(833-850.9375)2+ (869-850.9375)2+(835-850.9375)2+(835-850.9375)2+(884-850.9375)2+(849-850.9375)2+ (844-850.9375)2+(840-850.9375)2+(858-850.9375)2+(853-850.9375)2+(837-850.9375)2+ (881-850.9375)2+(873-850.9375)2+(889-850.9375)2+(836-850.9375)2+(815-850.9375)2 =

26716.76 / 48 = 556.599

Desviación estándar

= 556.599 = 23.59

Datos agrupados

Varianza

Donde la media es igual a 4067.5+4977+9212.5+4227.5+3414+2584.5+2608.5+1755+7969.5 / 48 = 850.33

Mc i fi Mc-µ (Mc-µ)2 (Mc-µ)2 . fi

813.5 810-817 5 -36.83 1356.45 6782.24

821.5 818-825 0 -28.83 831.17 0

829.5 826-833 6 -20.83 433.89 2603.33

837.5 834-841 11 -12.83 164.61 1810.69

845.5 842-849 5 -4.83 23.33 116.64

853.5 850-857 4 3.17 10.05 40.19

861.5 858-865 3 11.17 124.77 374.31

869.5 866-873 3 19.17 367.49 1102.47

877.5 874-881 2 27.17 738.21 1476.42

885.5 882-889 9 35.17 1236.93 11132.36

Total 25438.65

= 25438.65 / 48 = 529.97

Desviación estándar

= 529.97 = 23.02

...