VARIANZA

RECORRIDO

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

Re= 810-888=78

VARIANZA

En datos no agrupados

Fórmula σ^2=∑_(i=1)^n▒〖(Xi-■(-@X))〗^2

Para calcular la media se utiliza la fórmula: μ=(∑_(i=1)^N▒Xi)/N

Sustituyendo µ= 816+ 810+ 856+ 888 +833+ 839+ 853+ 837+ 881+ 873+ 889+836+ 815+860+ 830+ 888+ 830+ 844+ 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+ 815/48 = 40845/48= µ= 850.93

Sustituimos para la varianza: σ^2= (816-850.93)2+ (810-850.93)2+(856-850.93)2 888-850.93)2+(833- 850.93)2+ (839+850.93)2+ (853-850.93)2+ (837-850.93)2+ (881-850.93)2+ (873-850.93)2+ (889-850.93)2+ (850.93)2 +(836-850.93)2+ (815-850.93)2+ (860-850.96)2+ (830-850)2+ (888-850)2+ (830-850.93)2+ (844-850.93)2+ (830-850.93)2+ (831-850.93)2+ (840-850.93)2+ (844-850.93)2+ (840-850.93)2+ (858-850.93)2+ (810-850.93)2+ (888-850.93)2+ (883850.93)2+ (835-850.93)2+ (884-850.93)2+ (849-850.93)2+ (856850.93)2+ (888-850.93)2+ (833-850.93)2+ (869-850.93)2+ (835-850.93)2+ (835-850.93)2+ (884-850.93)2+ (849-850.93)2+ (844-850.93)2+ (840-850.93)2+ (858-850.93)2+ (853-850.93)2+ (837-850.93)2+ (881-850.93)2+ (873-850.93)2+ (889-850.93)2+ (836-850.93)2+ (815-850.96)2 / 48 =

σ2= 26716.8152/48 = 556.60 Por lo tanto la varianza es 556.60

Para datos agrupados por intervalos

En una población

La fórmula es σ^2=(∑_(i=1)^N▒〖f〖i(Mci-μ)〗^2 〗)/N

Se calcula primero la media μ=∑_(i=1)^N▒〖Mcifi=〗 (814x5)+(824.5x0)+(834.5x14)+(844.5x8)+(854.5x6)+(864.5x2)+(874.5x2)+(884.5x11) = 40843.5 =

48 48

µ=850.90625

σ^2=(∑_(i=1)^N▒〖f〖i(Mci-μ)〗^2 〗)/N = 24881.3552 = 518.361

48

σ2= 518.316

Desviación Típica

La fórmula es: σ^2=√(σ^2 )=√((∑_(i=1)^N▒〖fi(Mci-µ)〗^2 )/N) = √518.316 = 22.766

√(σ^2 ) = 22.766

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