π = ππ’ππππ ππ ππππ ππ π₯ = ππππππππ π = πΉππππ’πππππ πππ πππ’π‘π ππ ππ π β ππ πππ ππππ π = πΉππππ’πππππ πππππ‘ππ£π ππ ππ π β ππ πππ π
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π = ππ’ππππ ππ ππππ ππ π₯ = ππππππππ π = πΉππππ’πππππ πππ πππ’π‘π ππ ππ π β ππ πππ ππππ π = πΉππππ’πππππ πππππ‘ππ£π ππ ππ π β ππ πππ ππππ π = πΉππππ’πππππ πππ πππ’π‘π πππ’ππ’ππππ ππ ππ π β ππ πππ ππππ πΉ = πΉππππ’πππππ πππππ‘ππ£π πππ’ππ’ππππ ππ ππ π β ππ πππ ππππ πΉ β² = πΉππππ’πππππ πππππ‘ππ£π ππππ’ππ’ππππ ππ ππ π β ππ πππ ππππ π = ππ’ππππ π‘ππ‘ππ ππ πππ πππ£πππππππ Propiedades ConstrucciΓ³n del intervalo de clase I. Calcular el rango β π =π I. π
=π₯ βπ₯ II. π = II. Definir el nΓΊmero de intervalos, 4 β€ π β€ 20 β π =1 III. π = βπ IV. π =β π III. Calcular la amplitud de los intervalos, πΆ = V. πΉ =β π = Punto medio o marca d clase βπβ²π β π = 1,2, β¦ , π π₯ +π₯ ππΆ = 2 Medidas de posiciΓ³n Para datos no agrupados Para datos agrupados Media aritmΓ©tica Media armΓ³nica Media aritmΓ©tica Media armΓ³nica π π β π₯ β π₯ βπ π₯Μ
= π₯Μ
= π₯Μ
= π π₯Μ
= 1 β π π β π₯ π₯ Media geomΓ©trica Media geomΓ©trica Media CuadrΓ‘tica Media CuadrΓ‘tica π₯Μ
=
π₯ π₯Μ
Medidas de dispersiΓ³n Para datos no agrupados Varianza muestral (n) β (π₯ β π₯Μ
) π = πβ1 β π₯ π = β π₯Μ
πβ1 DesviaciΓ³n estΓ‘ndar o tΓpica (n) π=
β
(π₯ β π₯Μ
) πβ1
β π₯ β π₯Μ
πβ1 Covarianza (n) β (π₯ β π₯Μ
)(π¦ β π¦) π = πβ1 β π₯π¦ π = β π₯Μ
π¦ πβ1 π=
=
β
π₯
π=
=
π₯
π
Varianza poblacional (P) β (π₯ β π₯Μ
) π = π β π₯ π = β π₯Μ
π DesviaciΓ³n estΓ‘ndar o tΓpica (P) π=
π₯Μ
β
(π₯ β π₯Μ
) π
β
π₯
β π₯Μ
π Covarianza (P) β (π₯ β π₯Μ
)(π¦ β π¦) π = π β π₯π¦ π = β π₯Μ
π¦ π
Coeficiente de variaciΓ³n Coeficiente de correlaciΓ³n π π πΆπ = π= π₯Μ
π βπ Ing. Victor Joaquin Vargas Arce
Para datos agrupados Varianza muestral (n) β (π₯ β π₯Μ
) β π π = πβ1 β π₯ βπ π = β π₯Μ
πβ1 DesviaciΓ³n estΓ‘ndar o tΓpica (n) π=
β β
(π₯ β π₯Μ
) β π πβ1
π₯ βπ β π₯Μ
πβ1 Covarianza (n) β (π₯ β π₯Μ
)(π¦ β π¦)π π = πβ1 β π₯π¦π π = β π₯Μ
π¦ πβ1 π=
π₯Μ
=
β
π₯ βπ π
Varianza poblacional (P) β (π₯ β π₯Μ
) β π π = π β π₯ βπ π = β π₯Μ
π DesviaciΓ³n estΓ‘ndar o tΓpica (P) π=
β
(π₯ β π₯Μ
) β π π
β
π₯ βπ β π₯Μ
π Covarianza (P) β (π₯ β π₯Μ
)(π¦ β π¦)π π = π β π₯π¦π π = β π₯Μ
π¦ π π=
Coeficientes de regresiΓ³n lineal π π½= πΌ = π¦ β π½ π₯Μ
π