Medidas de tendencia central

MEDIDAS DE TENDENCIA CENTRAL

MEDIA ARITMETICA
Ẋ= ∑_(i=1)^n▒Xif/n

Ẋ= 6198/214
Ẋ= 28,96
Ẋ= 29
MEDIANA
Hallar clase mediana
n/2=214/2=107
〖 〗_( Me = L.R.I+((n/2-Fd)/fM)C)
〖 〗_( Me= 24,5+((107-103)/51)5)
Me= 24,5+o,08 (5)
Me = 24,5 +0,4
Me= 24,9
MODA
Clase modal: Mayor frecuencia
M_(o= L.R.I+ Δ_1/(Δ_1+Δ_2 ) (C))

M_(o=19,5+31/(31+16 ) (5))
M_O = 19,5 +0,66 (5)
M_O= 22,8
MEDIA GEOMETRICA
M_(g=antilog) ∑_(i=1)^n▒flogXi/n
M_(g=antilog) (301,585)/214
M_(g=antilog) 1,409
M_g= 25,644

MEDIA ARMONICA
M_a= n/(∑_(i=1)^n▒f/Xi)
M_a= 214/8,685
M_(a=24,64 )MEDIDA DE POSICION
CUARTILES
Clase cuartil
nK/4=214(2)/4=107
Q_(2=L.R.I+((nK/4-Fd)/fQk)C)
Q_(2=24,5+((107-103)/51)5)
Q_(2=24,5+0,4 )
Q_(2=24,9 )

nK/4=214(3)/4=160,5Q_(3=L.R.I+((nk/4-Fd)/fQk)C)
Q_(3=29,5+((160,5-154)/29)5)
Q_(3=29,5+1,120 )
Q_(3=30,62)
DECILES
Decil 4: Clase decíl
nK/10= (214(4))/10=85,6

D_(4=L.R.I+((nk/10-Fd)/fDk)C)
D_(4=19,5+((85,6-36)/67)5)D_(4=19,5+3,70 )
D_(4=23,2)
Decil 7
Clase decíl
nK/10= (214(7))/10=149,8

D_(7=L.R.I+((nk/10-Fd)/fDk)C)
D_(7=24,5+((149,8-103)/51)5)
D_(7=24,5+0,183 )
D_(7=24,683)
PERCENTILES
nK/100=(214(33))/100=70,62

P_(33=L.R.I+((nk/100-Fd)/fDk)C)
P_(33=19,5+((70,62-36)/67)5)
P_(33=19,5+2,66)
P_(33=22,16)
PERCENTIL 68
nK/100= (214(68))/100=145.52

P_(68=L.R.I+((nk/100-Fd)/fDk)C)P_(68=24,5+((145,52-103)/51)5)
P_(68=24,5+4,168 )
P_(68=28,668)
MEDIDE DE DISPERCION
VARIANZA
S^2= ∑_(i=1)^n▒(|Xi- Ẋ|^2 f)/n

S^2=17376/214
s^(2 )=81,2
ANALISIS
A edad de los estudiantes presenta unadispersión en unidades cuadradas de 81,2 años con respecto a la media aritmética.
DESVIACION TIPICA O ESTANDAR
S= ∑_(i=1)^n▒√(((Xi-Ẋ)^(2 ) f)/n)
S= √(17376/214)
S=√81,2
S=9.01
DESVIACIONCUARTILICA
D_(Q=Q_(3-Q_1 ) )
nK/4=214(3)/4=160,5
Q_(3=L.R.I+((nk/4-Fd)/fQk)C)
Q_(3=29,5+((160,5-154)/29)5)
Q_(3=29,5+1,120 )
Q_(3=30,62)
CUARTIL 1
nK/4=214(1)/4=53,5
Q_(1=L.R.I+((nk/4-Fd)/fQk)C)...