formule statistica descriptiva

Formule Statistica descriptiva R

Parametrii repartitiilor

σ x2 =

R

∑ Ni

=

∑ (x i =1

R

∑N i =1

(

)

R

Media geometrica

V REZ = σ

X 1 ⋅ ... ⋅ X n

2 Y/X

=

∑σ

2 i

Xh =

V EXP = σ = 2 Y

n 1 1 + ... + X1 Xn

2

⋅Nj

N

∑ (Y / x j =1

j

−Y

)

2

⋅ N. j

N

Abaterea medie patratica

σ x = σ x2

Valoarea mediana M e = x  N 

Coeficientul de variatie

   2  +1    

M e = x i −1

i

j =1

R

Media armonica

− X )2 ⋅ Ni

i

V ( X ) = M X 2 −( M ( X ))

X + ... + X n X = 1 n

Xg =

i =1

R

i =1

Media aritmetica

n

∑ ( xi − X ) 2

N − FN ( x M e ) + 2 ⋅ lM e FM e

σx

Vx =

X

⋅ 100

Analiza legaturii intre variabile Hi patrat

Valoarea modala

I

J

χ 2 = ∑∑

∆ −1 M o = x i −1 + ⋅lMo ∆ −1 + ∆ 1

( N ij − N ij∗ ) 2 N ij∗

i =1 j =1

N ij∗

N i − N i −1 = ∆−1

=

N i• ⋅ N • j N

, C=

;

χ2 N + χ2

N i − N i +1 = ∆1

Coeficientul de corelatie a rangurilor

Cuartile

al lui Spearman

q p = x i −1 +

Varianta

N (q p ) − N ( x i −1 ) Ni

n

⋅ ( x i − x i −1 )

η = 1−

6∑ d i2 i =1

n(n 2 − 1)

Coeficientul de corelatie a rangurilor a lui Kendall

τ=

P −Q P +Q

Coeficientul de corelatie rYX =

M ( XY ) − M ( X ) M (Y ) σY ⋅ σ X

Modelarea legaturii dintre variabile Parametrii regresiei simple M ( XY ) − M ( X ) M (Y ) M ( X 2 ) − [ M ( X )] 2

b=

a = M (Y ) −bM ( X )

Coeficientul de determinatie R2 =

V EXP VTOT

Analiza seriilor de timp n

Iy =

∑y t =2

n

t −1

∑y t =2

I y = n −1

; ∆y =

⋅ yt ;

2 t −1

yn = n −1 I yn / n −1 ⋅ I yn −1 / n −2 ⋅ ... ⋅ I y2 / 1 y1

y n − y1 n −1

Mediile mobile

yt −k + yt −k −1 + ... + yt + ... + yt +k ; p t = k +1, k + 2,..., n − k 0,5 y t −k + y t −k +1 + ... + y t + ... + y t +k −1 + 0,5 y t +k yt = p yt =

yt =

0,5 y t −2 + y t −1 + y t + y t +1 + 0,5 y t + 2 , 4