Ungroup: Regress in Analysis: Time Series Analysis:

Mean: x = ∑ x

n y on x: y = a + bx

GM: antilog∑ logx

n b=

n∑ xy – (∑x )(∑ y )n∑ x2−(∑x)2

a= y−bx

HM: n

∑ (1/ x ) Corelation Coefficient:

Group: r=n∑ xy−(∑x )(∑ y )

√ [n∑ x2−(∑ x )2 ] ¿¿¿

Mean: x= ∑ fx

∑ f Standard Error:

GM: antilog f logx

∑ f Se=√∑¿¿¿

HM: ∑ f

∑ ( f / x) x on y: x = c + dy (c=x−d y )

d=n∑ xy – (∑x)(∑ y)

n∑ y2−(∑ y )2

Median: ~x=l+ hf (∑f2

−C .F) Coefficient determination: r2×100

Mode: x=l+( fm−f 12 fm−f 1−f 2 )×h G.M of regression : r=√b×d

Skewed frequency dist: Multiple Regression Eq:

( x− x )=3 ( x−~x ) y = a + bx1 + cx2Mean deviation for ungroup: 1. ∑ y=na+b∑ x1+c∑ x2M

d=∑ (x−x)

n 2. ∑x1 y=a∑ x1+b∑¿¿

3.∑x2 y=a∑ x2+b∑ x1 x2+c∑¿¿

UNGROUP DATA:

Population Sample

Variance: σ 2= ∑x2

N−(∑x

N )2

¿2= 1

n−1¿¿¿

S.D: √σ2 √¿2

µ = ∑xN

x = ∑xn

Z = x−µσ

Z = x−x¿

Mean of Z: ∑zn

Coefficient of Variation: C.V = S .D

Mean ( x )×100

Variance of Z: ¿2 z = n∑ z2– ¿¿

Linear trend: y = a + bx

a=∑ y

n b=

∑ xy

∑ x2

Quadratic trend: y=a+bx+c x2

(i)∑ y=an+c ∑ x2

(ii)∑x2 y=a∑ x2+c∑ x4

(iii)b=∑ xy

∑ x2

Percent trend: yy

×100

Relative cyclic residual: y− y

y×100

Binomial Distribution:P(x)= nC x . px . qn−x

Poisson Distribution:

P(x) =e−λ . λx

x ! e = 2.718, λ= average

Normal Distribuion:

Z = x−μσ

Special Discrete Distributions:Mean of binomial: μ=n pVariance: σ 2=npqS.D: √npq

GROUP DATA:

Population Sample

Measures Of Dispersion:

Variance: σ 2= ∑fx 2

∑x−(∑fx

∑ f )2

¿2= 1

∑f¿¿¿