Statistics formulas specially for Pune University First Year B.Sc. Computer Science

1. Name:SumitSanjaySatam,(F.Y.:S-1)
Statistics 1 Formulae
1) Arithmetic Mean x¯ = (∑xi)/n =∑fixi / ∑fi
2) Median = value of ((n+1)/2)th observation , n is odd
= average of (n/2)th & (n/2 +1)th observation , n is even
= L + (((N/2)-c.f) / f)*h
3) Mode = observation occurring max no of times
= L + ((fm - f1) / (2fm - f1 - f2))*h
4) Weighted A.M. = ∑xiwi / ∑wi
5) Combined Mean = xc¯ = ( (n1 x1¯+ n2 x2¯) / ( n1+n2) )
6) Lower Quartile = Q1 = L + ((N/4 - c.f.) /f)*h
Upper Quartile = Q3 = L + ((3N/4- c.f.) /f)*h
7) Ith Decile = Di = L + ((iN/10- c.f.) /f)*h
Ith Percentile = Pi = L + ((iN/100-c.f.)/f)*h
8) Range = Max – Min
Coeff. Of Range = (Max-Min) / (Max+Min)
9) Quartile Deviation = (Q3 - Q1)/2
Coeff. Of Quartile Deviation = (Q3 - Q1) / (Q3 + Q1)
10) Variance= σ2
=∑(xi)2 / n – (x¯)2
= σ2
= (∑fi (xi)2 / ∑fi ) – (x¯)2

2. Name:SumitSanjaySatam,(F.Y.:S-1)
11) S.D. = σ = √var
12) Coeff. Of Variation = c.v.= σ/| x¯| * 100
13) Combined var=(σ c) 2
=( n1( (σ1)2
+(d1)2 ) + n2( (σ2)2
+(d2)2) ) /(n1+ n2)
Combined S.D. = √(σ c) 2
14) V(X+A) = V(X)
V(AX+B) = A2V(X)
15) Karl Pearson’s coeff of skewness
Skp = (mean-mode) / S.D. = 3(mean-median) / S.D.
16) Bowley’s coeff of skewness
Skb = ((Q3 - Q2) - (Q2 - Q1)) / ((Q3 - Q2) + (Q2 - Q1))
= (Q3 + Q1 - 2Q2) / (Q3 – Q1)
17) Pearson’s coeff of skewness
β1 = (μ3)2/ (μ2)3, γ1= +-√β1 (sign of γ1 is same as μ3)
18) Raw moments μr
’ = ∑(xi)r / n , ∑fi (xi)r / ∑fi
19) Central moments μr = ∑ (xi - x¯)r / n
μ1 = 0,
μ2 = μ2
’ – (μ1
’) 2
μ3 = μ3
’ – 3μ2
’ (μ1
’) +2(μ1
’) 3
μ4 = μ4
’ – 4μ3
’ (μ1
’) +6(μ2
’) (μ1
’) 2 – 3(μ1
’) 4

3. Name:SumitSanjaySatam,(F.Y.:S-1)
20) Person’s coeff of kurtosis
β2 = μ4 / (μ2)2, γ2 = β2 -3
21) Covariance=cov(X,Y)= ∑(X - X¯) (Y - Y¯) / n
= ∑XY / n - X¯ Y¯
22) Karl Pearson’s coeff of correlation
r = cov(X,Y) / σx σy (-1<= r <=1)
23) Coeff of determination r2 = Explained var. / Total var.
24) Person’s rank correln. Coeff R= 1 – ( 6∑(d i)2 / n(n2-1))
25) Regression lines : y on x
Y = a + bX / y - y¯ = byx (x - x¯)
byx = r (σy / σx) = cov(x,y) / (σ x) 2
= (∑xy - nX¯ Y¯) / (∑x2 – n(x¯)2
)
26) Regression lines : x on y
X = a + bY / x - x¯ = bxy (y - y¯)
byx = r (σx / σy) = cov(x,y) / (σ y) 2
= (∑xy - nX¯ Y¯) / (∑y2 – n (y¯)2
)
27) Least square fit y = a + bx
∑y = na + b∑x
∑xy = a ∑x + b ∑x2
28) Coeff of correlation r = √(bxy * byx)

4. Name:SumitSanjaySatam,(F.Y.:S-1)
29) Fitting second degree curve
Y = a + bX + cX2
∑y = an + b∑x + c∑x2
∑xy = a∑x + b∑x2 + c∑x3
∑x2y = a∑x2 + b∑x3 + c∑x4
30) Fitting of exponential curve y = abx
Log y = log a + x log b
V = A + xB
∑V = nA + B∑x
∑Vx = A∑x + B∑x2
31) Eqn of plane of regression of X1 on X2 & X3
X1 = a + b12.3 X2 + b13.2 X3
X2 = a + b21.3 X1 + b23.1 X3
X3 = a + b31.2 X1 + b32.1 X3
32) Partial regression coeff of eqn of X1 on X2 & X3
b12.3 = (σ1 /σ2) * (r12 - r13 r23 / 1- (r23)2
) = -(σ1 / σ2) (R12 / R11)
b13.2 = (σ1 /σ3) * (r13 - r12 r23 / 1- (r23)2
) = -(σ1 / σ3) (R13 / R11)
R11, R12, R13 are cofactors in matrix R
33) Multiple regression eqn, deviations taken from means Xi=Xi –(Xi)¯
Regression eqn of X1 on X2 & X3
(R11 / σ1) * x1 + (R12 / σ2) * x2 + (R13 / σ3) * x3 = 0
(R21 / σ1) * x1 + (R22 / σ2) * x2 + (R23 / σ3) * x3 = 0
(R31 / σ1) * x1 + (R32 / σ2) * x2 + (R33 / σ3) * x3 = 0

5. Name:SumitSanjaySatam,(F.Y.:S-1)
34) Multiple correlation coeff
R1.23 = √((r12)2
+(r13)2
- 2r12 r13 r23 ) / (1- (r23)2
)
R2.13 = √((r12)2
+(r23)2
- 2r12 r13 r23 ) / (1- (r23)2
)
R3.12 = √((r13)2
+(r23)2
- 2r12 r13 r23 ) / (1- (r12)2
)
(0<= Ri.jk <= 1)
35) Partial correlation coeff
r12.3 = (r12 - r13 r23 ) / √((1- (r13)2
) (1- (r23)2
)
r13.2 = (r13 - r12 r23 ) / √((1- (r12)2
) (1- (r23)2
)
r23.1 = (r23 - r12 r13 ) / √((1- (r12)2
) (1- (r13)2
)
(-1<= ri.jk <= 1)
35) m –yearly moving average for the time series
T t1 t2 t3 -------- tn
Y y1 y2 y3 -------- yn
y1¯ = (y1 + y2 + -------- +ym)/m , y2¯ = (y2 + y3 + -------- +ym+1)/m
(centering of moving average)
36) Fitting linear tend y = a + bt
Use ∑y = na + b∑X
∑yX = a∑X + b∑x2 , X = t - A, A = mid pt of time
= (½) (2middle year)
37) Exponential smoothing
S0 = y0
S1 = α yt + (1- α) St-1 0< α <1
38) Methods of measuring seasonal variations
a) Ratio to trend method

6. Name:SumitSanjaySatam,(F.Y.:S-1)
(y /T)*100
Correction factor= ((1200/Total of indices) / (400/Total of indices)
b) Link relative method
Link relative for any period
= (current period figure / previous period figure) *100
Chain relative
= (C.R. of previous period * L.R. of current period) /100
Thanks for Reading 