mean,meadian,mode,index number,correlation,regression

1. BADDI UNIVERSITY OF EMERGING
SCIENCE AND TECHNOLOGY
STATISTICS FORMULA’S
Sahil Gautam
17PBA058

2. MEAN
Formula Individual Discrete Continuous
Direct ∑ X
N
∑f X
N
∑ f m
N
Short Cut
A+∑d
N
A+∑ f d
N
A+∑ f d
N
Step Deviation A+∑ f d * i
N
A+∑ f d * i
N

3. COMBINED MEAN WEIGHTED MEAN
N1 X1 + N2 X2
N1 + N2
∑ W X
∑ W

4. MEDIAN
Individual Continuous
N+1/2(when in points add L+U/2) N -cf
M= 2 *i
f

5. MODE
Z= L1+ f1-f0 *i or Z= 3Meadian-2Mean
2f1-f0-f2

6. RANGE
Range (R) = Largest value- Small value (L-S)
Cofficient CR= L-S
L+S

7. QUARTILES DEVIATION
Individual Contionuos
Q1= N+1
4
Q3 = [3(N+1)]
4
QD= Q3-Q1
2
N – cf
QD= L+ 4 *i
f
Coeff. = Q3-Q1
Q3+Q1

8. MEAN DEVIATION
Individual Discrete &
Continuous
Cofficent
MD= ∑ d
N
MD= ∑f d
N
MD
Median or Mean

9. STANDARD DEVIATION
C Direct Short cut Step deviation
Individual SD= ∑ (X-X)
N
2
∑dx2 - ∑dx
N N
∑dx2 - ∑dx 2 *C
N N
Discrete &
Continuous
∑fdx2 - ∑fdx 2
N N
∑dx2 - ∑dx 2 *C
N N

10. COEFFICIENT OF SD AND COEFFICIENT OF
VARIATION OR C.VD
Coefficient of SD Coefficient of Variation or
C.VD
=σ
x
= σ *100
x
Combined SD = N1σ 1 + N2σ 2 + N1d1 + N2d2
N1 + N2

11. SKEWNESS
Karl pearson Bowleey Kelly
Mean-Mode
SD
Q3+Q1-2Median
Q3-Q1
d9+d1-2med
d9-d1

12. INDEX NUMBER
SIMPLE METHODS
Formula Price Quantity
Simple aggregative ∑p1 *100
∑p0
∑q1 *100
∑q0
Price Relative ∑ * p1 *100
p0
N
∑ * q1 *100
q0
N

13. WEIGHTED AGGREGATIVE METHOD
Formula Price Quantity
Laspeyre’s ∑p1q0 *100
∑p0q0
∑q1p0 *100
∑q0p0
Paaschee’s ∑p1q1 *100
∑p0q1
∑q1p1 *100
∑q0p1
Fisher’s ∑p1q0 * ∑p1q1 *100
∑p0q0 ∑p0q1
∑q1p0 * ∑q1p1 *100
∑q0p0 ∑q0p1
Dorbish & Bowley’s ∑p1q0 + ∑p1q1 *100
∑p0q0 ∑p0q1
2
∑q1p0 + ∑q1p1 *100
∑q0p0 ∑q0p1
2
Marshall edgeworth’s ∑p1q0 + ∑p1q1 *100
∑p0q0 + ∑p0q1
∑q1q0 + ∑q1p1 *100
∑q0p0 + ∑q0p1
Time Reversal Test Factor Reversal Test
P01 X P10 =1 P01 X Q01= ∑P1q1/ ∑P0q0

14. CORRELATION
A-KARL PEARSON
Actual mean r = ∑xy
∑x2 . ∑y2
Assumed mean r = N. ∑dxdy-∑dx. ∑dy
N.∑dx2 –(∑dx)2 . N. ∑dy 2 – (∑dy)2
Actual data r = N. ∑XY-∑X. ∑Y
N. ∑X 2 – (∑X)2 . N.∑Y2 – (∑Y)2

15. REGRESSION
A-LEAST SQUARE METHOD
(using normal equation)
1. Y on X
Y= a+bX
∑Y = Na + b∑X
∑XY = a∑X + b∑X 2
2. X on Y
X= a+ bY
∑X= Na+ b∑Y
∑XY= a∑Y + b∑Y2
B- Equation using coefficient (Using Mean)
1. Y on X
Y-Y= byx (X-X)
byx= N. ∑xy-∑x. ∑y
N. ∑x2 – (∑x)2
2. X on Y
X-X= bxy (Y-Y)
bxy= N. ∑xy-∑y. ∑x
N. ∑y2- (∑y)2

16. (Assumed Mean)
1. Y on X
Y-Y = byx(X-X)
byx= N. ∑dxdy-∑dx. ∑dy
N. ∑dx2 – (∑dx)2
2. X on Y
X-X=bxy(Y-Y)
bxy= N. ∑dxdy- ∑dy. ∑dx
N. ∑dy2- (∑dy)2
Time Series
Least Square Method
yc= a+bx
If x=0 then
a= ∑y
N
b= ∑xy
∑x2