Submitted by Harjeet Singh MBA- I semester

1. Submitted By :- Harjeet Singh
MBA – I Semester
Baddi University Emerging Technology & Science

2. Formula Individual Series Discrete Series Continuous
Series
Direct
_ ∑X
X = -----
N
_ ∑fX
X = -----
N
_ ∑fm
X = ------
N
Short cut
_ ∑d
X = A + -----
N
_ ∑fd
X = A + -----
N
_ ∑fd
X = A + -----
N
Step Deviation
_ ∑fd
X = A + ----- *
i
N
_
(d= X - X)
_ ∑fd
X = A + ----- *
i
N
_
(d= X - X)

3. Correcting Incorrect
Mean
Average Mean
 Correct ∑X = Incorrect
∑X – Wrong Item +
Correct Item
_
Correct ∑X
 Correct X = --------
--------
N
 Combined Average
Mean:-
_ _
_ N1 X1 + N2 X2
X = --------------
---
N1 + N2
 Weighted Average
Mean:-
_ ∑WX
X = --------
∑W

4. Individual Series Discrete Series Continuous Series
N+1
Size of --------- th
item
2
N+1
Size of --------- th
item
2
{ N/2 – Cf}
L1 + ------------ *
i
f
(Size of N/2 th item)

5. Individual & Discrete
Series
Continuous series
N + 1
 Q1 = Size of -------- th item
4
3(N + 1)
 Q3 =Size of ----------- th
item
4
Q3 - Q1
 QD = ----------
2
N
 Q1 = Size of ---- th item
4
3(N)
 Q3 = Size of ------- th item
4
 QD = { N/4 – Cf}
L1 + ------------
* i
f
Q3 - Q1
 QD Coeff. = -----------
Q3 + Q1

6.  Individual series :- 60(N + 1)
P60 = Size of ------------ th item
100
 Continuous Series :- 50(N)
P50 = Size of --------- th item
100
 P = { N/100 – Cf}
L1 + ------------ * i
f

7. f1 – f0
 Z = L1 + ------------ * i
2f1 – f0 – f2
Z = 3*median – 2*mean

8. 1) Range :- L – S
L – S
Coeff. :- ---------
L + S
2) Quartile Deviation :-
 Individual & Discrete Series :- Q3 - Q1 / 2
 Continues series :- Q3 - Q1 / 2
Q3 - Q1
 Coeff. = -----------
Q3 + Q1

9. 3) Mean Deviation :-
∑|d|
 Individual Series = --------
N
∑f|d|
 Discrete & Continues Series = ---------
N
Mean Deviation
 Coeff. = -----------------------
Median

10. 4) Standard Deviation :-
 Individual Series:- _______
 Actual Mean (σ) = ⎷ ∑x2 / N
________________
 Assumed Mean (σ) = ⎷ ∑d2 /N - (∑d / N) 2
 Discrete Series:- ________
 Actual Mean (σ) = ⎷ ∑fx2 / N
_______________
 Assumed Mean (σ) = ⎷ ∑fd 2 /N - (∑fd / N) 2
________________
 Continues Series (σ) = ⎷ ∑fd2 /N - (∑fd / N) 2 * i

11. _ _
_ N1 X1 + N2 X2
5) Combined Mean X12 = ------------------
N1 + N2
6) Combined Standard Deviation :-
________________________________________
| N1 σ1
2 + N2 σ2
2 + N3 σ3
2 + N1 d1
2 + N2 d2
2 + N3 d3
2
(σ) =⎷ -------------------------------------------------------------
----
N1 + N2 + N3
_ _ _ _
d1 = |X1 - X123| d2 = |X2 - X123|
_ _
d3 = |X3 - X123|
_
Coefficient of Variance = σ / X * 100

12. 1) Karl Pearson's Skewness :-
SKP = Mean – Mode / Standard Deviation
2) Bowley’s Skewness :-
SKB = Q3 + Q1 – 2 Median / Q3 - Q1
3) Kelly’s Skewness :-
SKK = P10 + P90 – 2 Median / P90 - P10

13. 1) Laspayer’s Method P01 = ∑p1 q0 / ∑p0 q0 * 100
2) Paasch’s Method P01 = ∑p1 q1 / ∑p0 q1 * 100
3) Bowley’s Method = Laspayer’s + Paasch’s / 2
___________________
4) Fisher’s Method = ⎷ Laspayer’s * Paasch’s
5) Marshal Method = ∑p1 q0 + ∑p1 q1 / ∑p0 q0 + ∑p0 q1 * 100
6) Kelly ‘s Method = p1q / p1 q *100

14.  Time reversal Test :- P01 * P10 = 1
 Factor Reversal Test:- p01 * q01 = ∑p1 q1 /
∑p0 q0
 Weighted Average Relative Method:-
P01 = ∑pv / ∑v
= ∑p1 / ∑p0 * 100
(P = Price Relative )

15.  Actual Mean :-
∑ xy ∑xy
r = --------- or ------------
N σx σy ⎷ ∑ x2 * ∑ y2
 Assumed Mean :-
N ∑dx dy - ∑dx * ∑dy
r = ---------------------------------
⎷ N ∑dx2 - (∑dx)2 * ⎷ N ∑dy2 - (∑dy)2

16. 1) Regression Equation of (X on Y) :-
_ σy _
(X – X) = r ------ (Y - Y)
σx
σx N ∑dx dy - ∑dx * ∑dy
r------ = ------------------
σy ⎷ N ∑dy2 - (∑dy)2

17. 2) Regression Equation of (Y on X) :-
_ σy _
(Y – Y) = r ------ (X - X)
σx
σy N ∑dx dy - ∑dx * ∑dy
r------ = --------------------
σx ⎷ N ∑dx2 - (∑dx)2
_ ∑x _ ∑y
X = ------ ; Y = ------
N N

18.  Regression Coefficient :-
r = ⎷bxy * byx
 Time Series:-
Yc = a + bx
a = ∑y / n
b = ∑xy / ∑x2