The document provides formulas and explanations for various statistical concepts related to measures of central tendency (mean, median, mode), measures of dispersion (range, quartile deviation, standard deviation), skewness, index numbers, time series analysis, and regression analysis. Key formulas include those for individual series, discrete series, and continuous series means and standard deviations. Methods for calculating index numbers, regression coefficients, and time series equations are also summarized.

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