these slides shows the some formulas for statistics

1. Statistical Formulas
Gaurav Sharma
BUPIN: 17pba015
MBA 1st

2. Direct Method:
Individual series:
X̅ =
𝜮𝑿
𝑵
Discrete Series:
X̅ =
𝜮𝒇𝑿
𝑵
Continuous Series:
X̅ =
𝜮𝒇𝒎
𝑵
Short-cut Method:
Individual Series:
X̅ =A+
𝜮𝒅
𝑵
Discrete Series:
X̅ =A+
𝜮𝒇𝒅
𝑵
Continuous Series:
X̅ = A+
𝜮𝒇𝒅
𝑵
Step-deviation Method:
Discrete Series:
X̅ = A+
𝜮𝒇𝒅′
𝑵
× i
Continuous Series:
X̅ = A+
𝜮𝒇𝒅
𝑵
× i
Here X̅ = Mean

3. Combined Mean:
X̅ =
𝑵 𝟏X͞ 𝟏+𝑵 𝟐X͞ 𝟐
𝑵𝟏+𝑵𝟐
Weighted Mean:
X̅ =
∑𝑾𝑿
∑𝑾

4. Individual Series:
Size of N+1/2th item
Continuous Series:
Size of N/2th item
M=
𝑵
𝟐
−𝒄𝒇
𝒇
× i
Here M=median

5. Individual Series:
The value that has higher
frequency in a frequency distribution.
Continuous Series:
Z= L1 +
𝒇𝟏−𝒇𝟎
𝟐𝒇𝟏−𝒇𝟎−𝒇𝟐
× i
Empirical Node
Z= 3M - 2X̅
Here Z=Mode

6. Individual Series:
Q1 =
𝑁+1
4
Q3 =
3 𝑁+1
4
Q.D =
𝑄3−𝑄1
2
Continuous Series:
QD = L1 +
𝑁
4
−𝑐𝑓
𝑓
× i
Coeff. QD=
𝑄3−𝑄1
𝑄3+𝑄1

7. Individual Series:
MD =
Σ|d|
N
Discrete Series:
MD =
Σf|d|
N
Coefficient:
Coeff. MD =
MD
M orX̅

8. Individual Series:
Direct Method: σ=
ΣX
2
𝑁
Short-cut Method: σ=
𝛴𝑑𝑥2
𝑁
− (
𝛴𝑑𝑥
𝑁
)²
Step- Deviation Method: σ =
𝛴𝑑𝑥2
𝑁
− (
𝛴𝑑𝑥
𝑁
)²×𝑖
Descrete & Continuous Series:
Short-Cut Method : σ=
𝛴𝑓𝑑𝑥²
𝑁
− (
𝛴𝑓𝑑𝑥
𝑁
)²
Step Deviation Method: σ=
𝛴𝑑𝑥′2
𝑁
− (
𝛴𝑑𝑥′
𝑁
)²×𝑖

9. Coefficient of SD:
σ= =
ϭ
𝑋
Coefficient of variation :
C.Vd =
σ
𝑋
×100
Combined SD =
𝑵 𝟏ϭ 𝟏+𝑵 𝟐ϭ 𝟐+𝑵 𝟏 𝒅 𝟏+𝑵₂𝒅₂
𝑵 𝟏+𝑵₂

10. Karl Pearson Skewness:
SKp =
X̅ −𝒁
σ
Bowley’s Skewnes:
SKb =
𝑸𝟑+𝑸𝟏−𝟐𝑴
𝑸𝟑−𝑸𝟏
Kelly’s Skewness:
SKk =
𝒅𝟗+𝒅𝟏−𝟐𝑴
𝒅𝟗−𝒅𝟏

11. Simple Aggregative Method
Simple Relative Method:
Price method =
Σp1
Σp0
×100
Quantity Method =
Σq1
Σq0
×100
Price Relative Method:
Price Method =
Σ
p1
p0
×100
N
Quantity Method =
Σ
q1
q0
×100
N

12. Weighted Aggregative Method
Lespeyer’s Method =
Σp1q0
Σp0q0
×100
Pashche’s Method =
Σp1q1
Σp0q1
×100
Fisher’s Method =
Σp1q0
Σp0q0
×
Σp1q1
Σp0q1
×100
Dorbish & Bowley’s Method=
Σp1q0
Σp0q0
+
Σp1q1
Σp0q1
×100
2
Marshell’s Method =
Σp1q0+Σp1q1
p0q0+p0q1
×100
 Time Reversal Test : P01 X P10 = 1
 Factor Reversal Test P01 XQ01 = ΣP1q1/ΣP0q0

13. Actual Mean:
r=
𝛴𝑥𝑦
𝛴𝑥2.𝛴𝑦2
Assumed Mean:
r=
𝑁.𝛴𝑑𝑥𝑑𝑦−𝛴𝑑𝑥.𝛴𝑑𝑦
𝑁𝛴𝑑𝑥²− 𝛴𝑑𝑥 2. 𝑁.𝛴𝑑𝑦²−(𝛴𝑑𝑦)²

14. 1.Y on X
Y=a+ bX
ΣY=Na+bΣx
ΣXY=aΣX+bΣX²
2.X on Y
X=a+
bY
ΣX=Na+bΣY
ΣXY=aΣY+bΣY²
A-Least square method
(using normal equation.)
1.Y on X
Y-Y̅=byx(X-
X̅)
byx=
𝑁.𝛴𝑥𝑦−𝛴𝑥.𝛴𝑦
𝑁.𝛴𝑥²−(𝛴𝑥)²
2.X on Y
X-
X̅=bxy(Y-Y̅)
bxy=
𝑁.𝛴𝑥𝑦−𝛴𝑦.𝛴𝑥
𝑁.𝛴𝑦²−(𝛴𝑦)²
B-Equation using coefficient (Using Mean)

15. 1.Y on X
Y-Y̅=byx(X-X̅)
byx=
𝑁.𝛴𝑑𝑥𝑑𝑦−𝛴𝑑𝑥.𝛴𝑑𝑦
𝑁.𝛴𝑑𝑥²−(𝛴𝑑𝑥)²
2. X on Y
X-X̅=bxy(Y-Y̅)
bxy=
𝑁.𝛴𝑑𝑥𝑑𝑦−𝛴𝑑𝑦.𝛴𝑑𝑥
𝑁.𝛴𝑑𝑦²−(𝛴𝑑𝑦)²
Assumed mean):
Time series
Least square method
yс = a +bx
if x =0 then
a =
∑y
𝑁
b =
∑xy
∑x²