This document provides formulas for various statistical concepts: 1. It outlines formulas for calculating the mean, median, mode, quartiles, standard deviation, and other measures of central tendency and dispersion for both individual and combined data sets. 2. It also includes formulas for calculating weighted aggregative indexes, correlation, regression, and time series analysis using the least squares method. 3. Various tests for index numbers and formulas using coefficients and assumed means are presented.

1. STATISTICS FORMULA
SONIKA PRASHER
17PBA063
Baddi University of emerging
sciences and technology

2. Mean
Formula Individual Discrete Continuous
DIRECT 𝛴𝑋
𝑁
𝛴𝑓𝑋
𝑁
𝛴𝑓𝑚
𝑁
SHORT CUT
A+
𝛴𝑑
𝑁
A+
𝛴𝑓𝑑
𝑁
A+
𝛴𝑓𝑑
𝑁
STEP DEVIATION A+
𝛴𝑓𝑑′
𝑁
∗ 𝑖 A+
𝛴𝑓𝑑
𝑁
∗ i (d=X-X͞ )

3. Mean
COMBINED MEAN
𝑵 𝟏X͞ 𝟏+𝑵 𝟐X͞ 𝟐
𝑵𝟏+𝑵𝟐
,
WEIGHTED MEAN
∑𝑾𝑿
∑𝑾

4. Median
Individual
N+1/2 (when in points
add L+U/2)
Continuous
M= L+
𝑁
2
−𝑐𝑓
𝑓
∗ 𝑖

5. MODE
Z=𝐿1 +
𝑓1−𝑓0
2𝑓1−𝑓0−𝑓2
*I
OR
Z=3M-2X͞

6. QUARTILE DEVIATION
Individual Continuous
Q1=
𝑁+1
4
Q3=
3 𝑁+1
4
QD=
𝑄3−𝑄1
2
,
QD=𝐿 +
𝑁
4
−𝑐𝑓
𝑓
∗ 𝑖
Coeff. =
𝑄3−𝑄1
𝑄3+𝑄1

7. STANDARD DEVIATION
DIRECT SHORT CUT STEP DEVIATION
Individual
=SD=
𝚺𝐗 𝟐
𝐍
OR
𝚺(𝐗−𝐗͞
𝐍
𝚺𝐝𝐱 𝟐
𝐍
− (
𝚺𝐝𝐱
𝐍
)²
=
𝚺𝐝𝐱 𝟐
𝐍
− (
𝚺𝐝𝐱
𝐍
)² ∗
𝐂
Discrete &
continuous 𝚺𝐟𝐝𝐱²
𝐍
− (
𝚺𝐟𝐝𝐱
𝐍
)²
𝚺𝐝𝐱′ 𝟐
𝐍
− (
𝚺𝐝𝐱′
𝐍
)² ∗
𝐂
dx’=
𝐝𝐱
𝐂

8. STANDARD DEVIATION
Coefficient of SD=
ϭ
𝑋
AND
Coefficient of variation or C.V =
ϭ
𝑋
∗ 100
Combined SD=
𝑵 𝟏ϭ 𝟏+𝑵 𝟐ϭ 𝟐+𝑵 𝟏 𝒅 𝟏+𝑵₂𝒅₂
𝑵 𝟏+𝑵₂

9. MEAN DEVIATION
Individual Discrete &
CONTINOUS
COFFICENT
MD=
𝛴│𝑑
𝑁
MD=
𝛴𝑓│𝑑│
𝑁
𝑀𝐷
𝑀𝐸𝐷𝐼𝐴N 𝑂𝑅 𝑀𝐸𝐴𝑁

10. SKEWNESS
Karl pearson Bowleey Kelly
𝐦𝐞𝐚𝐧 − 𝐦𝐨𝐝𝐞
𝑺𝑫
𝑸𝟑 + 𝑸𝟏 − 𝟐 𝑴𝑬𝑫𝑰𝑨𝑵
𝑸𝟑 − 𝑸𝟏
𝒅𝟗 + 𝒅𝟏 − 𝟐𝒎𝒆𝒅
𝒅𝟗 − 𝒅𝟏

11. Weighted aggregative Methods
Formula Price Quantity
Laspeyre’s Σp1q0
Σp0q0
∗ 100
Σq1p0
Σq0p0
∗ 100
Paaschee’s Σp1q1
Σp0q1
∗ 100
Σq1p1
Σq0p1
∗ 100
Fisher’s
Σp1q0
Σp0q0
∗
Σp1q1
Σp0q1
∗ 100
Σq1p0
Σq0p0
∗
Σq1p1
Σq0p1
∗ 100
Dorbish & Bowley’s Σp1q0
Σp0q0
+
Σp1q1
Σp0q1
∗ 100
2
Σq1p0
Σq0p0
+
Σq1p1
Σq0p1
∗ 100
2
Marshall edgeworth’s Σp1q0 + Σp1q1
p0q0 + p0q1
∗ 100
Σq1q0 + Σq1p1
Σq0p0 + Σq0p1
∗ 100

12. INDEX NUMBERS
Time Reversal Test : P01 X P10 = 1
Factor Reversal Test P01 XQ01 = ΣP1q1/ΣP0q0

13. CORELATION
(Actual
mean)
Assumed mean) Actual data
r=
𝛴𝑥𝑦
𝛴𝑥2.𝛴𝑦2
r=
𝑁.𝛴𝑑𝑥𝑑𝑦−𝛴𝑑𝑥.𝛴𝑑𝑦
𝑁𝛴𝑑𝑥²− 𝛴𝑑𝑥 2. 𝑁.𝛴𝑑𝑦²−(𝛴𝑑𝑦)²
r=
𝑁.𝛴𝑋𝑌−𝛴𝑋.𝛴𝑌
𝑁.𝛴𝑋²− 𝛴𝑋 2. 𝛴𝑌²−(𝛴𝑌)²

14. When ranks are not given

15. Rank are equal
R = 1 −
6[∑𝐷2+
1
12
(𝑚3−𝑚)+
1
12
(𝑚3−𝑚)
𝑛3−𝑛

16. REGRESSION
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

17. Equation using coefficient (Using Mean)
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

18. Assumed mean
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

19. Time series
Least square method
YC = a +bx
if x =0 then
a =
∑y
𝑁
b =
∑xy
∑x²